TSTP Solution File: ITP227^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP227^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.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 03:22:13 EDT 2023
% Result : Theorem 8.14s 8.50s
% Output : Proof 8.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.45/2.46 % Problem : ITP227^3 : TPTP v8.1.2. Released v8.1.0.
% 2.45/2.47 % Command : do_cvc5 %s %d
% 2.47/2.68 % Computer : n002.cluster.edu
% 2.47/2.68 % Model : x86_64 x86_64
% 2.47/2.68 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.47/2.68 % Memory : 8042.1875MB
% 2.47/2.68 % OS : Linux 3.10.0-693.el7.x86_64
% 2.47/2.68 % CPULimit : 300
% 2.47/2.68 % WCLimit : 300
% 2.47/2.68 % DateTime : Sun Aug 27 15:24:06 EDT 2023
% 2.47/2.69 % CPUTime :
% 5.25/5.40 %----Proving TH0
% 5.25/5.40 %------------------------------------------------------------------------------
% 5.25/5.40 % File : ITP227^3 : TPTP v8.1.2. Released v8.1.0.
% 5.25/5.40 % Domain : Interactive Theorem Proving
% 5.25/5.40 % Problem : Sledgehammer problem VEBT_Insert 00186_011181
% 5.25/5.40 % Version : [Des22] axioms.
% 5.25/5.40 % English :
% 5.25/5.40
% 5.25/5.40 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.25/5.40 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.25/5.40 % Source : [Des22]
% 5.25/5.40 % Names : 0066_VEBT_Insert_00186_011181 [Des22]
% 5.25/5.40
% 5.25/5.40 % Status : Theorem
% 5.25/5.40 % Rating : 0.38 v8.1.0
% 5.25/5.40 % Syntax : Number of formulae : 11137 (6122 unt; 882 typ; 0 def)
% 5.25/5.40 % Number of atoms : 26294 (11873 equ; 0 cnn)
% 5.25/5.40 % Maximal formula atoms : 71 ( 2 avg)
% 5.25/5.40 % Number of connectives : 107262 (2509 ~; 554 |;1517 &;93910 @)
% 5.25/5.40 % ( 0 <=>;8772 =>; 0 <=; 0 <~>)
% 5.25/5.40 % Maximal formula depth : 39 ( 5 avg)
% 5.25/5.40 % Number of types : 71 ( 70 usr)
% 5.25/5.40 % Number of type conns : 2938 (2938 >; 0 *; 0 +; 0 <<)
% 5.25/5.40 % Number of symbols : 815 ( 812 usr; 56 con; 0-8 aty)
% 5.25/5.40 % Number of variables : 24222 (2029 ^;21611 !; 582 ?;24222 :)
% 5.25/5.40 % SPC : TH0_THM_EQU_NAR
% 5.25/5.40
% 5.25/5.40 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.25/5.40 % from the van Emde Boas Trees session in the Archive of Formal
% 5.25/5.40 % proofs -
% 5.25/5.40 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.25/5.40 % 2022-02-17 19:25:47.732
% 5.25/5.40 %------------------------------------------------------------------------------
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Finite__Set_Ocard_001_Eo,type,
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% 5.25/5.41 thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
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% 5.25/5.41 thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
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% 5.25/5.41 thf(sy_c_Finite__Set_Ocard_001t__String__Ochar,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
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% 5.25/5.41 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
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% 5.25/5.41
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% 5.25/5.41 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 5.25/5.41 lattic8265883725875713057ax_nat: set_nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.25/5.41 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Limits_Oat__infinity_001t__Real__Oreal,type,
% 5.25/5.41 at_infinity_real: filter_real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 5.25/5.41 append_int: list_int > list_int > list_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 5.25/5.41 append_nat: list_nat > list_nat > list_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 5.25/5.41 distinct_int: list_int > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 5.25/5.41 distinct_nat: list_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 5.25/5.41 drop_nat: nat > list_nat > list_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
% 5.25/5.41 linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.25/5.41 linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 5.25/5.41 linord2614967742042102400et_nat: set_nat > list_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 5.25/5.41 cons_int: int > list_int > list_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 5.25/5.41 cons_nat: nat > list_nat > list_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 5.25/5.41 nil_int: list_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 5.25/5.41 nil_nat: list_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 5.25/5.41 hd_nat: list_nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.25/5.41 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 5.25/5.41 set_o2: list_o > set_o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.25/5.41 set_complex2: list_complex > set_complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.25/5.41 set_int2: list_int > set_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.25/5.41 set_nat2: list_nat > set_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.25/5.41 set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.25/5.41 set_real2: list_real > set_real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.41 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.41 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 5.25/5.41 tl_nat: list_nat > list_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist__update_001_Eo,type,
% 5.25/5.41 list_update_o: list_o > nat > $o > list_o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist__update_001t__Complex__Ocomplex,type,
% 5.25/5.41 list_update_complex: list_complex > nat > complex > list_complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 5.25/5.41 list_update_int: list_int > nat > int > list_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 5.25/5.41 list_update_nat: list_nat > nat > nat > list_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.25/5.41 list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 5.25/5.41 list_update_real: list_real > nat > real > list_real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.41 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001_Eo,type,
% 5.25/5.41 nth_o: list_o > nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 5.25/5.41 nth_Code_integer: list_Code_integer > nat > code_integer ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 5.25/5.41 nth_complex: list_complex > nat > complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.25/5.41 nth_int: list_int > nat > int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.25/5.41 nth_nat: list_nat > nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 5.25/5.41 nth_num: list_num > nat > num ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 5.25/5.41 nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 5.25/5.41 nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 5.25/5.41 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.25/5.41 nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.25/5.41 nth_Pr8522763379788166057eger_o: list_P8526636022914148096eger_o > nat > produc6271795597528267376eger_o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.25/5.41 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.25/5.41 nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.25/5.41 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 5.25/5.41 nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.25/5.41 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.25/5.41 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 5.25/5.41 nth_real: list_real > nat > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.41 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 5.25/5.41 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 5.25/5.41 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 5.25/5.41 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.41 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001_Eo,type,
% 5.25/5.41 produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 5.25/5.41 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.41 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 5.25/5.41 product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.25/5.41 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.25/5.41 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.25/5.41 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.41 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 5.25/5.41 remdups_nat: list_nat > list_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oreplicate_001_Eo,type,
% 5.25/5.41 replicate_o: nat > $o > list_o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 5.25/5.41 replicate_complex: nat > complex > list_complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.25/5.41 replicate_int: nat > int > list_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.25/5.41 replicate_nat: nat > nat > list_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oreplicate_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.25/5.41 replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.25/5.41 replicate_real: nat > real > list_real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.41 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 5.25/5.41 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 5.25/5.41 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 5.25/5.41 take_nat: nat > list_nat > list_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oupt,type,
% 5.25/5.41 upt: nat > nat > list_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oupto,type,
% 5.25/5.41 upto: int > int > list_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oupto__aux,type,
% 5.25/5.41 upto_aux: int > int > list_int > list_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_List_Oupto__rel,type,
% 5.25/5.41 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_OSuc,type,
% 5.25/5.41 suc: nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.25/5.41 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.25/5.41 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.25/5.41 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.25/5.41 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Onat_Opred,type,
% 5.25/5.41 pred: nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.25/5.41 semiri4939895301339042750nteger: nat > code_integer ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.25/5.41 semiri8010041392384452111omplex: nat > complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 5.25/5.41 semiri4216267220026989637d_enat: nat > extended_enat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.25/5.41 semiri1314217659103216013at_int: nat > int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 5.25/5.41 semiri1316708129612266289at_nat: nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.25/5.41 semiri681578069525770553at_rat: nat > rat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.25/5.41 semiri5074537144036343181t_real: nat > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 5.25/5.41 semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 5.25/5.41 semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 5.25/5.41 semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 5.25/5.41 semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
% 5.25/5.41 semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 5.25/5.41 size_size_list_o: list_o > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 5.25/5.41 size_s3445333598471063425nteger: list_Code_integer > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.25/5.41 size_s3451745648224563538omplex: list_complex > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 5.25/5.41 size_size_list_int: list_int > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 5.25/5.41 size_size_list_nat: list_nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 5.25/5.41 size_size_list_num: list_num > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 5.25/5.41 size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 5.25/5.41 size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 5.25/5.41 size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.25/5.41 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 5.25/5.41 size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.25/5.41 size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.25/5.41 size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 5.25/5.41 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 5.25/5.41 size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 5.25/5.41 size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 5.25/5.41
% 5.25/5.41 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,
% 5.25/5.41 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.25/5.41 size_size_list_real: list_real > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.25/5.41 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.25/5.41 size_size_num: num > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.25/5.41 size_size_option_num: option_num > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 5.25/5.41 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.41 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 5.25/5.41 nat_list_encode: list_nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 5.25/5.41 nat_list_encode_rel: list_nat > list_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 5.25/5.41 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 5.25/5.41 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 5.25/5.41 nat_prod_encode: product_prod_nat_nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 5.25/5.41 nat_set_decode: nat > set_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 5.25/5.41 nat_set_encode: set_nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.25/5.41 nat_triangle: nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_NthRoot_Oroot,type,
% 5.25/5.41 root: nat > real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_NthRoot_Osqrt,type,
% 5.25/5.41 sqrt: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_OBitM,type,
% 5.25/5.41 bitM: num > num ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oinc,type,
% 5.25/5.41 inc: num > num ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 5.25/5.41 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 5.25/5.41 neg_nu7009210354673126013omplex: complex > complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 5.25/5.41 neg_numeral_dbl_int: int > int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 5.25/5.41 neg_numeral_dbl_rat: rat > rat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 5.25/5.41 neg_numeral_dbl_real: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 5.25/5.41 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 5.25/5.41 neg_nu6511756317524482435omplex: complex > complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 5.25/5.41 neg_nu3811975205180677377ec_int: int > int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 5.25/5.41 neg_nu3179335615603231917ec_rat: rat > rat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 5.25/5.41 neg_nu6075765906172075777c_real: real > real ).
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% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 5.25/5.41 neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 5.25/5.41 neg_nu8557863876264182079omplex: complex > complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 5.25/5.41 neg_nu5851722552734809277nc_int: int > int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 5.25/5.41 neg_nu5219082963157363817nc_rat: rat > rat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 5.25/5.41 neg_nu8295874005876285629c_real: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 5.25/5.41 neg_numeral_sub_int: num > num > int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Onum_OBit0,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Onum_OBit1,type,
% 5.25/5.41 bit1: num > num ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Onum_OOne,type,
% 5.25/5.41 one: num ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.25/5.41 case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Onum_Osize__num,type,
% 5.25/5.41 size_num: num > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Onum__of__nat,type,
% 5.25/5.41 num_of_nat: nat > num ).
% 5.25/5.41
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% 5.25/5.41 numera6620942414471956472nteger: num > code_integer ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 5.25/5.41 numera6690914467698888265omplex: num > complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
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% 5.25/5.41 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Opow,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Opred__numeral,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Num_Osqr,type,
% 5.25/5.41 sqr: num > num ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
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% 5.25/5.41 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
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% 5.25/5.41
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% 5.25/5.41
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% 5.25/5.41
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% 5.25/5.41
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% 5.25/5.41 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
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% 5.25/5.41
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Rat_OFract,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Rat_Onormalize,type,
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% 5.25/5.41 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
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% 5.25/5.41 thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
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% 5.25/5.41 thf(sy_c_Series_Osummable_001t__Nat__Onat,type,
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% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
% 5.25/5.41 set_or633870826150836451st_rat: rat > rat > set_rat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 5.25/5.41 set_or1222579329274155063t_real: real > real > set_real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Int__Oint_J,type,
% 5.25/5.41 set_or370866239135849197et_int: set_int > set_int > set_set_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 5.25/5.41 set_or4662586982721622107an_int: int > int > set_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 5.25/5.41 set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 5.25/5.41 set_ord_atLeast_nat: nat > set_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
% 5.25/5.41 set_ord_atLeast_real: real > set_real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
% 5.25/5.41 set_ord_atMost_int: int > set_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 5.25/5.41 set_ord_atMost_nat: nat > set_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Num__Onum,type,
% 5.25/5.41 set_ord_atMost_num: num > set_num ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Rat__Orat,type,
% 5.25/5.41 set_ord_atMost_rat: rat > set_rat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Real__Oreal,type,
% 5.25/5.41 set_ord_atMost_real: real > set_real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Int__Oint_J,type,
% 5.25/5.41 set_or58775011639299419et_int: set_int > set_set_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 5.25/5.41 set_or6656581121297822940st_int: int > int > set_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 5.25/5.41 set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 5.25/5.41 set_or5832277885323065728an_int: int > int > set_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 5.25/5.41 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 5.25/5.41 set_or1633881224788618240n_real: real > real > set_real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 5.25/5.41 set_or1210151606488870762an_nat: nat > set_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 5.25/5.41 set_or5849166863359141190n_real: real > set_real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Extended____Nat__Oenat,type,
% 5.25/5.41 set_or8419480210114673929d_enat: extended_enat > set_Extended_enat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 5.25/5.41 set_ord_lessThan_int: int > set_int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 5.25/5.41 set_ord_lessThan_nat: nat > set_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 5.25/5.41 set_ord_lessThan_num: num > set_num ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 5.25/5.41 set_ord_lessThan_rat: rat > set_rat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 5.25/5.41 set_or5984915006950818249n_real: real > set_real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_String_Oascii__of,type,
% 5.25/5.41 ascii_of: char > char ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_String_Ochar_OChar,type,
% 5.25/5.41 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 5.25/5.41 comm_s629917340098488124ar_nat: char > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_String_Ointeger__of__char,type,
% 5.25/5.41 integer_of_char: char > code_integer ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 5.25/5.41 unique3096191561947761185of_nat: nat > char ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.25/5.41 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.25/5.41 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Topological__Spaces_Omonoseq_001t__Int__Oint,type,
% 5.25/5.41 topolo4899668324122417113eq_int: ( nat > int ) > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
% 5.25/5.41 topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Topological__Spaces_Omonoseq_001t__Num__Onum,type,
% 5.25/5.41 topolo1459490580787246023eq_num: ( nat > num ) > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Topological__Spaces_Omonoseq_001t__Rat__Orat,type,
% 5.25/5.41 topolo4267028734544971653eq_rat: ( nat > rat ) > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 5.25/5.41 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Int__Oint_J,type,
% 5.25/5.41 topolo3100542954746470799et_int: ( nat > set_int ) > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 5.25/5.41 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 5.25/5.41 topolo2815343760600316023s_real: real > filter_real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 5.25/5.41 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Oarccos,type,
% 5.25/5.41 arccos: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 5.25/5.41 arcosh_real: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Oarcsin,type,
% 5.25/5.41 arcsin: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Oarctan,type,
% 5.25/5.41 arctan: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 5.25/5.41 arsinh_real: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 5.25/5.41 artanh_real: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 5.25/5.41 cos_complex: complex > complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 5.25/5.41 cos_real: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Ocos__coeff,type,
% 5.25/5.41 cos_coeff: nat > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 5.25/5.41 cosh_real: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 5.25/5.41 cot_real: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 5.25/5.41 diffs_complex: ( nat > complex ) > nat > complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Odiffs_001t__Int__Oint,type,
% 5.25/5.41 diffs_int: ( nat > int ) > nat > int ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Odiffs_001t__Rat__Orat,type,
% 5.25/5.41 diffs_rat: ( nat > rat ) > nat > rat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 5.25/5.41 diffs_real: ( nat > real ) > nat > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 5.25/5.41 exp_complex: complex > complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 5.25/5.41 exp_real: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 5.25/5.41 ln_ln_real: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Olog,type,
% 5.25/5.41 log: real > real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Opi,type,
% 5.25/5.41 pi: real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 5.25/5.41 powr_real: real > real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 5.25/5.41 sin_complex: complex > complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 5.25/5.41 sin_real: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Osin__coeff,type,
% 5.25/5.41 sin_coeff: nat > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 5.25/5.41 sinh_real: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 5.25/5.41 tan_complex: complex > complex ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 5.25/5.41 tan_real: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.25/5.41 tanh_real: real > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 5.25/5.41 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 5.25/5.41 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.25/5.41 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.25/5.41 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 5.25/5.41 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.25/5.41 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.25/5.41 vEBT_VEBT_high: nat > nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.25/5.41 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.25/5.41 vEBT_VEBT_low: nat > nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.25/5.41 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.25/5.41 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.25/5.41 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.25/5.41 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.25/5.41 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.25/5.41 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.25/5.41 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.25/5.41 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.25/5.41 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.25/5.41 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 5.25/5.41 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 5.25/5.41 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.25/5.41 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.25/5.41 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 5.25/5.41 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.25/5.41 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.25/5.41 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.25/5.41 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 5.25/5.41 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 5.25/5.41 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.25/5.41 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.25/5.41 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.25/5.41 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.25/5.41 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.41 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_Wellfounded_Opred__nat,type,
% 5.25/5.41 pred_nat: set_Pr1261947904930325089at_nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 5.25/5.41 fChoice_real: ( real > $o ) > real ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_member_001_Eo,type,
% 5.25/5.41 member_o: $o > set_o > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.25/5.41 member_complex: complex > set_complex > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_member_001t__Int__Oint,type,
% 5.25/5.41 member_int: int > set_int > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 5.25/5.41 member_list_nat: list_nat > set_list_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_member_001t__Nat__Onat,type,
% 5.25/5.41 member_nat: nat > set_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_member_001t__Num__Onum,type,
% 5.25/5.41 member_num: num > set_num > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.25/5.41 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_member_001t__Rat__Orat,type,
% 5.25/5.41 member_rat: rat > set_rat > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_member_001t__Real__Oreal,type,
% 5.25/5.41 member_real: real > set_real > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 5.25/5.41 member_set_int: set_int > set_set_int > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.41 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.25/5.41
% 5.25/5.41 thf(sy_v_deg____,type,
% 5.25/5.41 deg: nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_v_m____,type,
% 5.25/5.41 m: nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_v_ma____,type,
% 5.25/5.41 ma: nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_v_mi____,type,
% 5.25/5.41 mi: nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_v_na____,type,
% 5.25/5.41 na: nat ).
% 5.25/5.41
% 5.25/5.41 thf(sy_v_summary____,type,
% 5.25/5.41 summary: vEBT_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_v_treeList____,type,
% 5.25/5.41 treeList: list_VEBT_VEBT ).
% 5.25/5.41
% 5.25/5.41 thf(sy_v_xa____,type,
% 5.25/5.41 xa: nat ).
% 5.25/5.41
% 5.25/5.41 % Relevant facts (10212)
% 5.25/5.41 thf(fact_0_False,axiom,
% 5.25/5.41 ~ ( ( xa = mi )
% 5.25/5.41 | ( xa = ma ) ) ).
% 5.25/5.41
% 5.25/5.41 % False
% 5.25/5.41 thf(fact_1__C5_Ohyps_C_I7_J,axiom,
% 5.25/5.41 ord_less_eq_nat @ mi @ ma ).
% 5.25/5.41
% 5.25/5.41 % "5.hyps"(7)
% 5.25/5.41 thf(fact_2__C5_Ohyps_C_I6_J,axiom,
% 5.25/5.41 ( ( mi = ma )
% 5.25/5.41 => ! [X: vEBT_VEBT] :
% 5.25/5.41 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.25/5.41 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_1 ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % "5.hyps"(6)
% 5.25/5.41 thf(fact_3__092_060open_062high_Ax_An_A_060_Alength_AtreeList_092_060close_062,axiom,
% 5.25/5.41 ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ).
% 5.25/5.41
% 5.25/5.41 % \<open>high x n < length treeList\<close>
% 5.25/5.41 thf(fact_4__C5_Oprems_C,axiom,
% 5.25/5.41 ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.25/5.41
% 5.25/5.41 % "5.prems"
% 5.25/5.41 thf(fact_5__C5_Ohyps_C_I8_J,axiom,
% 5.25/5.41 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.25/5.41
% 5.25/5.41 % "5.hyps"(8)
% 5.25/5.41 thf(fact_6__092_060open_062mi_A_060_A2_A_094_Adeg_092_060close_062,axiom,
% 5.25/5.41 ord_less_nat @ mi @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.25/5.41
% 5.25/5.41 % \<open>mi < 2 ^ deg\<close>
% 5.25/5.41 thf(fact_7__C5_Ohyps_C_I2_J,axiom,
% 5.25/5.41 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.25/5.41 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.25/5.41
% 5.25/5.41 % "5.hyps"(2)
% 5.25/5.41 thf(fact_8__C5_OIH_C_I1_J,axiom,
% 5.25/5.41 ! [X: vEBT_VEBT] :
% 5.25/5.41 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.25/5.41 => ( ( vEBT_invar_vebt @ X @ na )
% 5.25/5.41 & ! [Xa: nat] :
% 5.25/5.41 ( ( ord_less_nat @ Xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
% 5.25/5.41 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ X @ Xa ) @ Xa ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % "5.IH"(1)
% 5.25/5.41 thf(fact_9_self__le__ge2__pow,axiom,
% 5.25/5.41 ! [K: nat,M: nat] :
% 5.25/5.41 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.25/5.41 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % self_le_ge2_pow
% 5.25/5.41 thf(fact_10_power2__nat__le__eq__le,axiom,
% 5.25/5.41 ! [M: nat,N: nat] :
% 5.25/5.41 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.41 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % power2_nat_le_eq_le
% 5.25/5.41 thf(fact_11_power2__nat__le__imp__le,axiom,
% 5.25/5.41 ! [M: nat,N: nat] :
% 5.25/5.41 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.25/5.41 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % power2_nat_le_imp_le
% 5.25/5.41 thf(fact_12_less__exp,axiom,
% 5.25/5.41 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % less_exp
% 5.25/5.41 thf(fact_13_semiring__norm_I85_J,axiom,
% 5.25/5.41 ! [M: num] :
% 5.25/5.41 ( ( bit0 @ M )
% 5.25/5.41 != one ) ).
% 5.25/5.41
% 5.25/5.41 % semiring_norm(85)
% 5.25/5.41 thf(fact_14_semiring__norm_I83_J,axiom,
% 5.25/5.41 ! [N: num] :
% 5.25/5.41 ( one
% 5.25/5.41 != ( bit0 @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % semiring_norm(83)
% 5.25/5.41 thf(fact_15_high__bound__aux,axiom,
% 5.25/5.41 ! [Ma: nat,N: nat,M: nat] :
% 5.25/5.41 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.25/5.41 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % high_bound_aux
% 5.25/5.41 thf(fact_16_numeral__less__iff,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.25/5.41 = ( ord_less_num @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_less_iff
% 5.25/5.41 thf(fact_17_numeral__less__iff,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.25/5.41 = ( ord_less_num @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_less_iff
% 5.25/5.41 thf(fact_18_numeral__less__iff,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.41 = ( ord_less_num @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_less_iff
% 5.25/5.41 thf(fact_19_numeral__less__iff,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.41 = ( ord_less_num @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_less_iff
% 5.25/5.41 thf(fact_20_numeral__le__iff,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.25/5.41 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_le_iff
% 5.25/5.41 thf(fact_21_numeral__le__iff,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.25/5.41 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_le_iff
% 5.25/5.41 thf(fact_22_numeral__le__iff,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.41 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_le_iff
% 5.25/5.41 thf(fact_23_numeral__le__iff,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.41 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_le_iff
% 5.25/5.41 thf(fact_24_high__def,axiom,
% 5.25/5.41 ( vEBT_VEBT_high
% 5.25/5.41 = ( ^ [X2: nat,N2: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % high_def
% 5.25/5.41 thf(fact_25_not__min__Null__member,axiom,
% 5.25/5.41 ! [T: vEBT_VEBT] :
% 5.25/5.41 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.25/5.41 => ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 ) ) ).
% 5.25/5.41
% 5.25/5.41 % not_min_Null_member
% 5.25/5.41 thf(fact_26__C5_Ohyps_C_I1_J,axiom,
% 5.25/5.41 vEBT_invar_vebt @ summary @ m ).
% 5.25/5.41
% 5.25/5.41 % "5.hyps"(1)
% 5.25/5.41 thf(fact_27__C5_Ohyps_C_I4_J,axiom,
% 5.25/5.41 ( deg
% 5.25/5.41 = ( plus_plus_nat @ na @ m ) ) ).
% 5.25/5.41
% 5.25/5.41 % "5.hyps"(4)
% 5.25/5.41 thf(fact_28_numeral__eq__iff,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ( numera6690914467698888265omplex @ M )
% 5.25/5.41 = ( numera6690914467698888265omplex @ N ) )
% 5.25/5.41 = ( M = N ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_eq_iff
% 5.25/5.41 thf(fact_29_numeral__eq__iff,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ( numeral_numeral_real @ M )
% 5.25/5.41 = ( numeral_numeral_real @ N ) )
% 5.25/5.41 = ( M = N ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_eq_iff
% 5.25/5.41 thf(fact_30_numeral__eq__iff,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ( numeral_numeral_rat @ M )
% 5.25/5.41 = ( numeral_numeral_rat @ N ) )
% 5.25/5.41 = ( M = N ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_eq_iff
% 5.25/5.41 thf(fact_31_numeral__eq__iff,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ( numeral_numeral_nat @ M )
% 5.25/5.41 = ( numeral_numeral_nat @ N ) )
% 5.25/5.41 = ( M = N ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_eq_iff
% 5.25/5.41 thf(fact_32_numeral__eq__iff,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ( numeral_numeral_int @ M )
% 5.25/5.41 = ( numeral_numeral_int @ N ) )
% 5.25/5.41 = ( M = N ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_eq_iff
% 5.25/5.41 thf(fact_33_semiring__norm_I87_J,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ( bit0 @ M )
% 5.25/5.41 = ( bit0 @ N ) )
% 5.25/5.41 = ( M = N ) ) ).
% 5.25/5.41
% 5.25/5.41 % semiring_norm(87)
% 5.25/5.41 thf(fact_34_pow__sum,axiom,
% 5.25/5.41 ! [A: nat,B: nat] :
% 5.25/5.41 ( ( 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 ) )
% 5.25/5.41 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 5.25/5.41
% 5.25/5.41 % pow_sum
% 5.25/5.41 thf(fact_35_numeral__plus__numeral,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.25/5.41 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_plus_numeral
% 5.25/5.41 thf(fact_36_numeral__plus__numeral,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.25/5.41 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_plus_numeral
% 5.25/5.41 thf(fact_37_numeral__plus__numeral,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.25/5.41 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_plus_numeral
% 5.25/5.41 thf(fact_38_numeral__plus__numeral,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.41 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_plus_numeral
% 5.25/5.41 thf(fact_39_numeral__plus__numeral,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.41 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_plus_numeral
% 5.25/5.41 thf(fact_40_add__numeral__left,axiom,
% 5.25/5.41 ! [V: num,W: num,Z: complex] :
% 5.25/5.41 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.25/5.41 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.41
% 5.25/5.41 % add_numeral_left
% 5.25/5.41 thf(fact_41_add__numeral__left,axiom,
% 5.25/5.41 ! [V: num,W: num,Z: real] :
% 5.25/5.41 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.25/5.41 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.41
% 5.25/5.41 % add_numeral_left
% 5.25/5.41 thf(fact_42_add__numeral__left,axiom,
% 5.25/5.41 ! [V: num,W: num,Z: rat] :
% 5.25/5.41 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.25/5.41 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.41
% 5.25/5.41 % add_numeral_left
% 5.25/5.41 thf(fact_43_add__numeral__left,axiom,
% 5.25/5.41 ! [V: num,W: num,Z: nat] :
% 5.25/5.41 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.25/5.41 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.41
% 5.25/5.41 % add_numeral_left
% 5.25/5.41 thf(fact_44_add__numeral__left,axiom,
% 5.25/5.41 ! [V: num,W: num,Z: int] :
% 5.25/5.41 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.25/5.41 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.41
% 5.25/5.41 % add_numeral_left
% 5.25/5.41 thf(fact_45_semiring__norm_I78_J,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.25/5.41 = ( ord_less_num @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % semiring_norm(78)
% 5.25/5.41 thf(fact_46_semiring__norm_I71_J,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.25/5.41 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % semiring_norm(71)
% 5.25/5.41 thf(fact_47_semiring__norm_I75_J,axiom,
% 5.25/5.41 ! [M: num] :
% 5.25/5.41 ~ ( ord_less_num @ M @ one ) ).
% 5.25/5.41
% 5.25/5.41 % semiring_norm(75)
% 5.25/5.41 thf(fact_48_semiring__norm_I68_J,axiom,
% 5.25/5.41 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 5.25/5.41
% 5.25/5.41 % semiring_norm(68)
% 5.25/5.41 thf(fact_49_semiring__norm_I76_J,axiom,
% 5.25/5.41 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % semiring_norm(76)
% 5.25/5.41 thf(fact_50_semiring__norm_I69_J,axiom,
% 5.25/5.41 ! [M: num] :
% 5.25/5.41 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.25/5.41
% 5.25/5.41 % semiring_norm(69)
% 5.25/5.41 thf(fact_51__C5_Ohyps_C_I3_J,axiom,
% 5.25/5.41 ( m
% 5.25/5.41 = ( suc @ na ) ) ).
% 5.25/5.41
% 5.25/5.41 % "5.hyps"(3)
% 5.25/5.41 thf(fact_52__C5_OIH_C_I2_J,axiom,
% 5.25/5.41 ! [X3: nat] :
% 5.25/5.41 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.25/5.41 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ summary @ X3 ) @ X3 ) ) ).
% 5.25/5.41
% 5.25/5.41 % "5.IH"(2)
% 5.25/5.41 thf(fact_53_is__num__normalize_I1_J,axiom,
% 5.25/5.41 ! [A: real,B: real,C: real] :
% 5.25/5.41 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.25/5.41 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % is_num_normalize(1)
% 5.25/5.41 thf(fact_54_is__num__normalize_I1_J,axiom,
% 5.25/5.41 ! [A: rat,B: rat,C: rat] :
% 5.25/5.41 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.25/5.41 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % is_num_normalize(1)
% 5.25/5.41 thf(fact_55_is__num__normalize_I1_J,axiom,
% 5.25/5.41 ! [A: int,B: int,C: int] :
% 5.25/5.41 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.41 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % is_num_normalize(1)
% 5.25/5.41 thf(fact_56_power__divide,axiom,
% 5.25/5.41 ! [A: complex,B: complex,N: nat] :
% 5.25/5.41 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 5.25/5.41 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % power_divide
% 5.25/5.41 thf(fact_57_power__divide,axiom,
% 5.25/5.41 ! [A: real,B: real,N: nat] :
% 5.25/5.41 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 5.25/5.41 = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % power_divide
% 5.25/5.41 thf(fact_58_power__divide,axiom,
% 5.25/5.41 ! [A: rat,B: rat,N: nat] :
% 5.25/5.41 ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 5.25/5.41 = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % power_divide
% 5.25/5.41 thf(fact_59_le__num__One__iff,axiom,
% 5.25/5.41 ! [X3: num] :
% 5.25/5.41 ( ( ord_less_eq_num @ X3 @ one )
% 5.25/5.41 = ( X3 = one ) ) ).
% 5.25/5.41
% 5.25/5.41 % le_num_One_iff
% 5.25/5.41 thf(fact_60_divide__numeral__1,axiom,
% 5.25/5.41 ! [A: complex] :
% 5.25/5.41 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.25/5.41 = A ) ).
% 5.25/5.41
% 5.25/5.41 % divide_numeral_1
% 5.25/5.41 thf(fact_61_divide__numeral__1,axiom,
% 5.25/5.41 ! [A: real] :
% 5.25/5.41 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.25/5.41 = A ) ).
% 5.25/5.41
% 5.25/5.41 % divide_numeral_1
% 5.25/5.41 thf(fact_62_divide__numeral__1,axiom,
% 5.25/5.41 ! [A: rat] :
% 5.25/5.41 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.25/5.41 = A ) ).
% 5.25/5.41
% 5.25/5.41 % divide_numeral_1
% 5.25/5.41 thf(fact_63_numeral__Bit0,axiom,
% 5.25/5.41 ! [N: num] :
% 5.25/5.41 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.25/5.41 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_Bit0
% 5.25/5.41 thf(fact_64_numeral__Bit0,axiom,
% 5.25/5.41 ! [N: num] :
% 5.25/5.41 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.25/5.41 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_Bit0
% 5.25/5.41 thf(fact_65_numeral__Bit0,axiom,
% 5.25/5.41 ! [N: num] :
% 5.25/5.41 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.25/5.41 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_Bit0
% 5.25/5.41 thf(fact_66_numeral__Bit0,axiom,
% 5.25/5.41 ! [N: num] :
% 5.25/5.41 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.25/5.41 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_Bit0
% 5.25/5.41 thf(fact_67_numeral__Bit0,axiom,
% 5.25/5.41 ! [N: num] :
% 5.25/5.41 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.25/5.41 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_Bit0
% 5.25/5.41 thf(fact_68_add__self__div__2,axiom,
% 5.25/5.41 ! [M: nat] :
% 5.25/5.41 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.41 = M ) ).
% 5.25/5.41
% 5.25/5.41 % add_self_div_2
% 5.25/5.41 thf(fact_69_member__bound,axiom,
% 5.25/5.41 ! [Tree: vEBT_VEBT,X3: nat,N: nat] :
% 5.25/5.41 ( ( vEBT_vebt_member @ Tree @ X3 )
% 5.25/5.41 => ( ( vEBT_invar_vebt @ Tree @ N )
% 5.25/5.41 => ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % member_bound
% 5.25/5.41 thf(fact_70__C5_Ohyps_C_I5_J,axiom,
% 5.25/5.41 ! [I: nat] :
% 5.25/5.41 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.25/5.41 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ X4 ) )
% 5.25/5.41 = ( vEBT_V8194947554948674370ptions @ summary @ I ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % "5.hyps"(5)
% 5.25/5.41 thf(fact_71_mem__Collect__eq,axiom,
% 5.25/5.41 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 5.25/5.41 ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 5.25/5.41 = ( P @ A ) ) ).
% 5.25/5.41
% 5.25/5.41 % mem_Collect_eq
% 5.25/5.41 thf(fact_72_mem__Collect__eq,axiom,
% 5.25/5.41 ! [A: complex,P: complex > $o] :
% 5.25/5.41 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 5.25/5.41 = ( P @ A ) ) ).
% 5.25/5.41
% 5.25/5.41 % mem_Collect_eq
% 5.25/5.41 thf(fact_73_mem__Collect__eq,axiom,
% 5.25/5.41 ! [A: real,P: real > $o] :
% 5.25/5.41 ( ( member_real @ A @ ( collect_real @ P ) )
% 5.25/5.41 = ( P @ A ) ) ).
% 5.25/5.41
% 5.25/5.41 % mem_Collect_eq
% 5.25/5.41 thf(fact_74_mem__Collect__eq,axiom,
% 5.25/5.41 ! [A: list_nat,P: list_nat > $o] :
% 5.25/5.41 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 5.25/5.41 = ( P @ A ) ) ).
% 5.25/5.41
% 5.25/5.41 % mem_Collect_eq
% 5.25/5.41 thf(fact_75_mem__Collect__eq,axiom,
% 5.25/5.41 ! [A: nat,P: nat > $o] :
% 5.25/5.41 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.25/5.41 = ( P @ A ) ) ).
% 5.25/5.41
% 5.25/5.41 % mem_Collect_eq
% 5.25/5.41 thf(fact_76_mem__Collect__eq,axiom,
% 5.25/5.41 ! [A: int,P: int > $o] :
% 5.25/5.41 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.25/5.41 = ( P @ A ) ) ).
% 5.25/5.41
% 5.25/5.41 % mem_Collect_eq
% 5.25/5.41 thf(fact_77_Collect__mem__eq,axiom,
% 5.25/5.41 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.25/5.41 ( ( collec3392354462482085612at_nat
% 5.25/5.41 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A2 ) )
% 5.25/5.41 = A2 ) ).
% 5.25/5.41
% 5.25/5.41 % Collect_mem_eq
% 5.25/5.41 thf(fact_78_Collect__mem__eq,axiom,
% 5.25/5.41 ! [A2: set_complex] :
% 5.25/5.41 ( ( collect_complex
% 5.25/5.41 @ ^ [X2: complex] : ( member_complex @ X2 @ A2 ) )
% 5.25/5.41 = A2 ) ).
% 5.25/5.41
% 5.25/5.41 % Collect_mem_eq
% 5.25/5.41 thf(fact_79_Collect__mem__eq,axiom,
% 5.25/5.41 ! [A2: set_real] :
% 5.25/5.41 ( ( collect_real
% 5.25/5.41 @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 5.25/5.41 = A2 ) ).
% 5.25/5.41
% 5.25/5.41 % Collect_mem_eq
% 5.25/5.41 thf(fact_80_Collect__mem__eq,axiom,
% 5.25/5.41 ! [A2: set_list_nat] :
% 5.25/5.41 ( ( collect_list_nat
% 5.25/5.41 @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A2 ) )
% 5.25/5.41 = A2 ) ).
% 5.25/5.41
% 5.25/5.41 % Collect_mem_eq
% 5.25/5.41 thf(fact_81_Collect__mem__eq,axiom,
% 5.25/5.41 ! [A2: set_nat] :
% 5.25/5.41 ( ( collect_nat
% 5.25/5.41 @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 5.25/5.41 = A2 ) ).
% 5.25/5.41
% 5.25/5.41 % Collect_mem_eq
% 5.25/5.41 thf(fact_82_Collect__mem__eq,axiom,
% 5.25/5.41 ! [A2: set_int] :
% 5.25/5.41 ( ( collect_int
% 5.25/5.41 @ ^ [X2: int] : ( member_int @ X2 @ A2 ) )
% 5.25/5.41 = A2 ) ).
% 5.25/5.41
% 5.25/5.41 % Collect_mem_eq
% 5.25/5.41 thf(fact_83_Collect__cong,axiom,
% 5.25/5.41 ! [P: complex > $o,Q: complex > $o] :
% 5.25/5.41 ( ! [X5: complex] :
% 5.25/5.41 ( ( P @ X5 )
% 5.25/5.41 = ( Q @ X5 ) )
% 5.25/5.41 => ( ( collect_complex @ P )
% 5.25/5.41 = ( collect_complex @ Q ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % Collect_cong
% 5.25/5.41 thf(fact_84_Collect__cong,axiom,
% 5.25/5.41 ! [P: real > $o,Q: real > $o] :
% 5.25/5.41 ( ! [X5: real] :
% 5.25/5.41 ( ( P @ X5 )
% 5.25/5.41 = ( Q @ X5 ) )
% 5.25/5.41 => ( ( collect_real @ P )
% 5.25/5.41 = ( collect_real @ Q ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % Collect_cong
% 5.25/5.41 thf(fact_85_Collect__cong,axiom,
% 5.25/5.41 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.25/5.41 ( ! [X5: list_nat] :
% 5.25/5.41 ( ( P @ X5 )
% 5.25/5.41 = ( Q @ X5 ) )
% 5.25/5.41 => ( ( collect_list_nat @ P )
% 5.25/5.41 = ( collect_list_nat @ Q ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % Collect_cong
% 5.25/5.41 thf(fact_86_Collect__cong,axiom,
% 5.25/5.41 ! [P: nat > $o,Q: nat > $o] :
% 5.25/5.41 ( ! [X5: nat] :
% 5.25/5.41 ( ( P @ X5 )
% 5.25/5.41 = ( Q @ X5 ) )
% 5.25/5.41 => ( ( collect_nat @ P )
% 5.25/5.41 = ( collect_nat @ Q ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % Collect_cong
% 5.25/5.41 thf(fact_87_Collect__cong,axiom,
% 5.25/5.41 ! [P: int > $o,Q: int > $o] :
% 5.25/5.41 ( ! [X5: int] :
% 5.25/5.41 ( ( P @ X5 )
% 5.25/5.41 = ( Q @ X5 ) )
% 5.25/5.41 => ( ( collect_int @ P )
% 5.25/5.41 = ( collect_int @ Q ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % Collect_cong
% 5.25/5.41 thf(fact_88_set__n__deg__not__0,axiom,
% 5.25/5.41 ! [TreeList: list_VEBT_VEBT,N: nat,M: nat] :
% 5.25/5.41 ( ! [X5: vEBT_VEBT] :
% 5.25/5.41 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.41 => ( vEBT_invar_vebt @ X5 @ N ) )
% 5.25/5.41 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.25/5.41 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.41 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % set_n_deg_not_0
% 5.25/5.41 thf(fact_89__C5_Ohyps_C_I9_J,axiom,
% 5.25/5.41 ( ( mi != ma )
% 5.25/5.41 => ! [I: nat] :
% 5.25/5.41 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.25/5.41 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.25/5.41 = I )
% 5.25/5.41 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.25/5.41 & ! [X: nat] :
% 5.25/5.41 ( ( ( ( vEBT_VEBT_high @ X @ na )
% 5.25/5.41 = I )
% 5.25/5.41 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ X @ na ) ) )
% 5.25/5.41 => ( ( ord_less_nat @ mi @ X )
% 5.25/5.41 & ( ord_less_eq_nat @ X @ ma ) ) ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % "5.hyps"(9)
% 5.25/5.41 thf(fact_90_div__exp__eq,axiom,
% 5.25/5.41 ! [A: nat,M: nat,N: nat] :
% 5.25/5.41 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.41 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % div_exp_eq
% 5.25/5.41 thf(fact_91_div__exp__eq,axiom,
% 5.25/5.41 ! [A: int,M: nat,N: nat] :
% 5.25/5.41 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.41 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % div_exp_eq
% 5.25/5.41 thf(fact_92_field__less__half__sum,axiom,
% 5.25/5.41 ! [X3: real,Y: real] :
% 5.25/5.41 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.41 => ( ord_less_real @ X3 @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % field_less_half_sum
% 5.25/5.41 thf(fact_93_field__less__half__sum,axiom,
% 5.25/5.41 ! [X3: rat,Y: rat] :
% 5.25/5.41 ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.41 => ( ord_less_rat @ X3 @ ( divide_divide_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % field_less_half_sum
% 5.25/5.41 thf(fact_94_high__inv,axiom,
% 5.25/5.41 ! [X3: nat,N: nat,Y: nat] :
% 5.25/5.41 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.41 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X3 ) @ N )
% 5.25/5.41 = Y ) ) ).
% 5.25/5.41
% 5.25/5.41 % high_inv
% 5.25/5.41 thf(fact_95_nat__add__left__cancel__le,axiom,
% 5.25/5.41 ! [K: nat,M: nat,N: nat] :
% 5.25/5.41 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.25/5.41 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % nat_add_left_cancel_le
% 5.25/5.41 thf(fact_96_nat__add__left__cancel__less,axiom,
% 5.25/5.41 ! [K: nat,M: nat,N: nat] :
% 5.25/5.41 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.25/5.41 = ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % nat_add_left_cancel_less
% 5.25/5.41 thf(fact_97_enat__ord__number_I1_J,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.25/5.41 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % enat_ord_number(1)
% 5.25/5.41 thf(fact_98_enat__ord__number_I2_J,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.25/5.41 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % enat_ord_number(2)
% 5.25/5.41 thf(fact_99_even__odd__cases,axiom,
% 5.25/5.41 ! [X3: nat] :
% 5.25/5.41 ( ! [N3: nat] :
% 5.25/5.41 ( X3
% 5.25/5.41 != ( plus_plus_nat @ N3 @ N3 ) )
% 5.25/5.41 => ~ ! [N3: nat] :
% 5.25/5.41 ( X3
% 5.25/5.41 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % even_odd_cases
% 5.25/5.41 thf(fact_100_min__Null__member,axiom,
% 5.25/5.41 ! [T: vEBT_VEBT,X3: nat] :
% 5.25/5.41 ( ( vEBT_VEBT_minNull @ T )
% 5.25/5.41 => ~ ( vEBT_vebt_member @ T @ X3 ) ) ).
% 5.25/5.41
% 5.25/5.41 % min_Null_member
% 5.25/5.41 thf(fact_101_both__member__options__equiv__member,axiom,
% 5.25/5.41 ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 5.25/5.41 ( ( vEBT_invar_vebt @ T @ N )
% 5.25/5.41 => ( ( vEBT_V8194947554948674370ptions @ T @ X3 )
% 5.25/5.41 = ( vEBT_vebt_member @ T @ X3 ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % both_member_options_equiv_member
% 5.25/5.41 thf(fact_102_valid__member__both__member__options,axiom,
% 5.25/5.41 ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 5.25/5.41 ( ( vEBT_invar_vebt @ T @ N )
% 5.25/5.41 => ( ( vEBT_V8194947554948674370ptions @ T @ X3 )
% 5.25/5.41 => ( vEBT_vebt_member @ T @ X3 ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % valid_member_both_member_options
% 5.25/5.41 thf(fact_103_inthall,axiom,
% 5.25/5.41 ! [Xs: list_real,P: real > $o,N: nat] :
% 5.25/5.41 ( ! [X5: real] :
% 5.25/5.41 ( ( member_real @ X5 @ ( set_real2 @ Xs ) )
% 5.25/5.41 => ( P @ X5 ) )
% 5.25/5.41 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.25/5.41 => ( P @ ( nth_real @ Xs @ N ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % inthall
% 5.25/5.41 thf(fact_104_inthall,axiom,
% 5.25/5.41 ! [Xs: list_complex,P: complex > $o,N: nat] :
% 5.25/5.41 ( ! [X5: complex] :
% 5.25/5.41 ( ( member_complex @ X5 @ ( set_complex2 @ Xs ) )
% 5.25/5.41 => ( P @ X5 ) )
% 5.25/5.41 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.25/5.41 => ( P @ ( nth_complex @ Xs @ N ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % inthall
% 5.25/5.41 thf(fact_105_inthall,axiom,
% 5.25/5.41 ! [Xs: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,N: nat] :
% 5.25/5.41 ( ! [X5: product_prod_nat_nat] :
% 5.25/5.41 ( ( member8440522571783428010at_nat @ X5 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 5.25/5.41 => ( P @ X5 ) )
% 5.25/5.41 => ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs ) )
% 5.25/5.41 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ N ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % inthall
% 5.25/5.41 thf(fact_106_inthall,axiom,
% 5.25/5.41 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 5.25/5.41 ( ! [X5: vEBT_VEBT] :
% 5.25/5.41 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.25/5.41 => ( P @ X5 ) )
% 5.25/5.41 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.41 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % inthall
% 5.25/5.41 thf(fact_107_inthall,axiom,
% 5.25/5.41 ! [Xs: list_o,P: $o > $o,N: nat] :
% 5.25/5.41 ( ! [X5: $o] :
% 5.25/5.41 ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 5.25/5.41 => ( P @ X5 ) )
% 5.25/5.41 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.25/5.41 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % inthall
% 5.25/5.41 thf(fact_108_inthall,axiom,
% 5.25/5.41 ! [Xs: list_nat,P: nat > $o,N: nat] :
% 5.25/5.41 ( ! [X5: nat] :
% 5.25/5.41 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 5.25/5.41 => ( P @ X5 ) )
% 5.25/5.41 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.25/5.41 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % inthall
% 5.25/5.41 thf(fact_109_inthall,axiom,
% 5.25/5.41 ! [Xs: list_int,P: int > $o,N: nat] :
% 5.25/5.41 ( ! [X5: int] :
% 5.25/5.41 ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 5.25/5.41 => ( P @ X5 ) )
% 5.25/5.41 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.25/5.41 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % inthall
% 5.25/5.41 thf(fact_110_bit__split__inv,axiom,
% 5.25/5.41 ! [X3: nat,D: nat] :
% 5.25/5.41 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X3 @ D ) @ ( vEBT_VEBT_low @ X3 @ D ) @ D )
% 5.25/5.41 = X3 ) ).
% 5.25/5.41
% 5.25/5.41 % bit_split_inv
% 5.25/5.41 thf(fact_111_nat_Oinject,axiom,
% 5.25/5.41 ! [X22: nat,Y2: nat] :
% 5.25/5.41 ( ( ( suc @ X22 )
% 5.25/5.41 = ( suc @ Y2 ) )
% 5.25/5.41 = ( X22 = Y2 ) ) ).
% 5.25/5.41
% 5.25/5.41 % nat.inject
% 5.25/5.41 thf(fact_112_old_Onat_Oinject,axiom,
% 5.25/5.41 ! [Nat: nat,Nat2: nat] :
% 5.25/5.41 ( ( ( suc @ Nat )
% 5.25/5.41 = ( suc @ Nat2 ) )
% 5.25/5.41 = ( Nat = Nat2 ) ) ).
% 5.25/5.41
% 5.25/5.41 % old.nat.inject
% 5.25/5.41 thf(fact_113_member__correct,axiom,
% 5.25/5.41 ! [T: vEBT_VEBT,N: nat,X3: nat] :
% 5.25/5.41 ( ( vEBT_invar_vebt @ T @ N )
% 5.25/5.41 => ( ( vEBT_vebt_member @ T @ X3 )
% 5.25/5.41 = ( member_nat @ X3 @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % member_correct
% 5.25/5.41 thf(fact_114_mult__numeral__left__semiring__numeral,axiom,
% 5.25/5.41 ! [V: num,W: num,Z: complex] :
% 5.25/5.41 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.25/5.41 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.41
% 5.25/5.41 % mult_numeral_left_semiring_numeral
% 5.25/5.41 thf(fact_115_mult__numeral__left__semiring__numeral,axiom,
% 5.25/5.41 ! [V: num,W: num,Z: real] :
% 5.25/5.41 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.25/5.41 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.41
% 5.25/5.41 % mult_numeral_left_semiring_numeral
% 5.25/5.41 thf(fact_116_mult__numeral__left__semiring__numeral,axiom,
% 5.25/5.41 ! [V: num,W: num,Z: rat] :
% 5.25/5.41 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.25/5.41 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.41
% 5.25/5.41 % mult_numeral_left_semiring_numeral
% 5.25/5.41 thf(fact_117_mult__numeral__left__semiring__numeral,axiom,
% 5.25/5.41 ! [V: num,W: num,Z: nat] :
% 5.25/5.41 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.25/5.41 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.41
% 5.25/5.41 % mult_numeral_left_semiring_numeral
% 5.25/5.41 thf(fact_118_mult__numeral__left__semiring__numeral,axiom,
% 5.25/5.41 ! [V: num,W: num,Z: int] :
% 5.25/5.41 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.25/5.41 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.41
% 5.25/5.41 % mult_numeral_left_semiring_numeral
% 5.25/5.41 thf(fact_119_numeral__times__numeral,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.25/5.41 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_times_numeral
% 5.25/5.41 thf(fact_120_numeral__times__numeral,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.25/5.41 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_times_numeral
% 5.25/5.41 thf(fact_121_numeral__times__numeral,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.25/5.41 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_times_numeral
% 5.25/5.41 thf(fact_122_numeral__times__numeral,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.41 = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_times_numeral
% 5.25/5.41 thf(fact_123_numeral__times__numeral,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.41 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_times_numeral
% 5.25/5.41 thf(fact_124_low__inv,axiom,
% 5.25/5.41 ! [X3: nat,N: nat,Y: nat] :
% 5.25/5.41 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.41 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X3 ) @ N )
% 5.25/5.41 = X3 ) ) ).
% 5.25/5.41
% 5.25/5.41 % low_inv
% 5.25/5.41 thf(fact_125_bits__div__by__1,axiom,
% 5.25/5.41 ! [A: nat] :
% 5.25/5.41 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.25/5.41 = A ) ).
% 5.25/5.41
% 5.25/5.41 % bits_div_by_1
% 5.25/5.41 thf(fact_126_bits__div__by__1,axiom,
% 5.25/5.41 ! [A: int] :
% 5.25/5.41 ( ( divide_divide_int @ A @ one_one_int )
% 5.25/5.41 = A ) ).
% 5.25/5.41
% 5.25/5.41 % bits_div_by_1
% 5.25/5.41 thf(fact_127_power__one,axiom,
% 5.25/5.41 ! [N: nat] :
% 5.25/5.41 ( ( power_power_rat @ one_one_rat @ N )
% 5.25/5.41 = one_one_rat ) ).
% 5.25/5.41
% 5.25/5.41 % power_one
% 5.25/5.41 thf(fact_128_power__one,axiom,
% 5.25/5.41 ! [N: nat] :
% 5.25/5.41 ( ( power_power_nat @ one_one_nat @ N )
% 5.25/5.41 = one_one_nat ) ).
% 5.25/5.41
% 5.25/5.41 % power_one
% 5.25/5.41 thf(fact_129_power__one,axiom,
% 5.25/5.41 ! [N: nat] :
% 5.25/5.41 ( ( power_power_real @ one_one_real @ N )
% 5.25/5.41 = one_one_real ) ).
% 5.25/5.41
% 5.25/5.41 % power_one
% 5.25/5.41 thf(fact_130_power__one,axiom,
% 5.25/5.41 ! [N: nat] :
% 5.25/5.41 ( ( power_power_int @ one_one_int @ N )
% 5.25/5.41 = one_one_int ) ).
% 5.25/5.41
% 5.25/5.41 % power_one
% 5.25/5.41 thf(fact_131_power__one,axiom,
% 5.25/5.41 ! [N: nat] :
% 5.25/5.41 ( ( power_power_complex @ one_one_complex @ N )
% 5.25/5.41 = one_one_complex ) ).
% 5.25/5.41
% 5.25/5.41 % power_one
% 5.25/5.41 thf(fact_132_lessI,axiom,
% 5.25/5.41 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % lessI
% 5.25/5.41 thf(fact_133_Suc__mono,axiom,
% 5.25/5.41 ! [M: nat,N: nat] :
% 5.25/5.41 ( ( ord_less_nat @ M @ N )
% 5.25/5.41 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % Suc_mono
% 5.25/5.41 thf(fact_134_Suc__less__eq,axiom,
% 5.25/5.41 ! [M: nat,N: nat] :
% 5.25/5.41 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.25/5.41 = ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.41
% 5.25/5.41 % Suc_less_eq
% 5.25/5.41 thf(fact_135_Suc__le__mono,axiom,
% 5.25/5.41 ! [N: nat,M: nat] :
% 5.25/5.41 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 5.25/5.41 = ( ord_less_eq_nat @ N @ M ) ) ).
% 5.25/5.41
% 5.25/5.41 % Suc_le_mono
% 5.25/5.41 thf(fact_136_add__Suc__right,axiom,
% 5.25/5.41 ! [M: nat,N: nat] :
% 5.25/5.41 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 5.25/5.41 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % add_Suc_right
% 5.25/5.41 thf(fact_137_power__one__right,axiom,
% 5.25/5.41 ! [A: nat] :
% 5.25/5.41 ( ( power_power_nat @ A @ one_one_nat )
% 5.25/5.41 = A ) ).
% 5.25/5.41
% 5.25/5.41 % power_one_right
% 5.25/5.41 thf(fact_138_power__one__right,axiom,
% 5.25/5.41 ! [A: real] :
% 5.25/5.41 ( ( power_power_real @ A @ one_one_nat )
% 5.25/5.41 = A ) ).
% 5.25/5.41
% 5.25/5.41 % power_one_right
% 5.25/5.41 thf(fact_139_power__one__right,axiom,
% 5.25/5.41 ! [A: int] :
% 5.25/5.41 ( ( power_power_int @ A @ one_one_nat )
% 5.25/5.41 = A ) ).
% 5.25/5.41
% 5.25/5.41 % power_one_right
% 5.25/5.41 thf(fact_140_power__one__right,axiom,
% 5.25/5.41 ! [A: complex] :
% 5.25/5.41 ( ( power_power_complex @ A @ one_one_nat )
% 5.25/5.41 = A ) ).
% 5.25/5.41
% 5.25/5.41 % power_one_right
% 5.25/5.41 thf(fact_141_nat__1__eq__mult__iff,axiom,
% 5.25/5.41 ! [M: nat,N: nat] :
% 5.25/5.41 ( ( one_one_nat
% 5.25/5.41 = ( times_times_nat @ M @ N ) )
% 5.25/5.41 = ( ( M = one_one_nat )
% 5.25/5.41 & ( N = one_one_nat ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % nat_1_eq_mult_iff
% 5.25/5.41 thf(fact_142_nat__mult__eq__1__iff,axiom,
% 5.25/5.41 ! [M: nat,N: nat] :
% 5.25/5.41 ( ( ( times_times_nat @ M @ N )
% 5.25/5.41 = one_one_nat )
% 5.25/5.41 = ( ( M = one_one_nat )
% 5.25/5.41 & ( N = one_one_nat ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % nat_mult_eq_1_iff
% 5.25/5.41 thf(fact_143_semiring__norm_I6_J,axiom,
% 5.25/5.41 ! [M: num,N: num] :
% 5.25/5.41 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.25/5.41 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % semiring_norm(6)
% 5.25/5.41 thf(fact_144_bit__concat__def,axiom,
% 5.25/5.41 ( vEBT_VEBT_bit_concat
% 5.25/5.41 = ( ^ [H: nat,L: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % bit_concat_def
% 5.25/5.41 thf(fact_145_distrib__right__numeral,axiom,
% 5.25/5.41 ! [A: complex,B: complex,V: num] :
% 5.25/5.41 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.25/5.41 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % distrib_right_numeral
% 5.25/5.41 thf(fact_146_distrib__right__numeral,axiom,
% 5.25/5.41 ! [A: real,B: real,V: num] :
% 5.25/5.41 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.25/5.41 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % distrib_right_numeral
% 5.25/5.41 thf(fact_147_distrib__right__numeral,axiom,
% 5.25/5.41 ! [A: rat,B: rat,V: num] :
% 5.25/5.41 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.25/5.41 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % distrib_right_numeral
% 5.25/5.41 thf(fact_148_distrib__right__numeral,axiom,
% 5.25/5.41 ! [A: nat,B: nat,V: num] :
% 5.25/5.41 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 5.25/5.41 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % distrib_right_numeral
% 5.25/5.41 thf(fact_149_distrib__right__numeral,axiom,
% 5.25/5.41 ! [A: int,B: int,V: num] :
% 5.25/5.41 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.25/5.41 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % distrib_right_numeral
% 5.25/5.41 thf(fact_150_distrib__left__numeral,axiom,
% 5.25/5.41 ! [V: num,B: complex,C: complex] :
% 5.25/5.41 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 5.25/5.41 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % distrib_left_numeral
% 5.25/5.41 thf(fact_151_distrib__left__numeral,axiom,
% 5.25/5.41 ! [V: num,B: real,C: real] :
% 5.25/5.41 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 5.25/5.41 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % distrib_left_numeral
% 5.25/5.41 thf(fact_152_distrib__left__numeral,axiom,
% 5.25/5.41 ! [V: num,B: rat,C: rat] :
% 5.25/5.41 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.41 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % distrib_left_numeral
% 5.25/5.41 thf(fact_153_distrib__left__numeral,axiom,
% 5.25/5.41 ! [V: num,B: nat,C: nat] :
% 5.25/5.41 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.41 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % distrib_left_numeral
% 5.25/5.41 thf(fact_154_distrib__left__numeral,axiom,
% 5.25/5.41 ! [V: num,B: int,C: int] :
% 5.25/5.41 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 5.25/5.41 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.25/5.41
% 5.25/5.41 % distrib_left_numeral
% 5.25/5.41 thf(fact_155_numeral__eq__one__iff,axiom,
% 5.25/5.41 ! [N: num] :
% 5.25/5.41 ( ( ( numera6690914467698888265omplex @ N )
% 5.25/5.41 = one_one_complex )
% 5.25/5.41 = ( N = one ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_eq_one_iff
% 5.25/5.41 thf(fact_156_numeral__eq__one__iff,axiom,
% 5.25/5.41 ! [N: num] :
% 5.25/5.41 ( ( ( numeral_numeral_real @ N )
% 5.25/5.41 = one_one_real )
% 5.25/5.41 = ( N = one ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_eq_one_iff
% 5.25/5.41 thf(fact_157_numeral__eq__one__iff,axiom,
% 5.25/5.41 ! [N: num] :
% 5.25/5.41 ( ( ( numeral_numeral_rat @ N )
% 5.25/5.41 = one_one_rat )
% 5.25/5.41 = ( N = one ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_eq_one_iff
% 5.25/5.41 thf(fact_158_numeral__eq__one__iff,axiom,
% 5.25/5.41 ! [N: num] :
% 5.25/5.41 ( ( ( numeral_numeral_nat @ N )
% 5.25/5.41 = one_one_nat )
% 5.25/5.41 = ( N = one ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_eq_one_iff
% 5.25/5.41 thf(fact_159_numeral__eq__one__iff,axiom,
% 5.25/5.41 ! [N: num] :
% 5.25/5.41 ( ( ( numeral_numeral_int @ N )
% 5.25/5.41 = one_one_int )
% 5.25/5.41 = ( N = one ) ) ).
% 5.25/5.41
% 5.25/5.41 % numeral_eq_one_iff
% 5.25/5.41 thf(fact_160_one__eq__numeral__iff,axiom,
% 5.25/5.41 ! [N: num] :
% 5.25/5.42 ( ( one_one_complex
% 5.25/5.42 = ( numera6690914467698888265omplex @ N ) )
% 5.25/5.42 = ( one = N ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_eq_numeral_iff
% 5.25/5.42 thf(fact_161_one__eq__numeral__iff,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( one_one_real
% 5.25/5.42 = ( numeral_numeral_real @ N ) )
% 5.25/5.42 = ( one = N ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_eq_numeral_iff
% 5.25/5.42 thf(fact_162_one__eq__numeral__iff,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( one_one_rat
% 5.25/5.42 = ( numeral_numeral_rat @ N ) )
% 5.25/5.42 = ( one = N ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_eq_numeral_iff
% 5.25/5.42 thf(fact_163_one__eq__numeral__iff,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( one_one_nat
% 5.25/5.42 = ( numeral_numeral_nat @ N ) )
% 5.25/5.42 = ( one = N ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_eq_numeral_iff
% 5.25/5.42 thf(fact_164_one__eq__numeral__iff,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( one_one_int
% 5.25/5.42 = ( numeral_numeral_int @ N ) )
% 5.25/5.42 = ( one = N ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_eq_numeral_iff
% 5.25/5.42 thf(fact_165_power__inject__exp,axiom,
% 5.25/5.42 ! [A: real,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.42 => ( ( ( power_power_real @ A @ M )
% 5.25/5.42 = ( power_power_real @ A @ N ) )
% 5.25/5.42 = ( M = N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_inject_exp
% 5.25/5.42 thf(fact_166_power__inject__exp,axiom,
% 5.25/5.42 ! [A: rat,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.42 => ( ( ( power_power_rat @ A @ M )
% 5.25/5.42 = ( power_power_rat @ A @ N ) )
% 5.25/5.42 = ( M = N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_inject_exp
% 5.25/5.42 thf(fact_167_power__inject__exp,axiom,
% 5.25/5.42 ! [A: nat,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.42 => ( ( ( power_power_nat @ A @ M )
% 5.25/5.42 = ( power_power_nat @ A @ N ) )
% 5.25/5.42 = ( M = N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_inject_exp
% 5.25/5.42 thf(fact_168_power__inject__exp,axiom,
% 5.25/5.42 ! [A: int,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.42 => ( ( ( power_power_int @ A @ M )
% 5.25/5.42 = ( power_power_int @ A @ N ) )
% 5.25/5.42 = ( M = N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_inject_exp
% 5.25/5.42 thf(fact_169_mult__Suc__right,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( times_times_nat @ M @ ( suc @ N ) )
% 5.25/5.42 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_Suc_right
% 5.25/5.42 thf(fact_170_semiring__norm_I2_J,axiom,
% 5.25/5.42 ( ( plus_plus_num @ one @ one )
% 5.25/5.42 = ( bit0 @ one ) ) ).
% 5.25/5.42
% 5.25/5.42 % semiring_norm(2)
% 5.25/5.42 thf(fact_171_divide__le__eq__numeral1_I1_J,axiom,
% 5.25/5.42 ! [B: real,W: num,A: real] :
% 5.25/5.42 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.25/5.42 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % divide_le_eq_numeral1(1)
% 5.25/5.42 thf(fact_172_divide__le__eq__numeral1_I1_J,axiom,
% 5.25/5.42 ! [B: rat,W: num,A: rat] :
% 5.25/5.42 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.25/5.42 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % divide_le_eq_numeral1(1)
% 5.25/5.42 thf(fact_173_le__divide__eq__numeral1_I1_J,axiom,
% 5.25/5.42 ! [A: real,B: real,W: num] :
% 5.25/5.42 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.42 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_divide_eq_numeral1(1)
% 5.25/5.42 thf(fact_174_le__divide__eq__numeral1_I1_J,axiom,
% 5.25/5.42 ! [A: rat,B: rat,W: num] :
% 5.25/5.42 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.25/5.42 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_divide_eq_numeral1(1)
% 5.25/5.42 thf(fact_175_divide__less__eq__numeral1_I1_J,axiom,
% 5.25/5.42 ! [B: real,W: num,A: real] :
% 5.25/5.42 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.25/5.42 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % divide_less_eq_numeral1(1)
% 5.25/5.42 thf(fact_176_divide__less__eq__numeral1_I1_J,axiom,
% 5.25/5.42 ! [B: rat,W: num,A: rat] :
% 5.25/5.42 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.25/5.42 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % divide_less_eq_numeral1(1)
% 5.25/5.42 thf(fact_177_less__divide__eq__numeral1_I1_J,axiom,
% 5.25/5.42 ! [A: real,B: real,W: num] :
% 5.25/5.42 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.42 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_divide_eq_numeral1(1)
% 5.25/5.42 thf(fact_178_less__divide__eq__numeral1_I1_J,axiom,
% 5.25/5.42 ! [A: rat,B: rat,W: num] :
% 5.25/5.42 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.25/5.42 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_divide_eq_numeral1(1)
% 5.25/5.42 thf(fact_179_power__strict__increasing__iff,axiom,
% 5.25/5.42 ! [B: real,X3: nat,Y: nat] :
% 5.25/5.42 ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.42 => ( ( ord_less_real @ ( power_power_real @ B @ X3 ) @ ( power_power_real @ B @ Y ) )
% 5.25/5.42 = ( ord_less_nat @ X3 @ Y ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_strict_increasing_iff
% 5.25/5.42 thf(fact_180_power__strict__increasing__iff,axiom,
% 5.25/5.42 ! [B: rat,X3: nat,Y: nat] :
% 5.25/5.42 ( ( ord_less_rat @ one_one_rat @ B )
% 5.25/5.42 => ( ( ord_less_rat @ ( power_power_rat @ B @ X3 ) @ ( power_power_rat @ B @ Y ) )
% 5.25/5.42 = ( ord_less_nat @ X3 @ Y ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_strict_increasing_iff
% 5.25/5.42 thf(fact_181_power__strict__increasing__iff,axiom,
% 5.25/5.42 ! [B: nat,X3: nat,Y: nat] :
% 5.25/5.42 ( ( ord_less_nat @ one_one_nat @ B )
% 5.25/5.42 => ( ( ord_less_nat @ ( power_power_nat @ B @ X3 ) @ ( power_power_nat @ B @ Y ) )
% 5.25/5.42 = ( ord_less_nat @ X3 @ Y ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_strict_increasing_iff
% 5.25/5.42 thf(fact_182_power__strict__increasing__iff,axiom,
% 5.25/5.42 ! [B: int,X3: nat,Y: nat] :
% 5.25/5.42 ( ( ord_less_int @ one_one_int @ B )
% 5.25/5.42 => ( ( ord_less_int @ ( power_power_int @ B @ X3 ) @ ( power_power_int @ B @ Y ) )
% 5.25/5.42 = ( ord_less_nat @ X3 @ Y ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_strict_increasing_iff
% 5.25/5.42 thf(fact_183_power__add__numeral,axiom,
% 5.25/5.42 ! [A: complex,M: num,N: num] :
% 5.25/5.42 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.25/5.42 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add_numeral
% 5.25/5.42 thf(fact_184_power__add__numeral,axiom,
% 5.25/5.42 ! [A: real,M: num,N: num] :
% 5.25/5.42 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.25/5.42 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add_numeral
% 5.25/5.42 thf(fact_185_power__add__numeral,axiom,
% 5.25/5.42 ! [A: rat,M: num,N: num] :
% 5.25/5.42 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.25/5.42 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add_numeral
% 5.25/5.42 thf(fact_186_power__add__numeral,axiom,
% 5.25/5.42 ! [A: nat,M: num,N: num] :
% 5.25/5.42 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.25/5.42 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add_numeral
% 5.25/5.42 thf(fact_187_power__add__numeral,axiom,
% 5.25/5.42 ! [A: int,M: num,N: num] :
% 5.25/5.42 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.25/5.42 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add_numeral
% 5.25/5.42 thf(fact_188_power__add__numeral2,axiom,
% 5.25/5.42 ! [A: complex,M: num,N: num,B: complex] :
% 5.25/5.42 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.25/5.42 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add_numeral2
% 5.25/5.42 thf(fact_189_power__add__numeral2,axiom,
% 5.25/5.42 ! [A: real,M: num,N: num,B: real] :
% 5.25/5.42 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.25/5.42 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add_numeral2
% 5.25/5.42 thf(fact_190_power__add__numeral2,axiom,
% 5.25/5.42 ! [A: rat,M: num,N: num,B: rat] :
% 5.25/5.42 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.25/5.42 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add_numeral2
% 5.25/5.42 thf(fact_191_power__add__numeral2,axiom,
% 5.25/5.42 ! [A: nat,M: num,N: num,B: nat] :
% 5.25/5.42 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.25/5.42 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add_numeral2
% 5.25/5.42 thf(fact_192_power__add__numeral2,axiom,
% 5.25/5.42 ! [A: int,M: num,N: num,B: int] :
% 5.25/5.42 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.25/5.42 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add_numeral2
% 5.25/5.42 thf(fact_193_Suc__numeral,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 5.25/5.42 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_numeral
% 5.25/5.42 thf(fact_194_one__add__one,axiom,
% 5.25/5.42 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.25/5.42 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_add_one
% 5.25/5.42 thf(fact_195_one__add__one,axiom,
% 5.25/5.42 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.25/5.42 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_add_one
% 5.25/5.42 thf(fact_196_one__add__one,axiom,
% 5.25/5.42 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.25/5.42 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_add_one
% 5.25/5.42 thf(fact_197_one__add__one,axiom,
% 5.25/5.42 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.25/5.42 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_add_one
% 5.25/5.42 thf(fact_198_one__add__one,axiom,
% 5.25/5.42 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.25/5.42 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_add_one
% 5.25/5.42 thf(fact_199_power__increasing__iff,axiom,
% 5.25/5.42 ! [B: real,X3: nat,Y: nat] :
% 5.25/5.42 ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.42 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X3 ) @ ( power_power_real @ B @ Y ) )
% 5.25/5.42 = ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_increasing_iff
% 5.25/5.42 thf(fact_200_power__increasing__iff,axiom,
% 5.25/5.42 ! [B: rat,X3: nat,Y: nat] :
% 5.25/5.42 ( ( ord_less_rat @ one_one_rat @ B )
% 5.25/5.42 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X3 ) @ ( power_power_rat @ B @ Y ) )
% 5.25/5.42 = ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_increasing_iff
% 5.25/5.42 thf(fact_201_power__increasing__iff,axiom,
% 5.25/5.42 ! [B: nat,X3: nat,Y: nat] :
% 5.25/5.42 ( ( ord_less_nat @ one_one_nat @ B )
% 5.25/5.42 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X3 ) @ ( power_power_nat @ B @ Y ) )
% 5.25/5.42 = ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_increasing_iff
% 5.25/5.42 thf(fact_202_power__increasing__iff,axiom,
% 5.25/5.42 ! [B: int,X3: nat,Y: nat] :
% 5.25/5.42 ( ( ord_less_int @ one_one_int @ B )
% 5.25/5.42 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X3 ) @ ( power_power_int @ B @ Y ) )
% 5.25/5.42 = ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_increasing_iff
% 5.25/5.42 thf(fact_203_add__2__eq__Suc,axiom,
% 5.25/5.42 ! [N: nat] :
% 5.25/5.42 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.42 = ( suc @ ( suc @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_2_eq_Suc
% 5.25/5.42 thf(fact_204_add__2__eq__Suc_H,axiom,
% 5.25/5.42 ! [N: nat] :
% 5.25/5.42 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( suc @ ( suc @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_2_eq_Suc'
% 5.25/5.42 thf(fact_205_Suc__1,axiom,
% 5.25/5.42 ( ( suc @ one_one_nat )
% 5.25/5.42 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_1
% 5.25/5.42 thf(fact_206_div2__Suc__Suc,axiom,
% 5.25/5.42 ! [M: nat] :
% 5.25/5.42 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % div2_Suc_Suc
% 5.25/5.42 thf(fact_207_numeral__plus__one,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 5.25/5.42 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_plus_one
% 5.25/5.42 thf(fact_208_numeral__plus__one,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.25/5.42 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_plus_one
% 5.25/5.42 thf(fact_209_numeral__plus__one,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.25/5.42 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_plus_one
% 5.25/5.42 thf(fact_210_numeral__plus__one,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.25/5.42 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_plus_one
% 5.25/5.42 thf(fact_211_numeral__plus__one,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.25/5.42 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_plus_one
% 5.25/5.42 thf(fact_212_one__plus__numeral,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 5.25/5.42 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_plus_numeral
% 5.25/5.42 thf(fact_213_one__plus__numeral,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.25/5.42 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_plus_numeral
% 5.25/5.42 thf(fact_214_one__plus__numeral,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.25/5.42 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_plus_numeral
% 5.25/5.42 thf(fact_215_one__plus__numeral,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.25/5.42 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_plus_numeral
% 5.25/5.42 thf(fact_216_one__plus__numeral,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.25/5.42 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_plus_numeral
% 5.25/5.42 thf(fact_217_numeral__le__one__iff,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.25/5.42 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_le_one_iff
% 5.25/5.42 thf(fact_218_numeral__le__one__iff,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.25/5.42 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_le_one_iff
% 5.25/5.42 thf(fact_219_numeral__le__one__iff,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.25/5.42 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_le_one_iff
% 5.25/5.42 thf(fact_220_numeral__le__one__iff,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.25/5.42 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_le_one_iff
% 5.25/5.42 thf(fact_221_one__less__numeral__iff,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.25/5.42 = ( ord_less_num @ one @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_less_numeral_iff
% 5.25/5.42 thf(fact_222_one__less__numeral__iff,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.25/5.42 = ( ord_less_num @ one @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_less_numeral_iff
% 5.25/5.42 thf(fact_223_one__less__numeral__iff,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.25/5.42 = ( ord_less_num @ one @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_less_numeral_iff
% 5.25/5.42 thf(fact_224_one__less__numeral__iff,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.25/5.42 = ( ord_less_num @ one @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_less_numeral_iff
% 5.25/5.42 thf(fact_225_Suc__mult__le__cancel1,axiom,
% 5.25/5.42 ! [K: nat,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.25/5.42 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_mult_le_cancel1
% 5.25/5.42 thf(fact_226_Suc__mult__less__cancel1,axiom,
% 5.25/5.42 ! [K: nat,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.25/5.42 = ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_mult_less_cancel1
% 5.25/5.42 thf(fact_227_enat__less__induct,axiom,
% 5.25/5.42 ! [P: extended_enat > $o,N: extended_enat] :
% 5.25/5.42 ( ! [N3: extended_enat] :
% 5.25/5.42 ( ! [M2: extended_enat] :
% 5.25/5.42 ( ( ord_le72135733267957522d_enat @ M2 @ N3 )
% 5.25/5.42 => ( P @ M2 ) )
% 5.25/5.42 => ( P @ N3 ) )
% 5.25/5.42 => ( P @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % enat_less_induct
% 5.25/5.42 thf(fact_228_Suc__eq__plus1__left,axiom,
% 5.25/5.42 ( suc
% 5.25/5.42 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_eq_plus1_left
% 5.25/5.42 thf(fact_229_plus__1__eq__Suc,axiom,
% 5.25/5.42 ( ( plus_plus_nat @ one_one_nat )
% 5.25/5.42 = suc ) ).
% 5.25/5.42
% 5.25/5.42 % plus_1_eq_Suc
% 5.25/5.42 thf(fact_230_Suc__eq__plus1,axiom,
% 5.25/5.42 ( suc
% 5.25/5.42 = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_eq_plus1
% 5.25/5.42 thf(fact_231_mult__Suc,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( times_times_nat @ ( suc @ M ) @ N )
% 5.25/5.42 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_Suc
% 5.25/5.42 thf(fact_232_Suc__inject,axiom,
% 5.25/5.42 ! [X3: nat,Y: nat] :
% 5.25/5.42 ( ( ( suc @ X3 )
% 5.25/5.42 = ( suc @ Y ) )
% 5.25/5.42 => ( X3 = Y ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_inject
% 5.25/5.42 thf(fact_233_nat__mult__1,axiom,
% 5.25/5.42 ! [N: nat] :
% 5.25/5.42 ( ( times_times_nat @ one_one_nat @ N )
% 5.25/5.42 = N ) ).
% 5.25/5.42
% 5.25/5.42 % nat_mult_1
% 5.25/5.42 thf(fact_234_n__not__Suc__n,axiom,
% 5.25/5.42 ! [N: nat] :
% 5.25/5.42 ( N
% 5.25/5.42 != ( suc @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % n_not_Suc_n
% 5.25/5.42 thf(fact_235_Suc__mult__cancel1,axiom,
% 5.25/5.42 ! [K: nat,M: nat,N: nat] :
% 5.25/5.42 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.25/5.42 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.25/5.42 = ( M = N ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_mult_cancel1
% 5.25/5.42 thf(fact_236_nat__mult__1__right,axiom,
% 5.25/5.42 ! [N: nat] :
% 5.25/5.42 ( ( times_times_nat @ N @ one_one_nat )
% 5.25/5.42 = N ) ).
% 5.25/5.42
% 5.25/5.42 % nat_mult_1_right
% 5.25/5.42 thf(fact_237_power__Suc2,axiom,
% 5.25/5.42 ! [A: complex,N: nat] :
% 5.25/5.42 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.25/5.42 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_Suc2
% 5.25/5.42 thf(fact_238_power__Suc2,axiom,
% 5.25/5.42 ! [A: real,N: nat] :
% 5.25/5.42 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.25/5.42 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_Suc2
% 5.25/5.42 thf(fact_239_power__Suc2,axiom,
% 5.25/5.42 ! [A: rat,N: nat] :
% 5.25/5.42 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.25/5.42 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_Suc2
% 5.25/5.42 thf(fact_240_power__Suc2,axiom,
% 5.25/5.42 ! [A: nat,N: nat] :
% 5.25/5.42 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.25/5.42 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_Suc2
% 5.25/5.42 thf(fact_241_power__Suc2,axiom,
% 5.25/5.42 ! [A: int,N: nat] :
% 5.25/5.42 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.25/5.42 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_Suc2
% 5.25/5.42 thf(fact_242_power__Suc,axiom,
% 5.25/5.42 ! [A: complex,N: nat] :
% 5.25/5.42 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.25/5.42 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_Suc
% 5.25/5.42 thf(fact_243_power__Suc,axiom,
% 5.25/5.42 ! [A: real,N: nat] :
% 5.25/5.42 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.25/5.42 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_Suc
% 5.25/5.42 thf(fact_244_power__Suc,axiom,
% 5.25/5.42 ! [A: rat,N: nat] :
% 5.25/5.42 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.25/5.42 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_Suc
% 5.25/5.42 thf(fact_245_power__Suc,axiom,
% 5.25/5.42 ! [A: nat,N: nat] :
% 5.25/5.42 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.25/5.42 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_Suc
% 5.25/5.42 thf(fact_246_power__Suc,axiom,
% 5.25/5.42 ! [A: int,N: nat] :
% 5.25/5.42 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.25/5.42 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_Suc
% 5.25/5.42 thf(fact_247_left__right__inverse__power,axiom,
% 5.25/5.42 ! [X3: complex,Y: complex,N: nat] :
% 5.25/5.42 ( ( ( times_times_complex @ X3 @ Y )
% 5.25/5.42 = one_one_complex )
% 5.25/5.42 => ( ( times_times_complex @ ( power_power_complex @ X3 @ N ) @ ( power_power_complex @ Y @ N ) )
% 5.25/5.42 = one_one_complex ) ) ).
% 5.25/5.42
% 5.25/5.42 % left_right_inverse_power
% 5.25/5.42 thf(fact_248_left__right__inverse__power,axiom,
% 5.25/5.42 ! [X3: real,Y: real,N: nat] :
% 5.25/5.42 ( ( ( times_times_real @ X3 @ Y )
% 5.25/5.42 = one_one_real )
% 5.25/5.42 => ( ( times_times_real @ ( power_power_real @ X3 @ N ) @ ( power_power_real @ Y @ N ) )
% 5.25/5.42 = one_one_real ) ) ).
% 5.25/5.42
% 5.25/5.42 % left_right_inverse_power
% 5.25/5.42 thf(fact_249_left__right__inverse__power,axiom,
% 5.25/5.42 ! [X3: rat,Y: rat,N: nat] :
% 5.25/5.42 ( ( ( times_times_rat @ X3 @ Y )
% 5.25/5.42 = one_one_rat )
% 5.25/5.42 => ( ( times_times_rat @ ( power_power_rat @ X3 @ N ) @ ( power_power_rat @ Y @ N ) )
% 5.25/5.42 = one_one_rat ) ) ).
% 5.25/5.42
% 5.25/5.42 % left_right_inverse_power
% 5.25/5.42 thf(fact_250_left__right__inverse__power,axiom,
% 5.25/5.42 ! [X3: nat,Y: nat,N: nat] :
% 5.25/5.42 ( ( ( times_times_nat @ X3 @ Y )
% 5.25/5.42 = one_one_nat )
% 5.25/5.42 => ( ( times_times_nat @ ( power_power_nat @ X3 @ N ) @ ( power_power_nat @ Y @ N ) )
% 5.25/5.42 = one_one_nat ) ) ).
% 5.25/5.42
% 5.25/5.42 % left_right_inverse_power
% 5.25/5.42 thf(fact_251_left__right__inverse__power,axiom,
% 5.25/5.42 ! [X3: int,Y: int,N: nat] :
% 5.25/5.42 ( ( ( times_times_int @ X3 @ Y )
% 5.25/5.42 = one_one_int )
% 5.25/5.42 => ( ( times_times_int @ ( power_power_int @ X3 @ N ) @ ( power_power_int @ Y @ N ) )
% 5.25/5.42 = one_one_int ) ) ).
% 5.25/5.42
% 5.25/5.42 % left_right_inverse_power
% 5.25/5.42 thf(fact_252_Nat_OlessE,axiom,
% 5.25/5.42 ! [I2: nat,K: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I2 @ K )
% 5.25/5.42 => ( ( K
% 5.25/5.42 != ( suc @ I2 ) )
% 5.25/5.42 => ~ ! [J: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I2 @ J )
% 5.25/5.42 => ( K
% 5.25/5.42 != ( suc @ J ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % Nat.lessE
% 5.25/5.42 thf(fact_253_Suc__lessD,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 5.25/5.42 => ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_lessD
% 5.25/5.42 thf(fact_254_Suc__lessE,axiom,
% 5.25/5.42 ! [I2: nat,K: nat] :
% 5.25/5.42 ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 5.25/5.42 => ~ ! [J: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I2 @ J )
% 5.25/5.42 => ( K
% 5.25/5.42 != ( suc @ J ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_lessE
% 5.25/5.42 thf(fact_255_Suc__lessI,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ M @ N )
% 5.25/5.42 => ( ( ( suc @ M )
% 5.25/5.42 != N )
% 5.25/5.42 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_lessI
% 5.25/5.42 thf(fact_256_less__SucE,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.25/5.42 => ( ~ ( ord_less_nat @ M @ N )
% 5.25/5.42 => ( M = N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_SucE
% 5.25/5.42 thf(fact_257_less__SucI,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ M @ N )
% 5.25/5.42 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_SucI
% 5.25/5.42 thf(fact_258_Ex__less__Suc,axiom,
% 5.25/5.42 ! [N: nat,P: nat > $o] :
% 5.25/5.42 ( ( ? [I3: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 5.25/5.42 & ( P @ I3 ) ) )
% 5.25/5.42 = ( ( P @ N )
% 5.25/5.42 | ? [I3: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I3 @ N )
% 5.25/5.42 & ( P @ I3 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % Ex_less_Suc
% 5.25/5.42 thf(fact_259_less__Suc__eq,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.25/5.42 = ( ( ord_less_nat @ M @ N )
% 5.25/5.42 | ( M = N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_Suc_eq
% 5.25/5.42 thf(fact_260_not__less__eq,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ~ ( ord_less_nat @ M @ N ) )
% 5.25/5.42 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % not_less_eq
% 5.25/5.42 thf(fact_261_All__less__Suc,axiom,
% 5.25/5.42 ! [N: nat,P: nat > $o] :
% 5.25/5.42 ( ( ! [I3: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 5.25/5.42 => ( P @ I3 ) ) )
% 5.25/5.42 = ( ( P @ N )
% 5.25/5.42 & ! [I3: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I3 @ N )
% 5.25/5.42 => ( P @ I3 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % All_less_Suc
% 5.25/5.42 thf(fact_262_Suc__less__eq2,axiom,
% 5.25/5.42 ! [N: nat,M: nat] :
% 5.25/5.42 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.42 = ( ? [M3: nat] :
% 5.25/5.42 ( ( M
% 5.25/5.42 = ( suc @ M3 ) )
% 5.25/5.42 & ( ord_less_nat @ N @ M3 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_less_eq2
% 5.25/5.42 thf(fact_263_less__antisym,axiom,
% 5.25/5.42 ! [N: nat,M: nat] :
% 5.25/5.42 ( ~ ( ord_less_nat @ N @ M )
% 5.25/5.42 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.25/5.42 => ( M = N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_antisym
% 5.25/5.42 thf(fact_264_Suc__less__SucD,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.25/5.42 => ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_less_SucD
% 5.25/5.42 thf(fact_265_less__trans__Suc,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.42 => ( ( ord_less_nat @ J2 @ K )
% 5.25/5.42 => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_trans_Suc
% 5.25/5.42 thf(fact_266_less__Suc__induct,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,P: nat > nat > $o] :
% 5.25/5.42 ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.42 => ( ! [I4: nat] : ( P @ I4 @ ( suc @ I4 ) )
% 5.25/5.42 => ( ! [I4: nat,J: nat,K2: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I4 @ J )
% 5.25/5.42 => ( ( ord_less_nat @ J @ K2 )
% 5.25/5.42 => ( ( P @ I4 @ J )
% 5.25/5.42 => ( ( P @ J @ K2 )
% 5.25/5.42 => ( P @ I4 @ K2 ) ) ) ) )
% 5.25/5.42 => ( P @ I2 @ J2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_Suc_induct
% 5.25/5.42 thf(fact_267_strict__inc__induct,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,P: nat > $o] :
% 5.25/5.42 ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.42 => ( ! [I4: nat] :
% 5.25/5.42 ( ( J2
% 5.25/5.42 = ( suc @ I4 ) )
% 5.25/5.42 => ( P @ I4 ) )
% 5.25/5.42 => ( ! [I4: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I4 @ J2 )
% 5.25/5.42 => ( ( P @ ( suc @ I4 ) )
% 5.25/5.42 => ( P @ I4 ) ) )
% 5.25/5.42 => ( P @ I2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % strict_inc_induct
% 5.25/5.42 thf(fact_268_not__less__less__Suc__eq,axiom,
% 5.25/5.42 ! [N: nat,M: nat] :
% 5.25/5.42 ( ~ ( ord_less_nat @ N @ M )
% 5.25/5.42 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.25/5.42 = ( N = M ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % not_less_less_Suc_eq
% 5.25/5.42 thf(fact_269_Suc__leD,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.25/5.42 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_leD
% 5.25/5.42 thf(fact_270_le__SucE,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.42 => ( ~ ( ord_less_eq_nat @ M @ N )
% 5.25/5.42 => ( M
% 5.25/5.42 = ( suc @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_SucE
% 5.25/5.42 thf(fact_271_le__SucI,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.42 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_SucI
% 5.25/5.42 thf(fact_272_Suc__le__D,axiom,
% 5.25/5.42 ! [N: nat,M4: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( suc @ N ) @ M4 )
% 5.25/5.42 => ? [M5: nat] :
% 5.25/5.42 ( M4
% 5.25/5.42 = ( suc @ M5 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_le_D
% 5.25/5.42 thf(fact_273_le__Suc__eq,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.42 = ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.42 | ( M
% 5.25/5.42 = ( suc @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_Suc_eq
% 5.25/5.42 thf(fact_274_Suc__n__not__le__n,axiom,
% 5.25/5.42 ! [N: nat] :
% 5.25/5.42 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_n_not_le_n
% 5.25/5.42 thf(fact_275_not__less__eq__eq,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 5.25/5.42 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 5.25/5.42
% 5.25/5.42 % not_less_eq_eq
% 5.25/5.42 thf(fact_276_full__nat__induct,axiom,
% 5.25/5.42 ! [P: nat > $o,N: nat] :
% 5.25/5.42 ( ! [N3: nat] :
% 5.25/5.42 ( ! [M2: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N3 )
% 5.25/5.42 => ( P @ M2 ) )
% 5.25/5.42 => ( P @ N3 ) )
% 5.25/5.42 => ( P @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % full_nat_induct
% 5.25/5.42 thf(fact_277_nat__induct__at__least,axiom,
% 5.25/5.42 ! [M: nat,N: nat,P: nat > $o] :
% 5.25/5.42 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.42 => ( ( P @ M )
% 5.25/5.42 => ( ! [N3: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ M @ N3 )
% 5.25/5.42 => ( ( P @ N3 )
% 5.25/5.42 => ( P @ ( suc @ N3 ) ) ) )
% 5.25/5.42 => ( P @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % nat_induct_at_least
% 5.25/5.42 thf(fact_278_transitive__stepwise__le,axiom,
% 5.25/5.42 ! [M: nat,N: nat,R: nat > nat > $o] :
% 5.25/5.42 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.42 => ( ! [X5: nat] : ( R @ X5 @ X5 )
% 5.25/5.42 => ( ! [X5: nat,Y3: nat,Z2: nat] :
% 5.25/5.42 ( ( R @ X5 @ Y3 )
% 5.25/5.42 => ( ( R @ Y3 @ Z2 )
% 5.25/5.42 => ( R @ X5 @ Z2 ) ) )
% 5.25/5.42 => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 5.25/5.42 => ( R @ M @ N ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % transitive_stepwise_le
% 5.25/5.42 thf(fact_279_le__cube,axiom,
% 5.25/5.42 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_cube
% 5.25/5.42 thf(fact_280_le__square,axiom,
% 5.25/5.42 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_square
% 5.25/5.42 thf(fact_281_mult__le__mono,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,K: nat,L2: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.42 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.25/5.42 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J2 @ L2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_le_mono
% 5.25/5.42 thf(fact_282_mult__le__mono1,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.42 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J2 @ K ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_le_mono1
% 5.25/5.42 thf(fact_283_mult__le__mono2,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.42 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J2 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_le_mono2
% 5.25/5.42 thf(fact_284_nat__arith_Osuc1,axiom,
% 5.25/5.42 ! [A2: nat,K: nat,A: nat] :
% 5.25/5.42 ( ( A2
% 5.25/5.42 = ( plus_plus_nat @ K @ A ) )
% 5.25/5.42 => ( ( suc @ A2 )
% 5.25/5.42 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % nat_arith.suc1
% 5.25/5.42 thf(fact_285_add__Suc,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.25/5.42 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_Suc
% 5.25/5.42 thf(fact_286_add__Suc__shift,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.25/5.42 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_Suc_shift
% 5.25/5.42 thf(fact_287_add__mult__distrib,axiom,
% 5.25/5.42 ! [M: nat,N: nat,K: nat] :
% 5.25/5.42 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 5.25/5.42 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_mult_distrib
% 5.25/5.42 thf(fact_288_add__mult__distrib2,axiom,
% 5.25/5.42 ! [K: nat,M: nat,N: nat] :
% 5.25/5.42 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.42 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_mult_distrib2
% 5.25/5.42 thf(fact_289_div__mult2__eq,axiom,
% 5.25/5.42 ! [M: nat,N: nat,Q2: nat] :
% 5.25/5.42 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.25/5.42 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) ).
% 5.25/5.42
% 5.25/5.42 % div_mult2_eq
% 5.25/5.42 thf(fact_290_power__gt1,axiom,
% 5.25/5.42 ! [A: real,N: nat] :
% 5.25/5.42 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.42 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_gt1
% 5.25/5.42 thf(fact_291_power__gt1,axiom,
% 5.25/5.42 ! [A: rat,N: nat] :
% 5.25/5.42 ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.42 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_gt1
% 5.25/5.42 thf(fact_292_power__gt1,axiom,
% 5.25/5.42 ! [A: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.42 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_gt1
% 5.25/5.42 thf(fact_293_power__gt1,axiom,
% 5.25/5.42 ! [A: int,N: nat] :
% 5.25/5.42 ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.42 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_gt1
% 5.25/5.42 thf(fact_294_power__gt1__lemma,axiom,
% 5.25/5.42 ! [A: real,N: nat] :
% 5.25/5.42 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.42 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_gt1_lemma
% 5.25/5.42 thf(fact_295_power__gt1__lemma,axiom,
% 5.25/5.42 ! [A: rat,N: nat] :
% 5.25/5.42 ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.42 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_gt1_lemma
% 5.25/5.42 thf(fact_296_power__gt1__lemma,axiom,
% 5.25/5.42 ! [A: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.42 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_gt1_lemma
% 5.25/5.42 thf(fact_297_power__gt1__lemma,axiom,
% 5.25/5.42 ! [A: int,N: nat] :
% 5.25/5.42 ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.42 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_gt1_lemma
% 5.25/5.42 thf(fact_298_power__less__power__Suc,axiom,
% 5.25/5.42 ! [A: real,N: nat] :
% 5.25/5.42 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.42 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_less_power_Suc
% 5.25/5.42 thf(fact_299_power__less__power__Suc,axiom,
% 5.25/5.42 ! [A: rat,N: nat] :
% 5.25/5.42 ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.42 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_less_power_Suc
% 5.25/5.42 thf(fact_300_power__less__power__Suc,axiom,
% 5.25/5.42 ! [A: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.42 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_less_power_Suc
% 5.25/5.42 thf(fact_301_power__less__power__Suc,axiom,
% 5.25/5.42 ! [A: int,N: nat] :
% 5.25/5.42 ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.42 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_less_power_Suc
% 5.25/5.42 thf(fact_302_div__nat__eqI,axiom,
% 5.25/5.42 ! [N: nat,Q2: nat,M: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 5.25/5.42 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 5.25/5.42 => ( ( divide_divide_nat @ M @ N )
% 5.25/5.42 = Q2 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % div_nat_eqI
% 5.25/5.42 thf(fact_303_add__One__commute,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( plus_plus_num @ one @ N )
% 5.25/5.42 = ( plus_plus_num @ N @ one ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_One_commute
% 5.25/5.42 thf(fact_304_power__commutes,axiom,
% 5.25/5.42 ! [A: complex,N: nat] :
% 5.25/5.42 ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 5.25/5.42 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_commutes
% 5.25/5.42 thf(fact_305_power__commutes,axiom,
% 5.25/5.42 ! [A: real,N: nat] :
% 5.25/5.42 ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 5.25/5.42 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_commutes
% 5.25/5.42 thf(fact_306_power__commutes,axiom,
% 5.25/5.42 ! [A: rat,N: nat] :
% 5.25/5.42 ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 5.25/5.42 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_commutes
% 5.25/5.42 thf(fact_307_power__commutes,axiom,
% 5.25/5.42 ! [A: nat,N: nat] :
% 5.25/5.42 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 5.25/5.42 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_commutes
% 5.25/5.42 thf(fact_308_power__commutes,axiom,
% 5.25/5.42 ! [A: int,N: nat] :
% 5.25/5.42 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 5.25/5.42 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_commutes
% 5.25/5.42 thf(fact_309_power__mult__distrib,axiom,
% 5.25/5.42 ! [A: complex,B: complex,N: nat] :
% 5.25/5.42 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 5.25/5.42 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_mult_distrib
% 5.25/5.42 thf(fact_310_power__mult__distrib,axiom,
% 5.25/5.42 ! [A: real,B: real,N: nat] :
% 5.25/5.42 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 5.25/5.42 = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_mult_distrib
% 5.25/5.42 thf(fact_311_power__mult__distrib,axiom,
% 5.25/5.42 ! [A: rat,B: rat,N: nat] :
% 5.25/5.42 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 5.25/5.42 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_mult_distrib
% 5.25/5.42 thf(fact_312_power__mult__distrib,axiom,
% 5.25/5.42 ! [A: nat,B: nat,N: nat] :
% 5.25/5.42 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 5.25/5.42 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_mult_distrib
% 5.25/5.42 thf(fact_313_power__mult__distrib,axiom,
% 5.25/5.42 ! [A: int,B: int,N: nat] :
% 5.25/5.42 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 5.25/5.42 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_mult_distrib
% 5.25/5.42 thf(fact_314_power__commuting__commutes,axiom,
% 5.25/5.42 ! [X3: complex,Y: complex,N: nat] :
% 5.25/5.42 ( ( ( times_times_complex @ X3 @ Y )
% 5.25/5.42 = ( times_times_complex @ Y @ X3 ) )
% 5.25/5.42 => ( ( times_times_complex @ ( power_power_complex @ X3 @ N ) @ Y )
% 5.25/5.42 = ( times_times_complex @ Y @ ( power_power_complex @ X3 @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_commuting_commutes
% 5.25/5.42 thf(fact_315_power__commuting__commutes,axiom,
% 5.25/5.42 ! [X3: real,Y: real,N: nat] :
% 5.25/5.42 ( ( ( times_times_real @ X3 @ Y )
% 5.25/5.42 = ( times_times_real @ Y @ X3 ) )
% 5.25/5.42 => ( ( times_times_real @ ( power_power_real @ X3 @ N ) @ Y )
% 5.25/5.42 = ( times_times_real @ Y @ ( power_power_real @ X3 @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_commuting_commutes
% 5.25/5.42 thf(fact_316_power__commuting__commutes,axiom,
% 5.25/5.42 ! [X3: rat,Y: rat,N: nat] :
% 5.25/5.42 ( ( ( times_times_rat @ X3 @ Y )
% 5.25/5.42 = ( times_times_rat @ Y @ X3 ) )
% 5.25/5.42 => ( ( times_times_rat @ ( power_power_rat @ X3 @ N ) @ Y )
% 5.25/5.42 = ( times_times_rat @ Y @ ( power_power_rat @ X3 @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_commuting_commutes
% 5.25/5.42 thf(fact_317_power__commuting__commutes,axiom,
% 5.25/5.42 ! [X3: nat,Y: nat,N: nat] :
% 5.25/5.42 ( ( ( times_times_nat @ X3 @ Y )
% 5.25/5.42 = ( times_times_nat @ Y @ X3 ) )
% 5.25/5.42 => ( ( times_times_nat @ ( power_power_nat @ X3 @ N ) @ Y )
% 5.25/5.42 = ( times_times_nat @ Y @ ( power_power_nat @ X3 @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_commuting_commutes
% 5.25/5.42 thf(fact_318_power__commuting__commutes,axiom,
% 5.25/5.42 ! [X3: int,Y: int,N: nat] :
% 5.25/5.42 ( ( ( times_times_int @ X3 @ Y )
% 5.25/5.42 = ( times_times_int @ Y @ X3 ) )
% 5.25/5.42 => ( ( times_times_int @ ( power_power_int @ X3 @ N ) @ Y )
% 5.25/5.42 = ( times_times_int @ Y @ ( power_power_int @ X3 @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_commuting_commutes
% 5.25/5.42 thf(fact_319_power__mult,axiom,
% 5.25/5.42 ! [A: nat,M: nat,N: nat] :
% 5.25/5.42 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 5.25/5.42 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_mult
% 5.25/5.42 thf(fact_320_power__mult,axiom,
% 5.25/5.42 ! [A: real,M: nat,N: nat] :
% 5.25/5.42 ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 5.25/5.42 = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_mult
% 5.25/5.42 thf(fact_321_power__mult,axiom,
% 5.25/5.42 ! [A: int,M: nat,N: nat] :
% 5.25/5.42 ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 5.25/5.42 = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_mult
% 5.25/5.42 thf(fact_322_power__mult,axiom,
% 5.25/5.42 ! [A: complex,M: nat,N: nat] :
% 5.25/5.42 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 5.25/5.42 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_mult
% 5.25/5.42 thf(fact_323_le__numeral__extra_I4_J,axiom,
% 5.25/5.42 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.25/5.42
% 5.25/5.42 % le_numeral_extra(4)
% 5.25/5.42 thf(fact_324_le__numeral__extra_I4_J,axiom,
% 5.25/5.42 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.25/5.42
% 5.25/5.42 % le_numeral_extra(4)
% 5.25/5.42 thf(fact_325_le__numeral__extra_I4_J,axiom,
% 5.25/5.42 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.25/5.42
% 5.25/5.42 % le_numeral_extra(4)
% 5.25/5.42 thf(fact_326_le__numeral__extra_I4_J,axiom,
% 5.25/5.42 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.25/5.42
% 5.25/5.42 % le_numeral_extra(4)
% 5.25/5.42 thf(fact_327_less__numeral__extra_I4_J,axiom,
% 5.25/5.42 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.25/5.42
% 5.25/5.42 % less_numeral_extra(4)
% 5.25/5.42 thf(fact_328_less__numeral__extra_I4_J,axiom,
% 5.25/5.42 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.25/5.42
% 5.25/5.42 % less_numeral_extra(4)
% 5.25/5.42 thf(fact_329_less__numeral__extra_I4_J,axiom,
% 5.25/5.42 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.25/5.42
% 5.25/5.42 % less_numeral_extra(4)
% 5.25/5.42 thf(fact_330_less__numeral__extra_I4_J,axiom,
% 5.25/5.42 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.25/5.42
% 5.25/5.42 % less_numeral_extra(4)
% 5.25/5.42 thf(fact_331_left__add__mult__distrib,axiom,
% 5.25/5.42 ! [I2: nat,U: nat,J2: nat,K: nat] :
% 5.25/5.42 ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ K ) )
% 5.25/5.42 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J2 ) @ U ) @ K ) ) ).
% 5.25/5.42
% 5.25/5.42 % left_add_mult_distrib
% 5.25/5.42 thf(fact_332_power__odd__eq,axiom,
% 5.25/5.42 ! [A: complex,N: nat] :
% 5.25/5.42 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.42 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_odd_eq
% 5.25/5.42 thf(fact_333_power__odd__eq,axiom,
% 5.25/5.42 ! [A: real,N: nat] :
% 5.25/5.42 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.42 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_odd_eq
% 5.25/5.42 thf(fact_334_power__odd__eq,axiom,
% 5.25/5.42 ! [A: rat,N: nat] :
% 5.25/5.42 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.42 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_odd_eq
% 5.25/5.42 thf(fact_335_power__odd__eq,axiom,
% 5.25/5.42 ! [A: nat,N: nat] :
% 5.25/5.42 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.42 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_odd_eq
% 5.25/5.42 thf(fact_336_power__odd__eq,axiom,
% 5.25/5.42 ! [A: int,N: nat] :
% 5.25/5.42 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.42 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_odd_eq
% 5.25/5.42 thf(fact_337_lift__Suc__mono__less,axiom,
% 5.25/5.42 ! [F: nat > real,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_real @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_less
% 5.25/5.42 thf(fact_338_lift__Suc__mono__less,axiom,
% 5.25/5.42 ! [F: nat > rat,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_rat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_less
% 5.25/5.42 thf(fact_339_lift__Suc__mono__less,axiom,
% 5.25/5.42 ! [F: nat > num,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_num @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_less
% 5.25/5.42 thf(fact_340_lift__Suc__mono__less,axiom,
% 5.25/5.42 ! [F: nat > nat,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_less
% 5.25/5.42 thf(fact_341_lift__Suc__mono__less,axiom,
% 5.25/5.42 ! [F: nat > int,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_int @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_less
% 5.25/5.42 thf(fact_342_lift__Suc__mono__less__iff,axiom,
% 5.25/5.42 ! [F: nat > real,N: nat,M: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 5.25/5.42 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_less_iff
% 5.25/5.42 thf(fact_343_lift__Suc__mono__less__iff,axiom,
% 5.25/5.42 ! [F: nat > rat,N: nat,M: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 5.25/5.42 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_less_iff
% 5.25/5.42 thf(fact_344_lift__Suc__mono__less__iff,axiom,
% 5.25/5.42 ! [F: nat > num,N: nat,M: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 5.25/5.42 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_less_iff
% 5.25/5.42 thf(fact_345_lift__Suc__mono__less__iff,axiom,
% 5.25/5.42 ! [F: nat > nat,N: nat,M: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 5.25/5.42 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_less_iff
% 5.25/5.42 thf(fact_346_lift__Suc__mono__less__iff,axiom,
% 5.25/5.42 ! [F: nat > int,N: nat,M: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 5.25/5.42 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_less_iff
% 5.25/5.42 thf(fact_347_lift__Suc__mono__le,axiom,
% 5.25/5.42 ! [F: nat > set_int,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_eq_set_int @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_le
% 5.25/5.42 thf(fact_348_lift__Suc__mono__le,axiom,
% 5.25/5.42 ! [F: nat > rat,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_le
% 5.25/5.42 thf(fact_349_lift__Suc__mono__le,axiom,
% 5.25/5.42 ! [F: nat > num,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_le
% 5.25/5.42 thf(fact_350_lift__Suc__mono__le,axiom,
% 5.25/5.42 ! [F: nat > nat,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_le
% 5.25/5.42 thf(fact_351_lift__Suc__mono__le,axiom,
% 5.25/5.42 ! [F: nat > int,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.42 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_mono_le
% 5.25/5.42 thf(fact_352_lift__Suc__antimono__le,axiom,
% 5.25/5.42 ! [F: nat > set_int,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.25/5.42 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_eq_set_int @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_antimono_le
% 5.25/5.42 thf(fact_353_lift__Suc__antimono__le,axiom,
% 5.25/5.42 ! [F: nat > rat,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.25/5.42 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_eq_rat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_antimono_le
% 5.25/5.42 thf(fact_354_lift__Suc__antimono__le,axiom,
% 5.25/5.42 ! [F: nat > num,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.25/5.42 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_eq_num @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_antimono_le
% 5.25/5.42 thf(fact_355_lift__Suc__antimono__le,axiom,
% 5.25/5.42 ! [F: nat > nat,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.25/5.42 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_antimono_le
% 5.25/5.42 thf(fact_356_lift__Suc__antimono__le,axiom,
% 5.25/5.42 ! [F: nat > int,N: nat,N4: nat] :
% 5.25/5.42 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.25/5.42 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.25/5.42 => ( ord_less_eq_int @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % lift_Suc_antimono_le
% 5.25/5.42 thf(fact_357_Suc__leI,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ M @ N )
% 5.25/5.42 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_leI
% 5.25/5.42 thf(fact_358_Suc__le__eq,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.25/5.42 = ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_le_eq
% 5.25/5.42 thf(fact_359_dec__induct,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,P: nat > $o] :
% 5.25/5.42 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.42 => ( ( P @ I2 )
% 5.25/5.42 => ( ! [N3: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ I2 @ N3 )
% 5.25/5.42 => ( ( ord_less_nat @ N3 @ J2 )
% 5.25/5.42 => ( ( P @ N3 )
% 5.25/5.42 => ( P @ ( suc @ N3 ) ) ) ) )
% 5.25/5.42 => ( P @ J2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % dec_induct
% 5.25/5.42 thf(fact_360_inc__induct,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,P: nat > $o] :
% 5.25/5.42 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.42 => ( ( P @ J2 )
% 5.25/5.42 => ( ! [N3: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ I2 @ N3 )
% 5.25/5.42 => ( ( ord_less_nat @ N3 @ J2 )
% 5.25/5.42 => ( ( P @ ( suc @ N3 ) )
% 5.25/5.42 => ( P @ N3 ) ) ) )
% 5.25/5.42 => ( P @ I2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % inc_induct
% 5.25/5.42 thf(fact_361_Suc__le__lessD,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.25/5.42 => ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_le_lessD
% 5.25/5.42 thf(fact_362_le__less__Suc__eq,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.42 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.25/5.42 = ( N = M ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_less_Suc_eq
% 5.25/5.42 thf(fact_363_less__Suc__eq__le,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.25/5.42 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_Suc_eq_le
% 5.25/5.42 thf(fact_364_less__eq__Suc__le,axiom,
% 5.25/5.42 ( ord_less_nat
% 5.25/5.42 = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_eq_Suc_le
% 5.25/5.42 thf(fact_365_le__imp__less__Suc,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.42 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_imp_less_Suc
% 5.25/5.42 thf(fact_366_less__imp__Suc__add,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ M @ N )
% 5.25/5.42 => ? [K2: nat] :
% 5.25/5.42 ( N
% 5.25/5.42 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_imp_Suc_add
% 5.25/5.42 thf(fact_367_less__iff__Suc__add,axiom,
% 5.25/5.42 ( ord_less_nat
% 5.25/5.42 = ( ^ [M6: nat,N2: nat] :
% 5.25/5.42 ? [K3: nat] :
% 5.25/5.42 ( N2
% 5.25/5.42 = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_iff_Suc_add
% 5.25/5.42 thf(fact_368_less__add__Suc2,axiom,
% 5.25/5.42 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M @ I2 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_add_Suc2
% 5.25/5.42 thf(fact_369_less__add__Suc1,axiom,
% 5.25/5.42 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_add_Suc1
% 5.25/5.42 thf(fact_370_less__natE,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ M @ N )
% 5.25/5.42 => ~ ! [Q3: nat] :
% 5.25/5.42 ( N
% 5.25/5.42 != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_natE
% 5.25/5.42 thf(fact_371_Suc__div__le__mono,axiom,
% 5.25/5.42 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_div_le_mono
% 5.25/5.42 thf(fact_372_less__mult__imp__div__less,axiom,
% 5.25/5.42 ! [M: nat,I2: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N ) )
% 5.25/5.42 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I2 ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_mult_imp_div_less
% 5.25/5.42 thf(fact_373_times__div__less__eq__dividend,axiom,
% 5.25/5.42 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 5.25/5.42
% 5.25/5.42 % times_div_less_eq_dividend
% 5.25/5.42 thf(fact_374_div__times__less__eq__dividend,axiom,
% 5.25/5.42 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 5.25/5.42
% 5.25/5.42 % div_times_less_eq_dividend
% 5.25/5.42 thf(fact_375_Suc__nat__number__of__add,axiom,
% 5.25/5.42 ! [V: num,N: nat] :
% 5.25/5.42 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 5.25/5.42 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_nat_number_of_add
% 5.25/5.42 thf(fact_376_mult__numeral__1,axiom,
% 5.25/5.42 ! [A: complex] :
% 5.25/5.42 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_numeral_1
% 5.25/5.42 thf(fact_377_mult__numeral__1,axiom,
% 5.25/5.42 ! [A: real] :
% 5.25/5.42 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_numeral_1
% 5.25/5.42 thf(fact_378_mult__numeral__1,axiom,
% 5.25/5.42 ! [A: rat] :
% 5.25/5.42 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_numeral_1
% 5.25/5.42 thf(fact_379_mult__numeral__1,axiom,
% 5.25/5.42 ! [A: nat] :
% 5.25/5.42 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_numeral_1
% 5.25/5.42 thf(fact_380_mult__numeral__1,axiom,
% 5.25/5.42 ! [A: int] :
% 5.25/5.42 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_numeral_1
% 5.25/5.42 thf(fact_381_mult__numeral__1__right,axiom,
% 5.25/5.42 ! [A: complex] :
% 5.25/5.42 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_numeral_1_right
% 5.25/5.42 thf(fact_382_mult__numeral__1__right,axiom,
% 5.25/5.42 ! [A: real] :
% 5.25/5.42 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_numeral_1_right
% 5.25/5.42 thf(fact_383_mult__numeral__1__right,axiom,
% 5.25/5.42 ! [A: rat] :
% 5.25/5.42 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_numeral_1_right
% 5.25/5.42 thf(fact_384_mult__numeral__1__right,axiom,
% 5.25/5.42 ! [A: nat] :
% 5.25/5.42 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_numeral_1_right
% 5.25/5.42 thf(fact_385_mult__numeral__1__right,axiom,
% 5.25/5.42 ! [A: int] :
% 5.25/5.42 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_numeral_1_right
% 5.25/5.42 thf(fact_386_power__add,axiom,
% 5.25/5.42 ! [A: complex,M: nat,N: nat] :
% 5.25/5.42 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.42 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add
% 5.25/5.42 thf(fact_387_power__add,axiom,
% 5.25/5.42 ! [A: real,M: nat,N: nat] :
% 5.25/5.42 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.42 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add
% 5.25/5.42 thf(fact_388_power__add,axiom,
% 5.25/5.42 ! [A: rat,M: nat,N: nat] :
% 5.25/5.42 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.42 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add
% 5.25/5.42 thf(fact_389_power__add,axiom,
% 5.25/5.42 ! [A: nat,M: nat,N: nat] :
% 5.25/5.42 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.42 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add
% 5.25/5.42 thf(fact_390_power__add,axiom,
% 5.25/5.42 ! [A: int,M: nat,N: nat] :
% 5.25/5.42 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.42 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_add
% 5.25/5.42 thf(fact_391_one__le__numeral,axiom,
% 5.25/5.42 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_le_numeral
% 5.25/5.42 thf(fact_392_one__le__numeral,axiom,
% 5.25/5.42 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_le_numeral
% 5.25/5.42 thf(fact_393_one__le__numeral,axiom,
% 5.25/5.42 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_le_numeral
% 5.25/5.42 thf(fact_394_one__le__numeral,axiom,
% 5.25/5.42 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_le_numeral
% 5.25/5.42 thf(fact_395_not__numeral__less__one,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 5.25/5.42
% 5.25/5.42 % not_numeral_less_one
% 5.25/5.42 thf(fact_396_not__numeral__less__one,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 5.25/5.42
% 5.25/5.42 % not_numeral_less_one
% 5.25/5.42 thf(fact_397_not__numeral__less__one,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 5.25/5.42
% 5.25/5.42 % not_numeral_less_one
% 5.25/5.42 thf(fact_398_not__numeral__less__one,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 5.25/5.42
% 5.25/5.42 % not_numeral_less_one
% 5.25/5.42 thf(fact_399_one__plus__numeral__commute,axiom,
% 5.25/5.42 ! [X3: num] :
% 5.25/5.42 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X3 ) )
% 5.25/5.42 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X3 ) @ one_one_complex ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_plus_numeral_commute
% 5.25/5.42 thf(fact_400_one__plus__numeral__commute,axiom,
% 5.25/5.42 ! [X3: num] :
% 5.25/5.42 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X3 ) )
% 5.25/5.42 = ( plus_plus_real @ ( numeral_numeral_real @ X3 ) @ one_one_real ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_plus_numeral_commute
% 5.25/5.42 thf(fact_401_one__plus__numeral__commute,axiom,
% 5.25/5.42 ! [X3: num] :
% 5.25/5.42 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X3 ) )
% 5.25/5.42 = ( plus_plus_rat @ ( numeral_numeral_rat @ X3 ) @ one_one_rat ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_plus_numeral_commute
% 5.25/5.42 thf(fact_402_one__plus__numeral__commute,axiom,
% 5.25/5.42 ! [X3: num] :
% 5.25/5.42 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X3 ) )
% 5.25/5.42 = ( plus_plus_nat @ ( numeral_numeral_nat @ X3 ) @ one_one_nat ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_plus_numeral_commute
% 5.25/5.42 thf(fact_403_one__plus__numeral__commute,axiom,
% 5.25/5.42 ! [X3: num] :
% 5.25/5.42 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X3 ) )
% 5.25/5.42 = ( plus_plus_int @ ( numeral_numeral_int @ X3 ) @ one_one_int ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_plus_numeral_commute
% 5.25/5.42 thf(fact_404_numeral__One,axiom,
% 5.25/5.42 ( ( numera6690914467698888265omplex @ one )
% 5.25/5.42 = one_one_complex ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_One
% 5.25/5.42 thf(fact_405_numeral__One,axiom,
% 5.25/5.42 ( ( numeral_numeral_real @ one )
% 5.25/5.42 = one_one_real ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_One
% 5.25/5.42 thf(fact_406_numeral__One,axiom,
% 5.25/5.42 ( ( numeral_numeral_rat @ one )
% 5.25/5.42 = one_one_rat ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_One
% 5.25/5.42 thf(fact_407_numeral__One,axiom,
% 5.25/5.42 ( ( numeral_numeral_nat @ one )
% 5.25/5.42 = one_one_nat ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_One
% 5.25/5.42 thf(fact_408_numeral__One,axiom,
% 5.25/5.42 ( ( numeral_numeral_int @ one )
% 5.25/5.42 = one_one_int ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_One
% 5.25/5.42 thf(fact_409_one__le__power,axiom,
% 5.25/5.42 ! [A: real,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.25/5.42 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_le_power
% 5.25/5.42 thf(fact_410_one__le__power,axiom,
% 5.25/5.42 ! [A: rat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.25/5.42 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_le_power
% 5.25/5.42 thf(fact_411_one__le__power,axiom,
% 5.25/5.42 ! [A: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.25/5.42 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_le_power
% 5.25/5.42 thf(fact_412_one__le__power,axiom,
% 5.25/5.42 ! [A: int,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.25/5.42 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_le_power
% 5.25/5.42 thf(fact_413_power__one__over,axiom,
% 5.25/5.42 ! [A: complex,N: nat] :
% 5.25/5.42 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 5.25/5.42 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_one_over
% 5.25/5.42 thf(fact_414_power__one__over,axiom,
% 5.25/5.42 ! [A: real,N: nat] :
% 5.25/5.42 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 5.25/5.42 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_one_over
% 5.25/5.42 thf(fact_415_power__one__over,axiom,
% 5.25/5.42 ! [A: rat,N: nat] :
% 5.25/5.42 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 5.25/5.42 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_one_over
% 5.25/5.42 thf(fact_416_numerals_I1_J,axiom,
% 5.25/5.42 ( ( numeral_numeral_nat @ one )
% 5.25/5.42 = one_one_nat ) ).
% 5.25/5.42
% 5.25/5.42 % numerals(1)
% 5.25/5.42 thf(fact_417_power__less__imp__less__exp,axiom,
% 5.25/5.42 ! [A: real,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.42 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.25/5.42 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_less_imp_less_exp
% 5.25/5.42 thf(fact_418_power__less__imp__less__exp,axiom,
% 5.25/5.42 ! [A: rat,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.42 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.25/5.42 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_less_imp_less_exp
% 5.25/5.42 thf(fact_419_power__less__imp__less__exp,axiom,
% 5.25/5.42 ! [A: nat,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.42 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.25/5.42 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_less_imp_less_exp
% 5.25/5.42 thf(fact_420_power__less__imp__less__exp,axiom,
% 5.25/5.42 ! [A: int,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.42 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.25/5.42 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_less_imp_less_exp
% 5.25/5.42 thf(fact_421_power__strict__increasing,axiom,
% 5.25/5.42 ! [N: nat,N5: nat,A: real] :
% 5.25/5.42 ( ( ord_less_nat @ N @ N5 )
% 5.25/5.42 => ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.42 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_strict_increasing
% 5.25/5.42 thf(fact_422_power__strict__increasing,axiom,
% 5.25/5.42 ! [N: nat,N5: nat,A: rat] :
% 5.25/5.42 ( ( ord_less_nat @ N @ N5 )
% 5.25/5.42 => ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.42 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_strict_increasing
% 5.25/5.42 thf(fact_423_power__strict__increasing,axiom,
% 5.25/5.42 ! [N: nat,N5: nat,A: nat] :
% 5.25/5.42 ( ( ord_less_nat @ N @ N5 )
% 5.25/5.42 => ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.42 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_strict_increasing
% 5.25/5.42 thf(fact_424_power__strict__increasing,axiom,
% 5.25/5.42 ! [N: nat,N5: nat,A: int] :
% 5.25/5.42 ( ( ord_less_nat @ N @ N5 )
% 5.25/5.42 => ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.42 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_strict_increasing
% 5.25/5.42 thf(fact_425_power__increasing,axiom,
% 5.25/5.42 ! [N: nat,N5: nat,A: real] :
% 5.25/5.42 ( ( ord_less_eq_nat @ N @ N5 )
% 5.25/5.42 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.25/5.42 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_increasing
% 5.25/5.42 thf(fact_426_power__increasing,axiom,
% 5.25/5.42 ! [N: nat,N5: nat,A: rat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ N @ N5 )
% 5.25/5.42 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.25/5.42 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_increasing
% 5.25/5.42 thf(fact_427_power__increasing,axiom,
% 5.25/5.42 ! [N: nat,N5: nat,A: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ N @ N5 )
% 5.25/5.42 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.25/5.42 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_increasing
% 5.25/5.42 thf(fact_428_power__increasing,axiom,
% 5.25/5.42 ! [N: nat,N5: nat,A: int] :
% 5.25/5.42 ( ( ord_less_eq_nat @ N @ N5 )
% 5.25/5.42 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.25/5.42 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_increasing
% 5.25/5.42 thf(fact_429_nat__neq__iff,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( M != N )
% 5.25/5.42 = ( ( ord_less_nat @ M @ N )
% 5.25/5.42 | ( ord_less_nat @ N @ M ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % nat_neq_iff
% 5.25/5.42 thf(fact_430_less__not__refl,axiom,
% 5.25/5.42 ! [N: nat] :
% 5.25/5.42 ~ ( ord_less_nat @ N @ N ) ).
% 5.25/5.42
% 5.25/5.42 % less_not_refl
% 5.25/5.42 thf(fact_431_less__not__refl2,axiom,
% 5.25/5.42 ! [N: nat,M: nat] :
% 5.25/5.42 ( ( ord_less_nat @ N @ M )
% 5.25/5.42 => ( M != N ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_not_refl2
% 5.25/5.42 thf(fact_432_less__not__refl3,axiom,
% 5.25/5.42 ! [S: nat,T: nat] :
% 5.25/5.42 ( ( ord_less_nat @ S @ T )
% 5.25/5.42 => ( S != T ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_not_refl3
% 5.25/5.42 thf(fact_433_less__irrefl__nat,axiom,
% 5.25/5.42 ! [N: nat] :
% 5.25/5.42 ~ ( ord_less_nat @ N @ N ) ).
% 5.25/5.42
% 5.25/5.42 % less_irrefl_nat
% 5.25/5.42 thf(fact_434_nat__less__induct,axiom,
% 5.25/5.42 ! [P: nat > $o,N: nat] :
% 5.25/5.42 ( ! [N3: nat] :
% 5.25/5.42 ( ! [M2: nat] :
% 5.25/5.42 ( ( ord_less_nat @ M2 @ N3 )
% 5.25/5.42 => ( P @ M2 ) )
% 5.25/5.42 => ( P @ N3 ) )
% 5.25/5.42 => ( P @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % nat_less_induct
% 5.25/5.42 thf(fact_435_infinite__descent,axiom,
% 5.25/5.42 ! [P: nat > $o,N: nat] :
% 5.25/5.42 ( ! [N3: nat] :
% 5.25/5.42 ( ~ ( P @ N3 )
% 5.25/5.42 => ? [M2: nat] :
% 5.25/5.42 ( ( ord_less_nat @ M2 @ N3 )
% 5.25/5.42 & ~ ( P @ M2 ) ) )
% 5.25/5.42 => ( P @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % infinite_descent
% 5.25/5.42 thf(fact_436_linorder__neqE__nat,axiom,
% 5.25/5.42 ! [X3: nat,Y: nat] :
% 5.25/5.42 ( ( X3 != Y )
% 5.25/5.42 => ( ~ ( ord_less_nat @ X3 @ Y )
% 5.25/5.42 => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % linorder_neqE_nat
% 5.25/5.42 thf(fact_437_le__refl,axiom,
% 5.25/5.42 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 5.25/5.42
% 5.25/5.42 % le_refl
% 5.25/5.42 thf(fact_438_le__trans,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.42 => ( ( ord_less_eq_nat @ J2 @ K )
% 5.25/5.42 => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_trans
% 5.25/5.42 thf(fact_439_eq__imp__le,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( M = N )
% 5.25/5.42 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % eq_imp_le
% 5.25/5.42 thf(fact_440_le__antisym,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.42 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.42 => ( M = N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_antisym
% 5.25/5.42 thf(fact_441_nat__le__linear,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.42 | ( ord_less_eq_nat @ N @ M ) ) ).
% 5.25/5.42
% 5.25/5.42 % nat_le_linear
% 5.25/5.42 thf(fact_442_Nat_Oex__has__greatest__nat,axiom,
% 5.25/5.42 ! [P: nat > $o,K: nat,B: nat] :
% 5.25/5.42 ( ( P @ K )
% 5.25/5.42 => ( ! [Y3: nat] :
% 5.25/5.42 ( ( P @ Y3 )
% 5.25/5.42 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.25/5.42 => ? [X5: nat] :
% 5.25/5.42 ( ( P @ X5 )
% 5.25/5.42 & ! [Y4: nat] :
% 5.25/5.42 ( ( P @ Y4 )
% 5.25/5.42 => ( ord_less_eq_nat @ Y4 @ X5 ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % Nat.ex_has_greatest_nat
% 5.25/5.42 thf(fact_443_size__neq__size__imp__neq,axiom,
% 5.25/5.42 ! [X3: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 5.25/5.42 ( ( ( size_s6755466524823107622T_VEBT @ X3 )
% 5.25/5.42 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 5.25/5.42 => ( X3 != Y ) ) ).
% 5.25/5.42
% 5.25/5.42 % size_neq_size_imp_neq
% 5.25/5.42 thf(fact_444_size__neq__size__imp__neq,axiom,
% 5.25/5.42 ! [X3: list_o,Y: list_o] :
% 5.25/5.42 ( ( ( size_size_list_o @ X3 )
% 5.25/5.42 != ( size_size_list_o @ Y ) )
% 5.25/5.42 => ( X3 != Y ) ) ).
% 5.25/5.42
% 5.25/5.42 % size_neq_size_imp_neq
% 5.25/5.42 thf(fact_445_size__neq__size__imp__neq,axiom,
% 5.25/5.42 ! [X3: list_nat,Y: list_nat] :
% 5.25/5.42 ( ( ( size_size_list_nat @ X3 )
% 5.25/5.42 != ( size_size_list_nat @ Y ) )
% 5.25/5.42 => ( X3 != Y ) ) ).
% 5.25/5.42
% 5.25/5.42 % size_neq_size_imp_neq
% 5.25/5.42 thf(fact_446_size__neq__size__imp__neq,axiom,
% 5.25/5.42 ! [X3: list_int,Y: list_int] :
% 5.25/5.42 ( ( ( size_size_list_int @ X3 )
% 5.25/5.42 != ( size_size_list_int @ Y ) )
% 5.25/5.42 => ( X3 != Y ) ) ).
% 5.25/5.42
% 5.25/5.42 % size_neq_size_imp_neq
% 5.25/5.42 thf(fact_447_size__neq__size__imp__neq,axiom,
% 5.25/5.42 ! [X3: num,Y: num] :
% 5.25/5.42 ( ( ( size_size_num @ X3 )
% 5.25/5.42 != ( size_size_num @ Y ) )
% 5.25/5.42 => ( X3 != Y ) ) ).
% 5.25/5.42
% 5.25/5.42 % size_neq_size_imp_neq
% 5.25/5.42 thf(fact_448_mult__2,axiom,
% 5.25/5.42 ! [Z: complex] :
% 5.25/5.42 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 5.25/5.42 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_2
% 5.25/5.42 thf(fact_449_mult__2,axiom,
% 5.25/5.42 ! [Z: real] :
% 5.25/5.42 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 5.25/5.42 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_2
% 5.25/5.42 thf(fact_450_mult__2,axiom,
% 5.25/5.42 ! [Z: rat] :
% 5.25/5.42 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 5.25/5.42 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_2
% 5.25/5.42 thf(fact_451_mult__2,axiom,
% 5.25/5.42 ! [Z: nat] :
% 5.25/5.42 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 5.25/5.42 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_2
% 5.25/5.42 thf(fact_452_mult__2,axiom,
% 5.25/5.42 ! [Z: int] :
% 5.25/5.42 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 5.25/5.42 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_2
% 5.25/5.42 thf(fact_453_mult__2__right,axiom,
% 5.25/5.42 ! [Z: complex] :
% 5.25/5.42 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_2_right
% 5.25/5.42 thf(fact_454_mult__2__right,axiom,
% 5.25/5.42 ! [Z: real] :
% 5.25/5.42 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_2_right
% 5.25/5.42 thf(fact_455_mult__2__right,axiom,
% 5.25/5.42 ! [Z: rat] :
% 5.25/5.42 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_2_right
% 5.25/5.42 thf(fact_456_mult__2__right,axiom,
% 5.25/5.42 ! [Z: nat] :
% 5.25/5.42 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_2_right
% 5.25/5.42 thf(fact_457_mult__2__right,axiom,
% 5.25/5.42 ! [Z: int] :
% 5.25/5.42 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult_2_right
% 5.25/5.42 thf(fact_458_left__add__twice,axiom,
% 5.25/5.42 ! [A: complex,B: complex] :
% 5.25/5.42 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.25/5.42 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % left_add_twice
% 5.25/5.42 thf(fact_459_left__add__twice,axiom,
% 5.25/5.42 ! [A: real,B: real] :
% 5.25/5.42 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.25/5.42 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % left_add_twice
% 5.25/5.42 thf(fact_460_left__add__twice,axiom,
% 5.25/5.42 ! [A: rat,B: rat] :
% 5.25/5.42 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.25/5.42 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % left_add_twice
% 5.25/5.42 thf(fact_461_left__add__twice,axiom,
% 5.25/5.42 ! [A: nat,B: nat] :
% 5.25/5.42 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.25/5.42 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % left_add_twice
% 5.25/5.42 thf(fact_462_left__add__twice,axiom,
% 5.25/5.42 ! [A: int,B: int] :
% 5.25/5.42 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.25/5.42 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % left_add_twice
% 5.25/5.42 thf(fact_463_power4__eq__xxxx,axiom,
% 5.25/5.42 ! [X3: complex] :
% 5.25/5.42 ( ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.25/5.42 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 5.25/5.42
% 5.25/5.42 % power4_eq_xxxx
% 5.25/5.42 thf(fact_464_power4__eq__xxxx,axiom,
% 5.25/5.42 ! [X3: real] :
% 5.25/5.42 ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.25/5.42 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 5.25/5.42
% 5.25/5.42 % power4_eq_xxxx
% 5.25/5.42 thf(fact_465_power4__eq__xxxx,axiom,
% 5.25/5.42 ! [X3: rat] :
% 5.25/5.42 ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.25/5.42 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 5.25/5.42
% 5.25/5.42 % power4_eq_xxxx
% 5.25/5.42 thf(fact_466_power4__eq__xxxx,axiom,
% 5.25/5.42 ! [X3: nat] :
% 5.25/5.42 ( ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.25/5.42 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 5.25/5.42
% 5.25/5.42 % power4_eq_xxxx
% 5.25/5.42 thf(fact_467_power4__eq__xxxx,axiom,
% 5.25/5.42 ! [X3: int] :
% 5.25/5.42 ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.25/5.42 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X3 @ X3 ) @ X3 ) @ X3 ) ) ).
% 5.25/5.42
% 5.25/5.42 % power4_eq_xxxx
% 5.25/5.42 thf(fact_468_power2__eq__square,axiom,
% 5.25/5.42 ! [A: complex] :
% 5.25/5.42 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( times_times_complex @ A @ A ) ) ).
% 5.25/5.42
% 5.25/5.42 % power2_eq_square
% 5.25/5.42 thf(fact_469_power2__eq__square,axiom,
% 5.25/5.42 ! [A: real] :
% 5.25/5.42 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( times_times_real @ A @ A ) ) ).
% 5.25/5.42
% 5.25/5.42 % power2_eq_square
% 5.25/5.42 thf(fact_470_power2__eq__square,axiom,
% 5.25/5.42 ! [A: rat] :
% 5.25/5.42 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( times_times_rat @ A @ A ) ) ).
% 5.25/5.42
% 5.25/5.42 % power2_eq_square
% 5.25/5.42 thf(fact_471_power2__eq__square,axiom,
% 5.25/5.42 ! [A: nat] :
% 5.25/5.42 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( times_times_nat @ A @ A ) ) ).
% 5.25/5.42
% 5.25/5.42 % power2_eq_square
% 5.25/5.42 thf(fact_472_power2__eq__square,axiom,
% 5.25/5.42 ! [A: int] :
% 5.25/5.42 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( times_times_int @ A @ A ) ) ).
% 5.25/5.42
% 5.25/5.42 % power2_eq_square
% 5.25/5.42 thf(fact_473_power__even__eq,axiom,
% 5.25/5.42 ! [A: nat,N: nat] :
% 5.25/5.42 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.42 = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_even_eq
% 5.25/5.42 thf(fact_474_power__even__eq,axiom,
% 5.25/5.42 ! [A: real,N: nat] :
% 5.25/5.42 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.42 = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_even_eq
% 5.25/5.42 thf(fact_475_power__even__eq,axiom,
% 5.25/5.42 ! [A: int,N: nat] :
% 5.25/5.42 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.42 = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_even_eq
% 5.25/5.42 thf(fact_476_power__even__eq,axiom,
% 5.25/5.42 ! [A: complex,N: nat] :
% 5.25/5.42 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.42 = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_even_eq
% 5.25/5.42 thf(fact_477_power__le__imp__le__exp,axiom,
% 5.25/5.42 ! [A: real,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.42 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.25/5.42 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_le_imp_le_exp
% 5.25/5.42 thf(fact_478_power__le__imp__le__exp,axiom,
% 5.25/5.42 ! [A: rat,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.42 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.25/5.42 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_le_imp_le_exp
% 5.25/5.42 thf(fact_479_power__le__imp__le__exp,axiom,
% 5.25/5.42 ! [A: nat,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.42 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.25/5.42 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_le_imp_le_exp
% 5.25/5.42 thf(fact_480_power__le__imp__le__exp,axiom,
% 5.25/5.42 ! [A: int,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.42 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.25/5.42 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_le_imp_le_exp
% 5.25/5.42 thf(fact_481_one__power2,axiom,
% 5.25/5.42 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = one_one_rat ) ).
% 5.25/5.42
% 5.25/5.42 % one_power2
% 5.25/5.42 thf(fact_482_one__power2,axiom,
% 5.25/5.42 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = one_one_nat ) ).
% 5.25/5.42
% 5.25/5.42 % one_power2
% 5.25/5.42 thf(fact_483_one__power2,axiom,
% 5.25/5.42 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = one_one_real ) ).
% 5.25/5.42
% 5.25/5.42 % one_power2
% 5.25/5.42 thf(fact_484_one__power2,axiom,
% 5.25/5.42 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = one_one_int ) ).
% 5.25/5.42
% 5.25/5.42 % one_power2
% 5.25/5.42 thf(fact_485_one__power2,axiom,
% 5.25/5.42 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = one_one_complex ) ).
% 5.25/5.42
% 5.25/5.42 % one_power2
% 5.25/5.42 thf(fact_486_nat__1__add__1,axiom,
% 5.25/5.42 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.25/5.42 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % nat_1_add_1
% 5.25/5.42 thf(fact_487_power2__sum,axiom,
% 5.25/5.42 ! [X3: complex,Y: complex] :
% 5.25/5.42 ( ( power_power_complex @ ( plus_plus_complex @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power2_sum
% 5.25/5.42 thf(fact_488_power2__sum,axiom,
% 5.25/5.42 ! [X3: real,Y: real] :
% 5.25/5.42 ( ( power_power_real @ ( plus_plus_real @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( 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 ) ) @ X3 ) @ Y ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power2_sum
% 5.25/5.42 thf(fact_489_power2__sum,axiom,
% 5.25/5.42 ! [X3: rat,Y: rat] :
% 5.25/5.42 ( ( power_power_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power2_sum
% 5.25/5.42 thf(fact_490_power2__sum,axiom,
% 5.25/5.42 ! [X3: nat,Y: nat] :
% 5.25/5.42 ( ( power_power_nat @ ( plus_plus_nat @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X3 @ ( 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 ) ) @ X3 ) @ Y ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power2_sum
% 5.25/5.42 thf(fact_491_power2__sum,axiom,
% 5.25/5.42 ! [X3: int,Y: int] :
% 5.25/5.42 ( ( power_power_int @ ( plus_plus_int @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( 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 ) ) @ X3 ) @ Y ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power2_sum
% 5.25/5.42 thf(fact_492_nat__less__le,axiom,
% 5.25/5.42 ( ord_less_nat
% 5.25/5.42 = ( ^ [M6: nat,N2: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.25/5.42 & ( M6 != N2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % nat_less_le
% 5.25/5.42 thf(fact_493_less__imp__le__nat,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ M @ N )
% 5.25/5.42 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_imp_le_nat
% 5.25/5.42 thf(fact_494_le__eq__less__or__eq,axiom,
% 5.25/5.42 ( ord_less_eq_nat
% 5.25/5.42 = ( ^ [M6: nat,N2: nat] :
% 5.25/5.42 ( ( ord_less_nat @ M6 @ N2 )
% 5.25/5.42 | ( M6 = N2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_eq_less_or_eq
% 5.25/5.42 thf(fact_495_less__or__eq__imp__le,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ( ord_less_nat @ M @ N )
% 5.25/5.42 | ( M = N ) )
% 5.25/5.42 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_or_eq_imp_le
% 5.25/5.42 thf(fact_496_le__neq__implies__less,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.42 => ( ( M != N )
% 5.25/5.42 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_neq_implies_less
% 5.25/5.42 thf(fact_497_less__mono__imp__le__mono,axiom,
% 5.25/5.42 ! [F: nat > nat,I2: nat,J2: nat] :
% 5.25/5.42 ( ! [I4: nat,J: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I4 @ J )
% 5.25/5.42 => ( ord_less_nat @ ( F @ I4 ) @ ( F @ J ) ) )
% 5.25/5.42 => ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.42 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_mono_imp_le_mono
% 5.25/5.42 thf(fact_498_add__lessD1,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.42 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K )
% 5.25/5.42 => ( ord_less_nat @ I2 @ K ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_lessD1
% 5.25/5.42 thf(fact_499_add__less__mono,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,K: nat,L2: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.42 => ( ( ord_less_nat @ K @ L2 )
% 5.25/5.42 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J2 @ L2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_less_mono
% 5.25/5.42 thf(fact_500_not__add__less1,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat] :
% 5.25/5.42 ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J2 ) @ I2 ) ).
% 5.25/5.42
% 5.25/5.42 % not_add_less1
% 5.25/5.42 thf(fact_501_not__add__less2,axiom,
% 5.25/5.42 ! [J2: nat,I2: nat] :
% 5.25/5.42 ~ ( ord_less_nat @ ( plus_plus_nat @ J2 @ I2 ) @ I2 ) ).
% 5.25/5.42
% 5.25/5.42 % not_add_less2
% 5.25/5.42 thf(fact_502_add__less__mono1,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.42 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J2 @ K ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_less_mono1
% 5.25/5.42 thf(fact_503_trans__less__add1,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,M: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.42 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J2 @ M ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % trans_less_add1
% 5.25/5.42 thf(fact_504_trans__less__add2,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,M: nat] :
% 5.25/5.42 ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.42 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J2 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % trans_less_add2
% 5.25/5.42 thf(fact_505_less__add__eq__less,axiom,
% 5.25/5.42 ! [K: nat,L2: nat,M: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_nat @ K @ L2 )
% 5.25/5.42 => ( ( ( plus_plus_nat @ M @ L2 )
% 5.25/5.42 = ( plus_plus_nat @ K @ N ) )
% 5.25/5.42 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % less_add_eq_less
% 5.25/5.42 thf(fact_506_add__leE,axiom,
% 5.25/5.42 ! [M: nat,K: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.25/5.42 => ~ ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.42 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_leE
% 5.25/5.42 thf(fact_507_le__add1,axiom,
% 5.25/5.42 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_add1
% 5.25/5.42 thf(fact_508_le__add2,axiom,
% 5.25/5.42 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_add2
% 5.25/5.42 thf(fact_509_add__leD1,axiom,
% 5.25/5.42 ! [M: nat,K: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.25/5.42 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_leD1
% 5.25/5.42 thf(fact_510_add__leD2,axiom,
% 5.25/5.42 ! [M: nat,K: nat,N: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.25/5.42 => ( ord_less_eq_nat @ K @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_leD2
% 5.25/5.42 thf(fact_511_le__Suc__ex,axiom,
% 5.25/5.42 ! [K: nat,L2: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ K @ L2 )
% 5.25/5.42 => ? [N3: nat] :
% 5.25/5.42 ( L2
% 5.25/5.42 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % le_Suc_ex
% 5.25/5.42 thf(fact_512_add__le__mono,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,K: nat,L2: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.42 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.25/5.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J2 @ L2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_le_mono
% 5.25/5.42 thf(fact_513_add__le__mono1,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J2 @ K ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_le_mono1
% 5.25/5.42 thf(fact_514_trans__le__add1,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,M: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.42 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J2 @ M ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % trans_le_add1
% 5.25/5.42 thf(fact_515_trans__le__add2,axiom,
% 5.25/5.42 ! [I2: nat,J2: nat,M: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.42 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J2 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % trans_le_add2
% 5.25/5.42 thf(fact_516_nat__le__iff__add,axiom,
% 5.25/5.42 ( ord_less_eq_nat
% 5.25/5.42 = ( ^ [M6: nat,N2: nat] :
% 5.25/5.42 ? [K3: nat] :
% 5.25/5.42 ( N2
% 5.25/5.42 = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % nat_le_iff_add
% 5.25/5.42 thf(fact_517_div__le__mono,axiom,
% 5.25/5.42 ! [M: nat,N: nat,K: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.42 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % div_le_mono
% 5.25/5.42 thf(fact_518_div__le__dividend,axiom,
% 5.25/5.42 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 5.25/5.42
% 5.25/5.42 % div_le_dividend
% 5.25/5.42 thf(fact_519_ex__power__ivl1,axiom,
% 5.25/5.42 ! [B: nat,K: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.25/5.42 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.25/5.42 => ? [N3: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.25/5.42 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % ex_power_ivl1
% 5.25/5.42 thf(fact_520_ex__power__ivl2,axiom,
% 5.25/5.42 ! [B: nat,K: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.25/5.42 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.25/5.42 => ? [N3: nat] :
% 5.25/5.42 ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.25/5.42 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % ex_power_ivl2
% 5.25/5.42 thf(fact_521_mono__nat__linear__lb,axiom,
% 5.25/5.42 ! [F: nat > nat,M: nat,K: nat] :
% 5.25/5.42 ( ! [M5: nat,N3: nat] :
% 5.25/5.42 ( ( ord_less_nat @ M5 @ N3 )
% 5.25/5.42 => ( ord_less_nat @ ( F @ M5 ) @ ( F @ N3 ) ) )
% 5.25/5.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mono_nat_linear_lb
% 5.25/5.42 thf(fact_522_numeral__Bit0__div__2,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( numeral_numeral_nat @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_Bit0_div_2
% 5.25/5.42 thf(fact_523_numeral__Bit0__div__2,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.42 = ( numeral_numeral_int @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % numeral_Bit0_div_2
% 5.25/5.42 thf(fact_524_field__sum__of__halves,axiom,
% 5.25/5.42 ! [X3: real] :
% 5.25/5.42 ( ( plus_plus_real @ ( divide_divide_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.42 = X3 ) ).
% 5.25/5.42
% 5.25/5.42 % field_sum_of_halves
% 5.25/5.42 thf(fact_525_field__sum__of__halves,axiom,
% 5.25/5.42 ! [X3: rat] :
% 5.25/5.42 ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.25/5.42 = X3 ) ).
% 5.25/5.42
% 5.25/5.42 % field_sum_of_halves
% 5.25/5.42 thf(fact_526_in__children__def,axiom,
% 5.25/5.42 ( vEBT_V5917875025757280293ildren
% 5.25/5.42 = ( ^ [N2: nat,TreeList2: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ N2 ) ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % in_children_def
% 5.25/5.42 thf(fact_527_sum__squares__bound,axiom,
% 5.25/5.42 ! [X3: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % sum_squares_bound
% 5.25/5.42 thf(fact_528_sum__squares__bound,axiom,
% 5.25/5.42 ! [X3: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % sum_squares_bound
% 5.25/5.42 thf(fact_529_both__member__options__ding,axiom,
% 5.25/5.42 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X3: nat] :
% 5.25/5.42 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.25/5.42 => ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.25/5.42 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.42 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X3 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % both_member_options_ding
% 5.25/5.42 thf(fact_530_Suc__double__not__eq__double,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.42 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % Suc_double_not_eq_double
% 5.25/5.42 thf(fact_531_double__not__eq__Suc__double,axiom,
% 5.25/5.42 ! [M: nat,N: nat] :
% 5.25/5.42 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.25/5.42 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % double_not_eq_Suc_double
% 5.25/5.42 thf(fact_532_div__by__1,axiom,
% 5.25/5.42 ! [A: complex] :
% 5.25/5.42 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % div_by_1
% 5.25/5.42 thf(fact_533_div__by__1,axiom,
% 5.25/5.42 ! [A: real] :
% 5.25/5.42 ( ( divide_divide_real @ A @ one_one_real )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % div_by_1
% 5.25/5.42 thf(fact_534_div__by__1,axiom,
% 5.25/5.42 ! [A: rat] :
% 5.25/5.42 ( ( divide_divide_rat @ A @ one_one_rat )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % div_by_1
% 5.25/5.42 thf(fact_535_div__by__1,axiom,
% 5.25/5.42 ! [A: nat] :
% 5.25/5.42 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % div_by_1
% 5.25/5.42 thf(fact_536_div__by__1,axiom,
% 5.25/5.42 ! [A: int] :
% 5.25/5.42 ( ( divide_divide_int @ A @ one_one_int )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % div_by_1
% 5.25/5.42 thf(fact_537_times__divide__eq__left,axiom,
% 5.25/5.42 ! [B: complex,C: complex,A: complex] :
% 5.25/5.42 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 5.25/5.42 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 5.25/5.42
% 5.25/5.42 % times_divide_eq_left
% 5.25/5.42 thf(fact_538_times__divide__eq__left,axiom,
% 5.25/5.42 ! [B: real,C: real,A: real] :
% 5.25/5.42 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.25/5.42 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 5.25/5.42
% 5.25/5.42 % times_divide_eq_left
% 5.25/5.42 thf(fact_539_times__divide__eq__left,axiom,
% 5.25/5.42 ! [B: rat,C: rat,A: rat] :
% 5.25/5.42 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.25/5.42 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 5.25/5.42
% 5.25/5.42 % times_divide_eq_left
% 5.25/5.42 thf(fact_540_divide__divide__eq__left,axiom,
% 5.25/5.42 ! [A: complex,B: complex,C: complex] :
% 5.25/5.42 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.25/5.42 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % divide_divide_eq_left
% 5.25/5.42 thf(fact_541_divide__divide__eq__left,axiom,
% 5.25/5.42 ! [A: real,B: real,C: real] :
% 5.25/5.42 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.25/5.42 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % divide_divide_eq_left
% 5.25/5.42 thf(fact_542_divide__divide__eq__left,axiom,
% 5.25/5.42 ! [A: rat,B: rat,C: rat] :
% 5.25/5.42 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.25/5.42 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % divide_divide_eq_left
% 5.25/5.42 thf(fact_543_divide__divide__eq__right,axiom,
% 5.25/5.42 ! [A: complex,B: complex,C: complex] :
% 5.25/5.42 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.42 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % divide_divide_eq_right
% 5.25/5.42 thf(fact_544_divide__divide__eq__right,axiom,
% 5.25/5.42 ! [A: real,B: real,C: real] :
% 5.25/5.42 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.42 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % divide_divide_eq_right
% 5.25/5.42 thf(fact_545_divide__divide__eq__right,axiom,
% 5.25/5.42 ! [A: rat,B: rat,C: rat] :
% 5.25/5.42 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.42 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % divide_divide_eq_right
% 5.25/5.42 thf(fact_546_times__divide__eq__right,axiom,
% 5.25/5.42 ! [A: complex,B: complex,C: complex] :
% 5.25/5.42 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.42 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 5.25/5.42
% 5.25/5.42 % times_divide_eq_right
% 5.25/5.42 thf(fact_547_times__divide__eq__right,axiom,
% 5.25/5.42 ! [A: real,B: real,C: real] :
% 5.25/5.42 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.42 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 5.25/5.42
% 5.25/5.42 % times_divide_eq_right
% 5.25/5.42 thf(fact_548_times__divide__eq__right,axiom,
% 5.25/5.42 ! [A: rat,B: rat,C: rat] :
% 5.25/5.42 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.42 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 5.25/5.42
% 5.25/5.42 % times_divide_eq_right
% 5.25/5.42 thf(fact_549_mult_Oright__neutral,axiom,
% 5.25/5.42 ! [A: complex] :
% 5.25/5.42 ( ( times_times_complex @ A @ one_one_complex )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult.right_neutral
% 5.25/5.42 thf(fact_550_mult_Oright__neutral,axiom,
% 5.25/5.42 ! [A: real] :
% 5.25/5.42 ( ( times_times_real @ A @ one_one_real )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult.right_neutral
% 5.25/5.42 thf(fact_551_mult_Oright__neutral,axiom,
% 5.25/5.42 ! [A: rat] :
% 5.25/5.42 ( ( times_times_rat @ A @ one_one_rat )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult.right_neutral
% 5.25/5.42 thf(fact_552_mult_Oright__neutral,axiom,
% 5.25/5.42 ! [A: nat] :
% 5.25/5.42 ( ( times_times_nat @ A @ one_one_nat )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult.right_neutral
% 5.25/5.42 thf(fact_553_mult_Oright__neutral,axiom,
% 5.25/5.42 ! [A: int] :
% 5.25/5.42 ( ( times_times_int @ A @ one_one_int )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult.right_neutral
% 5.25/5.42 thf(fact_554_mult__1,axiom,
% 5.25/5.42 ! [A: complex] :
% 5.25/5.42 ( ( times_times_complex @ one_one_complex @ A )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_1
% 5.25/5.42 thf(fact_555_mult__1,axiom,
% 5.25/5.42 ! [A: real] :
% 5.25/5.42 ( ( times_times_real @ one_one_real @ A )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_1
% 5.25/5.42 thf(fact_556_mult__1,axiom,
% 5.25/5.42 ! [A: rat] :
% 5.25/5.42 ( ( times_times_rat @ one_one_rat @ A )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_1
% 5.25/5.42 thf(fact_557_mult__1,axiom,
% 5.25/5.42 ! [A: nat] :
% 5.25/5.42 ( ( times_times_nat @ one_one_nat @ A )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_1
% 5.25/5.42 thf(fact_558_mult__1,axiom,
% 5.25/5.42 ! [A: int] :
% 5.25/5.42 ( ( times_times_int @ one_one_int @ A )
% 5.25/5.42 = A ) ).
% 5.25/5.42
% 5.25/5.42 % mult_1
% 5.25/5.42 thf(fact_559_deg__deg__n,axiom,
% 5.25/5.42 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.25/5.42 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.25/5.42 => ( Deg = N ) ) ).
% 5.25/5.42
% 5.25/5.42 % deg_deg_n
% 5.25/5.42 thf(fact_560_deg__SUcn__Node,axiom,
% 5.25/5.42 ! [Tree: vEBT_VEBT,N: nat] :
% 5.25/5.42 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 5.25/5.42 => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.25/5.42 ( Tree
% 5.25/5.42 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList3 @ S2 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % deg_SUcn_Node
% 5.25/5.42 thf(fact_561_add__right__cancel,axiom,
% 5.25/5.42 ! [B: real,A: real,C: real] :
% 5.25/5.42 ( ( ( plus_plus_real @ B @ A )
% 5.25/5.42 = ( plus_plus_real @ C @ A ) )
% 5.25/5.42 = ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_right_cancel
% 5.25/5.42 thf(fact_562_add__right__cancel,axiom,
% 5.25/5.42 ! [B: rat,A: rat,C: rat] :
% 5.25/5.42 ( ( ( plus_plus_rat @ B @ A )
% 5.25/5.42 = ( plus_plus_rat @ C @ A ) )
% 5.25/5.42 = ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_right_cancel
% 5.25/5.42 thf(fact_563_add__right__cancel,axiom,
% 5.25/5.42 ! [B: nat,A: nat,C: nat] :
% 5.25/5.42 ( ( ( plus_plus_nat @ B @ A )
% 5.25/5.42 = ( plus_plus_nat @ C @ A ) )
% 5.25/5.42 = ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_right_cancel
% 5.25/5.42 thf(fact_564_add__right__cancel,axiom,
% 5.25/5.42 ! [B: int,A: int,C: int] :
% 5.25/5.42 ( ( ( plus_plus_int @ B @ A )
% 5.25/5.42 = ( plus_plus_int @ C @ A ) )
% 5.25/5.42 = ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_right_cancel
% 5.25/5.42 thf(fact_565_add__left__cancel,axiom,
% 5.25/5.42 ! [A: real,B: real,C: real] :
% 5.25/5.42 ( ( ( plus_plus_real @ A @ B )
% 5.25/5.42 = ( plus_plus_real @ A @ C ) )
% 5.25/5.42 = ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_left_cancel
% 5.25/5.42 thf(fact_566_add__left__cancel,axiom,
% 5.25/5.42 ! [A: rat,B: rat,C: rat] :
% 5.25/5.42 ( ( ( plus_plus_rat @ A @ B )
% 5.25/5.42 = ( plus_plus_rat @ A @ C ) )
% 5.25/5.42 = ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_left_cancel
% 5.25/5.42 thf(fact_567_add__left__cancel,axiom,
% 5.25/5.42 ! [A: nat,B: nat,C: nat] :
% 5.25/5.42 ( ( ( plus_plus_nat @ A @ B )
% 5.25/5.42 = ( plus_plus_nat @ A @ C ) )
% 5.25/5.42 = ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_left_cancel
% 5.25/5.42 thf(fact_568_add__left__cancel,axiom,
% 5.25/5.42 ! [A: int,B: int,C: int] :
% 5.25/5.42 ( ( ( plus_plus_int @ A @ B )
% 5.25/5.42 = ( plus_plus_int @ A @ C ) )
% 5.25/5.42 = ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_left_cancel
% 5.25/5.42 thf(fact_569_add__le__cancel__right,axiom,
% 5.25/5.42 ! [A: real,C: real,B: real] :
% 5.25/5.42 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.25/5.42 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_le_cancel_right
% 5.25/5.42 thf(fact_570_add__le__cancel__right,axiom,
% 5.25/5.42 ! [A: rat,C: rat,B: rat] :
% 5.25/5.42 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.42 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_le_cancel_right
% 5.25/5.42 thf(fact_571_add__le__cancel__right,axiom,
% 5.25/5.42 ! [A: nat,C: nat,B: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.42 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_le_cancel_right
% 5.25/5.42 thf(fact_572_add__le__cancel__right,axiom,
% 5.25/5.42 ! [A: int,C: int,B: int] :
% 5.25/5.42 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.25/5.42 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_le_cancel_right
% 5.25/5.42 thf(fact_573_add__le__cancel__left,axiom,
% 5.25/5.42 ! [C: real,A: real,B: real] :
% 5.25/5.42 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.25/5.42 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_le_cancel_left
% 5.25/5.42 thf(fact_574_add__le__cancel__left,axiom,
% 5.25/5.42 ! [C: rat,A: rat,B: rat] :
% 5.25/5.42 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.25/5.42 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_le_cancel_left
% 5.25/5.42 thf(fact_575_add__le__cancel__left,axiom,
% 5.25/5.42 ! [C: nat,A: nat,B: nat] :
% 5.25/5.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.25/5.42 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_le_cancel_left
% 5.25/5.42 thf(fact_576_add__le__cancel__left,axiom,
% 5.25/5.42 ! [C: int,A: int,B: int] :
% 5.25/5.42 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.25/5.42 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_le_cancel_left
% 5.25/5.42 thf(fact_577_add__less__cancel__right,axiom,
% 5.25/5.42 ! [A: real,C: real,B: real] :
% 5.25/5.42 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.25/5.42 = ( ord_less_real @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_less_cancel_right
% 5.25/5.42 thf(fact_578_add__less__cancel__right,axiom,
% 5.25/5.42 ! [A: rat,C: rat,B: rat] :
% 5.25/5.42 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.42 = ( ord_less_rat @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_less_cancel_right
% 5.25/5.42 thf(fact_579_add__less__cancel__right,axiom,
% 5.25/5.42 ! [A: nat,C: nat,B: nat] :
% 5.25/5.42 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.42 = ( ord_less_nat @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_less_cancel_right
% 5.25/5.42 thf(fact_580_add__less__cancel__right,axiom,
% 5.25/5.42 ! [A: int,C: int,B: int] :
% 5.25/5.42 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.25/5.42 = ( ord_less_int @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_less_cancel_right
% 5.25/5.42 thf(fact_581_add__less__cancel__left,axiom,
% 5.25/5.42 ! [C: real,A: real,B: real] :
% 5.25/5.42 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.25/5.42 = ( ord_less_real @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_less_cancel_left
% 5.25/5.42 thf(fact_582_add__less__cancel__left,axiom,
% 5.25/5.42 ! [C: rat,A: rat,B: rat] :
% 5.25/5.42 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.25/5.42 = ( ord_less_rat @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_less_cancel_left
% 5.25/5.42 thf(fact_583_add__less__cancel__left,axiom,
% 5.25/5.42 ! [C: nat,A: nat,B: nat] :
% 5.25/5.42 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.25/5.42 = ( ord_less_nat @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_less_cancel_left
% 5.25/5.42 thf(fact_584_add__less__cancel__left,axiom,
% 5.25/5.42 ! [C: int,A: int,B: int] :
% 5.25/5.42 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.25/5.42 = ( ord_less_int @ A @ B ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_less_cancel_left
% 5.25/5.42 thf(fact_585_semiring__norm_I13_J,axiom,
% 5.25/5.42 ! [M: num,N: num] :
% 5.25/5.42 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.25/5.42 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % semiring_norm(13)
% 5.25/5.42 thf(fact_586_semiring__norm_I11_J,axiom,
% 5.25/5.42 ! [M: num] :
% 5.25/5.42 ( ( times_times_num @ M @ one )
% 5.25/5.42 = M ) ).
% 5.25/5.42
% 5.25/5.42 % semiring_norm(11)
% 5.25/5.42 thf(fact_587_semiring__norm_I12_J,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( times_times_num @ one @ N )
% 5.25/5.42 = N ) ).
% 5.25/5.42
% 5.25/5.42 % semiring_norm(12)
% 5.25/5.42 thf(fact_588_set__vebt__set__vebt_H__valid,axiom,
% 5.25/5.42 ! [T: vEBT_VEBT,N: nat] :
% 5.25/5.42 ( ( vEBT_invar_vebt @ T @ N )
% 5.25/5.42 => ( ( vEBT_set_vebt @ T )
% 5.25/5.42 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % set_vebt_set_vebt'_valid
% 5.25/5.42 thf(fact_589_num__double,axiom,
% 5.25/5.42 ! [N: num] :
% 5.25/5.42 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 5.25/5.42 = ( bit0 @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % num_double
% 5.25/5.42 thf(fact_590_power__mult__numeral,axiom,
% 5.25/5.42 ! [A: nat,M: num,N: num] :
% 5.25/5.42 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.42 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_mult_numeral
% 5.25/5.42 thf(fact_591_power__mult__numeral,axiom,
% 5.25/5.42 ! [A: real,M: num,N: num] :
% 5.25/5.42 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.42 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_mult_numeral
% 5.25/5.42 thf(fact_592_power__mult__numeral,axiom,
% 5.25/5.42 ! [A: int,M: num,N: num] :
% 5.25/5.42 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.42 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_mult_numeral
% 5.25/5.42 thf(fact_593_power__mult__numeral,axiom,
% 5.25/5.42 ! [A: complex,M: num,N: num] :
% 5.25/5.42 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.42 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % power_mult_numeral
% 5.25/5.42 thf(fact_594_four__x__squared,axiom,
% 5.25/5.42 ! [X3: real] :
% 5.25/5.42 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.42 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % four_x_squared
% 5.25/5.42 thf(fact_595_L2__set__mult__ineq__lemma,axiom,
% 5.25/5.42 ! [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 ) ) ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % L2_set_mult_ineq_lemma
% 5.25/5.42 thf(fact_596_div__mult2__numeral__eq,axiom,
% 5.25/5.42 ! [A: nat,K: num,L2: num] :
% 5.25/5.42 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
% 5.25/5.42 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % div_mult2_numeral_eq
% 5.25/5.42 thf(fact_597_div__mult2__numeral__eq,axiom,
% 5.25/5.42 ! [A: int,K: num,L2: num] :
% 5.25/5.42 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L2 ) )
% 5.25/5.42 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % div_mult2_numeral_eq
% 5.25/5.42 thf(fact_598_two__realpow__ge__one,axiom,
% 5.25/5.42 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.42
% 5.25/5.42 % two_realpow_ge_one
% 5.25/5.42 thf(fact_599_linorder__neqE__linordered__idom,axiom,
% 5.25/5.42 ! [X3: real,Y: real] :
% 5.25/5.42 ( ( X3 != Y )
% 5.25/5.42 => ( ~ ( ord_less_real @ X3 @ Y )
% 5.25/5.42 => ( ord_less_real @ Y @ X3 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % linorder_neqE_linordered_idom
% 5.25/5.42 thf(fact_600_linorder__neqE__linordered__idom,axiom,
% 5.25/5.42 ! [X3: rat,Y: rat] :
% 5.25/5.42 ( ( X3 != Y )
% 5.25/5.42 => ( ~ ( ord_less_rat @ X3 @ Y )
% 5.25/5.42 => ( ord_less_rat @ Y @ X3 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % linorder_neqE_linordered_idom
% 5.25/5.42 thf(fact_601_linorder__neqE__linordered__idom,axiom,
% 5.25/5.42 ! [X3: int,Y: int] :
% 5.25/5.42 ( ( X3 != Y )
% 5.25/5.42 => ( ~ ( ord_less_int @ X3 @ Y )
% 5.25/5.42 => ( ord_less_int @ Y @ X3 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % linorder_neqE_linordered_idom
% 5.25/5.42 thf(fact_602_linordered__field__no__ub,axiom,
% 5.25/5.42 ! [X: real] :
% 5.25/5.42 ? [X_12: real] : ( ord_less_real @ X @ X_12 ) ).
% 5.25/5.42
% 5.25/5.42 % linordered_field_no_ub
% 5.25/5.42 thf(fact_603_linordered__field__no__ub,axiom,
% 5.25/5.42 ! [X: rat] :
% 5.25/5.42 ? [X_12: rat] : ( ord_less_rat @ X @ X_12 ) ).
% 5.25/5.42
% 5.25/5.42 % linordered_field_no_ub
% 5.25/5.42 thf(fact_604_linordered__field__no__lb,axiom,
% 5.25/5.42 ! [X: real] :
% 5.25/5.42 ? [Y3: real] : ( ord_less_real @ Y3 @ X ) ).
% 5.25/5.42
% 5.25/5.42 % linordered_field_no_lb
% 5.25/5.42 thf(fact_605_linordered__field__no__lb,axiom,
% 5.25/5.42 ! [X: rat] :
% 5.25/5.42 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X ) ).
% 5.25/5.42
% 5.25/5.42 % linordered_field_no_lb
% 5.25/5.42 thf(fact_606_mult_Oleft__commute,axiom,
% 5.25/5.42 ! [B: real,A: real,C: real] :
% 5.25/5.42 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 5.25/5.42 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult.left_commute
% 5.25/5.42 thf(fact_607_mult_Oleft__commute,axiom,
% 5.25/5.42 ! [B: rat,A: rat,C: rat] :
% 5.25/5.42 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 5.25/5.42 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult.left_commute
% 5.25/5.42 thf(fact_608_mult_Oleft__commute,axiom,
% 5.25/5.42 ! [B: nat,A: nat,C: nat] :
% 5.25/5.42 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 5.25/5.42 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult.left_commute
% 5.25/5.42 thf(fact_609_mult_Oleft__commute,axiom,
% 5.25/5.42 ! [B: int,A: int,C: int] :
% 5.25/5.42 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 5.25/5.42 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult.left_commute
% 5.25/5.42 thf(fact_610_mult_Ocommute,axiom,
% 5.25/5.42 ( times_times_real
% 5.25/5.42 = ( ^ [A3: real,B2: real] : ( times_times_real @ B2 @ A3 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult.commute
% 5.25/5.42 thf(fact_611_mult_Ocommute,axiom,
% 5.25/5.42 ( times_times_rat
% 5.25/5.42 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ B2 @ A3 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult.commute
% 5.25/5.42 thf(fact_612_mult_Ocommute,axiom,
% 5.25/5.42 ( times_times_nat
% 5.25/5.42 = ( ^ [A3: nat,B2: nat] : ( times_times_nat @ B2 @ A3 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult.commute
% 5.25/5.42 thf(fact_613_mult_Ocommute,axiom,
% 5.25/5.42 ( times_times_int
% 5.25/5.42 = ( ^ [A3: int,B2: int] : ( times_times_int @ B2 @ A3 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult.commute
% 5.25/5.42 thf(fact_614_mult_Oassoc,axiom,
% 5.25/5.42 ! [A: real,B: real,C: real] :
% 5.25/5.42 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.25/5.42 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult.assoc
% 5.25/5.42 thf(fact_615_mult_Oassoc,axiom,
% 5.25/5.42 ! [A: rat,B: rat,C: rat] :
% 5.25/5.42 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.25/5.42 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult.assoc
% 5.25/5.42 thf(fact_616_mult_Oassoc,axiom,
% 5.25/5.42 ! [A: nat,B: nat,C: nat] :
% 5.25/5.42 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.42 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult.assoc
% 5.25/5.42 thf(fact_617_mult_Oassoc,axiom,
% 5.25/5.42 ! [A: int,B: int,C: int] :
% 5.25/5.42 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.42 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % mult.assoc
% 5.25/5.42 thf(fact_618_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.25/5.42 ! [A: real,B: real,C: real] :
% 5.25/5.42 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.25/5.42 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % ab_semigroup_mult_class.mult_ac(1)
% 5.25/5.42 thf(fact_619_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.25/5.42 ! [A: rat,B: rat,C: rat] :
% 5.25/5.42 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.25/5.42 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % ab_semigroup_mult_class.mult_ac(1)
% 5.25/5.42 thf(fact_620_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.25/5.42 ! [A: nat,B: nat,C: nat] :
% 5.25/5.42 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.42 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % ab_semigroup_mult_class.mult_ac(1)
% 5.25/5.42 thf(fact_621_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.25/5.42 ! [A: int,B: int,C: int] :
% 5.25/5.42 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.42 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % ab_semigroup_mult_class.mult_ac(1)
% 5.25/5.42 thf(fact_622_one__reorient,axiom,
% 5.25/5.42 ! [X3: complex] :
% 5.25/5.42 ( ( one_one_complex = X3 )
% 5.25/5.42 = ( X3 = one_one_complex ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_reorient
% 5.25/5.42 thf(fact_623_one__reorient,axiom,
% 5.25/5.42 ! [X3: real] :
% 5.25/5.42 ( ( one_one_real = X3 )
% 5.25/5.42 = ( X3 = one_one_real ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_reorient
% 5.25/5.42 thf(fact_624_one__reorient,axiom,
% 5.25/5.42 ! [X3: rat] :
% 5.25/5.42 ( ( one_one_rat = X3 )
% 5.25/5.42 = ( X3 = one_one_rat ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_reorient
% 5.25/5.42 thf(fact_625_one__reorient,axiom,
% 5.25/5.42 ! [X3: nat] :
% 5.25/5.42 ( ( one_one_nat = X3 )
% 5.25/5.42 = ( X3 = one_one_nat ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_reorient
% 5.25/5.42 thf(fact_626_one__reorient,axiom,
% 5.25/5.42 ! [X3: int] :
% 5.25/5.42 ( ( one_one_int = X3 )
% 5.25/5.42 = ( X3 = one_one_int ) ) ).
% 5.25/5.42
% 5.25/5.42 % one_reorient
% 5.25/5.42 thf(fact_627_add__right__imp__eq,axiom,
% 5.25/5.42 ! [B: real,A: real,C: real] :
% 5.25/5.42 ( ( ( plus_plus_real @ B @ A )
% 5.25/5.42 = ( plus_plus_real @ C @ A ) )
% 5.25/5.42 => ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_right_imp_eq
% 5.25/5.42 thf(fact_628_add__right__imp__eq,axiom,
% 5.25/5.42 ! [B: rat,A: rat,C: rat] :
% 5.25/5.42 ( ( ( plus_plus_rat @ B @ A )
% 5.25/5.42 = ( plus_plus_rat @ C @ A ) )
% 5.25/5.42 => ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_right_imp_eq
% 5.25/5.42 thf(fact_629_add__right__imp__eq,axiom,
% 5.25/5.42 ! [B: nat,A: nat,C: nat] :
% 5.25/5.42 ( ( ( plus_plus_nat @ B @ A )
% 5.25/5.42 = ( plus_plus_nat @ C @ A ) )
% 5.25/5.42 => ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_right_imp_eq
% 5.25/5.42 thf(fact_630_add__right__imp__eq,axiom,
% 5.25/5.42 ! [B: int,A: int,C: int] :
% 5.25/5.42 ( ( ( plus_plus_int @ B @ A )
% 5.25/5.42 = ( plus_plus_int @ C @ A ) )
% 5.25/5.42 => ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_right_imp_eq
% 5.25/5.42 thf(fact_631_add__left__imp__eq,axiom,
% 5.25/5.42 ! [A: real,B: real,C: real] :
% 5.25/5.42 ( ( ( plus_plus_real @ A @ B )
% 5.25/5.42 = ( plus_plus_real @ A @ C ) )
% 5.25/5.42 => ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_left_imp_eq
% 5.25/5.42 thf(fact_632_add__left__imp__eq,axiom,
% 5.25/5.42 ! [A: rat,B: rat,C: rat] :
% 5.25/5.42 ( ( ( plus_plus_rat @ A @ B )
% 5.25/5.42 = ( plus_plus_rat @ A @ C ) )
% 5.25/5.42 => ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_left_imp_eq
% 5.25/5.42 thf(fact_633_add__left__imp__eq,axiom,
% 5.25/5.42 ! [A: nat,B: nat,C: nat] :
% 5.25/5.42 ( ( ( plus_plus_nat @ A @ B )
% 5.25/5.42 = ( plus_plus_nat @ A @ C ) )
% 5.25/5.42 => ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_left_imp_eq
% 5.25/5.42 thf(fact_634_add__left__imp__eq,axiom,
% 5.25/5.42 ! [A: int,B: int,C: int] :
% 5.25/5.42 ( ( ( plus_plus_int @ A @ B )
% 5.25/5.42 = ( plus_plus_int @ A @ C ) )
% 5.25/5.42 => ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add_left_imp_eq
% 5.25/5.42 thf(fact_635_add_Oleft__commute,axiom,
% 5.25/5.42 ! [B: real,A: real,C: real] :
% 5.25/5.42 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 5.25/5.42 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.left_commute
% 5.25/5.42 thf(fact_636_add_Oleft__commute,axiom,
% 5.25/5.42 ! [B: rat,A: rat,C: rat] :
% 5.25/5.42 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 5.25/5.42 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.left_commute
% 5.25/5.42 thf(fact_637_add_Oleft__commute,axiom,
% 5.25/5.42 ! [B: nat,A: nat,C: nat] :
% 5.25/5.42 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 5.25/5.42 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.left_commute
% 5.25/5.42 thf(fact_638_add_Oleft__commute,axiom,
% 5.25/5.42 ! [B: int,A: int,C: int] :
% 5.25/5.42 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 5.25/5.42 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.left_commute
% 5.25/5.42 thf(fact_639_add_Ocommute,axiom,
% 5.25/5.42 ( plus_plus_real
% 5.25/5.42 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ B2 @ A3 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.commute
% 5.25/5.42 thf(fact_640_add_Ocommute,axiom,
% 5.25/5.42 ( plus_plus_rat
% 5.25/5.42 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ B2 @ A3 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.commute
% 5.25/5.42 thf(fact_641_add_Ocommute,axiom,
% 5.25/5.42 ( plus_plus_nat
% 5.25/5.42 = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.commute
% 5.25/5.42 thf(fact_642_add_Ocommute,axiom,
% 5.25/5.42 ( plus_plus_int
% 5.25/5.42 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.commute
% 5.25/5.42 thf(fact_643_add_Oright__cancel,axiom,
% 5.25/5.42 ! [B: real,A: real,C: real] :
% 5.25/5.42 ( ( ( plus_plus_real @ B @ A )
% 5.25/5.42 = ( plus_plus_real @ C @ A ) )
% 5.25/5.42 = ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.right_cancel
% 5.25/5.42 thf(fact_644_add_Oright__cancel,axiom,
% 5.25/5.42 ! [B: rat,A: rat,C: rat] :
% 5.25/5.42 ( ( ( plus_plus_rat @ B @ A )
% 5.25/5.42 = ( plus_plus_rat @ C @ A ) )
% 5.25/5.42 = ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.right_cancel
% 5.25/5.42 thf(fact_645_add_Oright__cancel,axiom,
% 5.25/5.42 ! [B: int,A: int,C: int] :
% 5.25/5.42 ( ( ( plus_plus_int @ B @ A )
% 5.25/5.42 = ( plus_plus_int @ C @ A ) )
% 5.25/5.42 = ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.right_cancel
% 5.25/5.42 thf(fact_646_add_Oleft__cancel,axiom,
% 5.25/5.42 ! [A: real,B: real,C: real] :
% 5.25/5.42 ( ( ( plus_plus_real @ A @ B )
% 5.25/5.42 = ( plus_plus_real @ A @ C ) )
% 5.25/5.42 = ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.left_cancel
% 5.25/5.42 thf(fact_647_add_Oleft__cancel,axiom,
% 5.25/5.42 ! [A: rat,B: rat,C: rat] :
% 5.25/5.42 ( ( ( plus_plus_rat @ A @ B )
% 5.25/5.42 = ( plus_plus_rat @ A @ C ) )
% 5.25/5.42 = ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.left_cancel
% 5.25/5.42 thf(fact_648_add_Oleft__cancel,axiom,
% 5.25/5.42 ! [A: int,B: int,C: int] :
% 5.25/5.42 ( ( ( plus_plus_int @ A @ B )
% 5.25/5.42 = ( plus_plus_int @ A @ C ) )
% 5.25/5.42 = ( B = C ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.left_cancel
% 5.25/5.42 thf(fact_649_add_Oassoc,axiom,
% 5.25/5.42 ! [A: real,B: real,C: real] :
% 5.25/5.42 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.25/5.42 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.assoc
% 5.25/5.42 thf(fact_650_add_Oassoc,axiom,
% 5.25/5.42 ! [A: rat,B: rat,C: rat] :
% 5.25/5.42 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.25/5.42 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.assoc
% 5.25/5.42 thf(fact_651_add_Oassoc,axiom,
% 5.25/5.42 ! [A: nat,B: nat,C: nat] :
% 5.25/5.42 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.42 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.assoc
% 5.25/5.42 thf(fact_652_add_Oassoc,axiom,
% 5.25/5.42 ! [A: int,B: int,C: int] :
% 5.25/5.42 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.42 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % add.assoc
% 5.25/5.42 thf(fact_653_group__cancel_Oadd2,axiom,
% 5.25/5.42 ! [B3: real,K: real,B: real,A: real] :
% 5.25/5.42 ( ( B3
% 5.25/5.42 = ( plus_plus_real @ K @ B ) )
% 5.25/5.42 => ( ( plus_plus_real @ A @ B3 )
% 5.25/5.42 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.25/5.42
% 5.25/5.42 % group_cancel.add2
% 5.25/5.43 thf(fact_654_group__cancel_Oadd2,axiom,
% 5.25/5.43 ! [B3: rat,K: rat,B: rat,A: rat] :
% 5.25/5.43 ( ( B3
% 5.25/5.43 = ( plus_plus_rat @ K @ B ) )
% 5.25/5.43 => ( ( plus_plus_rat @ A @ B3 )
% 5.25/5.43 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % group_cancel.add2
% 5.25/5.43 thf(fact_655_group__cancel_Oadd2,axiom,
% 5.25/5.43 ! [B3: nat,K: nat,B: nat,A: nat] :
% 5.25/5.43 ( ( B3
% 5.25/5.43 = ( plus_plus_nat @ K @ B ) )
% 5.25/5.43 => ( ( plus_plus_nat @ A @ B3 )
% 5.25/5.43 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % group_cancel.add2
% 5.25/5.43 thf(fact_656_group__cancel_Oadd2,axiom,
% 5.25/5.43 ! [B3: int,K: int,B: int,A: int] :
% 5.25/5.43 ( ( B3
% 5.25/5.43 = ( plus_plus_int @ K @ B ) )
% 5.25/5.43 => ( ( plus_plus_int @ A @ B3 )
% 5.25/5.43 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % group_cancel.add2
% 5.25/5.43 thf(fact_657_group__cancel_Oadd1,axiom,
% 5.25/5.43 ! [A2: real,K: real,A: real,B: real] :
% 5.25/5.43 ( ( A2
% 5.25/5.43 = ( plus_plus_real @ K @ A ) )
% 5.25/5.43 => ( ( plus_plus_real @ A2 @ B )
% 5.25/5.43 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % group_cancel.add1
% 5.25/5.43 thf(fact_658_group__cancel_Oadd1,axiom,
% 5.25/5.43 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.25/5.43 ( ( A2
% 5.25/5.43 = ( plus_plus_rat @ K @ A ) )
% 5.25/5.43 => ( ( plus_plus_rat @ A2 @ B )
% 5.25/5.43 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % group_cancel.add1
% 5.25/5.43 thf(fact_659_group__cancel_Oadd1,axiom,
% 5.25/5.43 ! [A2: nat,K: nat,A: nat,B: nat] :
% 5.25/5.43 ( ( A2
% 5.25/5.43 = ( plus_plus_nat @ K @ A ) )
% 5.25/5.43 => ( ( plus_plus_nat @ A2 @ B )
% 5.25/5.43 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % group_cancel.add1
% 5.25/5.43 thf(fact_660_group__cancel_Oadd1,axiom,
% 5.25/5.43 ! [A2: int,K: int,A: int,B: int] :
% 5.25/5.43 ( ( A2
% 5.25/5.43 = ( plus_plus_int @ K @ A ) )
% 5.25/5.43 => ( ( plus_plus_int @ A2 @ B )
% 5.25/5.43 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % group_cancel.add1
% 5.25/5.43 thf(fact_661_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.25/5.43 ! [I2: real,J2: real,K: real,L2: real] :
% 5.25/5.43 ( ( ( I2 = J2 )
% 5.25/5.43 & ( K = L2 ) )
% 5.25/5.43 => ( ( plus_plus_real @ I2 @ K )
% 5.25/5.43 = ( plus_plus_real @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(4)
% 5.25/5.43 thf(fact_662_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.25/5.43 ! [I2: rat,J2: rat,K: rat,L2: rat] :
% 5.25/5.43 ( ( ( I2 = J2 )
% 5.25/5.43 & ( K = L2 ) )
% 5.25/5.43 => ( ( plus_plus_rat @ I2 @ K )
% 5.25/5.43 = ( plus_plus_rat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(4)
% 5.25/5.43 thf(fact_663_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.25/5.43 ! [I2: nat,J2: nat,K: nat,L2: nat] :
% 5.25/5.43 ( ( ( I2 = J2 )
% 5.25/5.43 & ( K = L2 ) )
% 5.25/5.43 => ( ( plus_plus_nat @ I2 @ K )
% 5.25/5.43 = ( plus_plus_nat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(4)
% 5.25/5.43 thf(fact_664_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.25/5.43 ! [I2: int,J2: int,K: int,L2: int] :
% 5.25/5.43 ( ( ( I2 = J2 )
% 5.25/5.43 & ( K = L2 ) )
% 5.25/5.43 => ( ( plus_plus_int @ I2 @ K )
% 5.25/5.43 = ( plus_plus_int @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(4)
% 5.25/5.43 thf(fact_665_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real] :
% 5.25/5.43 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % ab_semigroup_add_class.add_ac(1)
% 5.25/5.43 thf(fact_666_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat] :
% 5.25/5.43 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % ab_semigroup_add_class.add_ac(1)
% 5.25/5.43 thf(fact_667_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % ab_semigroup_add_class.add_ac(1)
% 5.25/5.43 thf(fact_668_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % ab_semigroup_add_class.add_ac(1)
% 5.25/5.43 thf(fact_669_add__le__imp__le__right,axiom,
% 5.25/5.43 ! [A: real,C: real,B: real] :
% 5.25/5.43 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.25/5.43 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_le_imp_le_right
% 5.25/5.43 thf(fact_670_add__le__imp__le__right,axiom,
% 5.25/5.43 ! [A: rat,C: rat,B: rat] :
% 5.25/5.43 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.43 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_le_imp_le_right
% 5.25/5.43 thf(fact_671_add__le__imp__le__right,axiom,
% 5.25/5.43 ! [A: nat,C: nat,B: nat] :
% 5.25/5.43 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.43 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_le_imp_le_right
% 5.25/5.43 thf(fact_672_add__le__imp__le__right,axiom,
% 5.25/5.43 ! [A: int,C: int,B: int] :
% 5.25/5.43 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.25/5.43 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_le_imp_le_right
% 5.25/5.43 thf(fact_673_add__le__imp__le__left,axiom,
% 5.25/5.43 ! [C: real,A: real,B: real] :
% 5.25/5.43 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.25/5.43 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_le_imp_le_left
% 5.25/5.43 thf(fact_674_add__le__imp__le__left,axiom,
% 5.25/5.43 ! [C: rat,A: rat,B: rat] :
% 5.25/5.43 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.25/5.43 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_le_imp_le_left
% 5.25/5.43 thf(fact_675_add__le__imp__le__left,axiom,
% 5.25/5.43 ! [C: nat,A: nat,B: nat] :
% 5.25/5.43 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.25/5.43 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_le_imp_le_left
% 5.25/5.43 thf(fact_676_add__le__imp__le__left,axiom,
% 5.25/5.43 ! [C: int,A: int,B: int] :
% 5.25/5.43 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.25/5.43 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_le_imp_le_left
% 5.25/5.43 thf(fact_677_le__iff__add,axiom,
% 5.25/5.43 ( ord_less_eq_nat
% 5.25/5.43 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.43 ? [C2: nat] :
% 5.25/5.43 ( B2
% 5.25/5.43 = ( plus_plus_nat @ A3 @ C2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % le_iff_add
% 5.25/5.43 thf(fact_678_add__right__mono,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real] :
% 5.25/5.43 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.43 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_right_mono
% 5.25/5.43 thf(fact_679_add__right__mono,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat] :
% 5.25/5.43 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.43 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_right_mono
% 5.25/5.43 thf(fact_680_add__right__mono,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.43 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_right_mono
% 5.25/5.43 thf(fact_681_add__right__mono,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.43 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_right_mono
% 5.25/5.43 thf(fact_682_less__eqE,axiom,
% 5.25/5.43 ! [A: nat,B: nat] :
% 5.25/5.43 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.43 => ~ ! [C3: nat] :
% 5.25/5.43 ( B
% 5.25/5.43 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % less_eqE
% 5.25/5.43 thf(fact_683_add__left__mono,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real] :
% 5.25/5.43 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.43 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_left_mono
% 5.25/5.43 thf(fact_684_add__left__mono,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat] :
% 5.25/5.43 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.43 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_left_mono
% 5.25/5.43 thf(fact_685_add__left__mono,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.43 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_left_mono
% 5.25/5.43 thf(fact_686_add__left__mono,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.43 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_left_mono
% 5.25/5.43 thf(fact_687_add__mono,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.43 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.43 => ( ( ord_less_eq_real @ C @ D )
% 5.25/5.43 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono
% 5.25/5.43 thf(fact_688_add__mono,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.43 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.43 => ( ( ord_less_eq_rat @ C @ D )
% 5.25/5.43 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono
% 5.25/5.43 thf(fact_689_add__mono,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.43 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.43 => ( ( ord_less_eq_nat @ C @ D )
% 5.25/5.43 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono
% 5.25/5.43 thf(fact_690_add__mono,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.43 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.43 => ( ( ord_less_eq_int @ C @ D )
% 5.25/5.43 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono
% 5.25/5.43 thf(fact_691_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.25/5.43 ! [I2: real,J2: real,K: real,L2: real] :
% 5.25/5.43 ( ( ( ord_less_eq_real @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_eq_real @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(1)
% 5.25/5.43 thf(fact_692_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.25/5.43 ! [I2: rat,J2: rat,K: rat,L2: rat] :
% 5.25/5.43 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(1)
% 5.25/5.43 thf(fact_693_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.25/5.43 ! [I2: nat,J2: nat,K: nat,L2: nat] :
% 5.25/5.43 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(1)
% 5.25/5.43 thf(fact_694_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.25/5.43 ! [I2: int,J2: int,K: int,L2: int] :
% 5.25/5.43 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_eq_int @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(1)
% 5.25/5.43 thf(fact_695_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.25/5.43 ! [I2: real,J2: real,K: real,L2: real] :
% 5.25/5.43 ( ( ( I2 = J2 )
% 5.25/5.43 & ( ord_less_eq_real @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(2)
% 5.25/5.43 thf(fact_696_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.25/5.43 ! [I2: rat,J2: rat,K: rat,L2: rat] :
% 5.25/5.43 ( ( ( I2 = J2 )
% 5.25/5.43 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(2)
% 5.25/5.43 thf(fact_697_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.25/5.43 ! [I2: nat,J2: nat,K: nat,L2: nat] :
% 5.25/5.43 ( ( ( I2 = J2 )
% 5.25/5.43 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(2)
% 5.25/5.43 thf(fact_698_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.25/5.43 ! [I2: int,J2: int,K: int,L2: int] :
% 5.25/5.43 ( ( ( I2 = J2 )
% 5.25/5.43 & ( ord_less_eq_int @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(2)
% 5.25/5.43 thf(fact_699_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.25/5.43 ! [I2: real,J2: real,K: real,L2: real] :
% 5.25/5.43 ( ( ( ord_less_eq_real @ I2 @ J2 )
% 5.25/5.43 & ( K = L2 ) )
% 5.25/5.43 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(3)
% 5.25/5.43 thf(fact_700_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.25/5.43 ! [I2: rat,J2: rat,K: rat,L2: rat] :
% 5.25/5.43 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 5.25/5.43 & ( K = L2 ) )
% 5.25/5.43 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(3)
% 5.25/5.43 thf(fact_701_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.25/5.43 ! [I2: nat,J2: nat,K: nat,L2: nat] :
% 5.25/5.43 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.43 & ( K = L2 ) )
% 5.25/5.43 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(3)
% 5.25/5.43 thf(fact_702_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.25/5.43 ! [I2: int,J2: int,K: int,L2: int] :
% 5.25/5.43 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 5.25/5.43 & ( K = L2 ) )
% 5.25/5.43 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_semiring(3)
% 5.25/5.43 thf(fact_703_add__less__imp__less__right,axiom,
% 5.25/5.43 ! [A: real,C: real,B: real] :
% 5.25/5.43 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.25/5.43 => ( ord_less_real @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_less_imp_less_right
% 5.25/5.43 thf(fact_704_add__less__imp__less__right,axiom,
% 5.25/5.43 ! [A: rat,C: rat,B: rat] :
% 5.25/5.43 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.43 => ( ord_less_rat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_less_imp_less_right
% 5.25/5.43 thf(fact_705_add__less__imp__less__right,axiom,
% 5.25/5.43 ! [A: nat,C: nat,B: nat] :
% 5.25/5.43 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.43 => ( ord_less_nat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_less_imp_less_right
% 5.25/5.43 thf(fact_706_add__less__imp__less__right,axiom,
% 5.25/5.43 ! [A: int,C: int,B: int] :
% 5.25/5.43 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.25/5.43 => ( ord_less_int @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_less_imp_less_right
% 5.25/5.43 thf(fact_707_add__less__imp__less__left,axiom,
% 5.25/5.43 ! [C: real,A: real,B: real] :
% 5.25/5.43 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.25/5.43 => ( ord_less_real @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_less_imp_less_left
% 5.25/5.43 thf(fact_708_add__less__imp__less__left,axiom,
% 5.25/5.43 ! [C: rat,A: rat,B: rat] :
% 5.25/5.43 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.25/5.43 => ( ord_less_rat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_less_imp_less_left
% 5.25/5.43 thf(fact_709_add__less__imp__less__left,axiom,
% 5.25/5.43 ! [C: nat,A: nat,B: nat] :
% 5.25/5.43 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.25/5.43 => ( ord_less_nat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_less_imp_less_left
% 5.25/5.43 thf(fact_710_add__less__imp__less__left,axiom,
% 5.25/5.43 ! [C: int,A: int,B: int] :
% 5.25/5.43 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.25/5.43 => ( ord_less_int @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_less_imp_less_left
% 5.25/5.43 thf(fact_711_add__strict__right__mono,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real] :
% 5.25/5.43 ( ( ord_less_real @ A @ B )
% 5.25/5.43 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_strict_right_mono
% 5.25/5.43 thf(fact_712_add__strict__right__mono,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat] :
% 5.25/5.43 ( ( ord_less_rat @ A @ B )
% 5.25/5.43 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_strict_right_mono
% 5.25/5.43 thf(fact_713_add__strict__right__mono,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( ord_less_nat @ A @ B )
% 5.25/5.43 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_strict_right_mono
% 5.25/5.43 thf(fact_714_add__strict__right__mono,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( ord_less_int @ A @ B )
% 5.25/5.43 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_strict_right_mono
% 5.25/5.43 thf(fact_715_add__strict__left__mono,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real] :
% 5.25/5.43 ( ( ord_less_real @ A @ B )
% 5.25/5.43 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_strict_left_mono
% 5.25/5.43 thf(fact_716_add__strict__left__mono,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat] :
% 5.25/5.43 ( ( ord_less_rat @ A @ B )
% 5.25/5.43 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_strict_left_mono
% 5.25/5.43 thf(fact_717_add__strict__left__mono,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( ord_less_nat @ A @ B )
% 5.25/5.43 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_strict_left_mono
% 5.25/5.43 thf(fact_718_add__strict__left__mono,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( ord_less_int @ A @ B )
% 5.25/5.43 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_strict_left_mono
% 5.25/5.43 thf(fact_719_add__strict__mono,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.43 ( ( ord_less_real @ A @ B )
% 5.25/5.43 => ( ( ord_less_real @ C @ D )
% 5.25/5.43 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_strict_mono
% 5.25/5.43 thf(fact_720_add__strict__mono,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.43 ( ( ord_less_rat @ A @ B )
% 5.25/5.43 => ( ( ord_less_rat @ C @ D )
% 5.25/5.43 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_strict_mono
% 5.25/5.43 thf(fact_721_add__strict__mono,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.43 ( ( ord_less_nat @ A @ B )
% 5.25/5.43 => ( ( ord_less_nat @ C @ D )
% 5.25/5.43 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_strict_mono
% 5.25/5.43 thf(fact_722_add__strict__mono,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.43 ( ( ord_less_int @ A @ B )
% 5.25/5.43 => ( ( ord_less_int @ C @ D )
% 5.25/5.43 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_strict_mono
% 5.25/5.43 thf(fact_723_add__mono__thms__linordered__field_I1_J,axiom,
% 5.25/5.43 ! [I2: real,J2: real,K: real,L2: real] :
% 5.25/5.43 ( ( ( ord_less_real @ I2 @ J2 )
% 5.25/5.43 & ( K = L2 ) )
% 5.25/5.43 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(1)
% 5.25/5.43 thf(fact_724_add__mono__thms__linordered__field_I1_J,axiom,
% 5.25/5.43 ! [I2: rat,J2: rat,K: rat,L2: rat] :
% 5.25/5.43 ( ( ( ord_less_rat @ I2 @ J2 )
% 5.25/5.43 & ( K = L2 ) )
% 5.25/5.43 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(1)
% 5.25/5.43 thf(fact_725_add__mono__thms__linordered__field_I1_J,axiom,
% 5.25/5.43 ! [I2: nat,J2: nat,K: nat,L2: nat] :
% 5.25/5.43 ( ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.43 & ( K = L2 ) )
% 5.25/5.43 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(1)
% 5.25/5.43 thf(fact_726_add__mono__thms__linordered__field_I1_J,axiom,
% 5.25/5.43 ! [I2: int,J2: int,K: int,L2: int] :
% 5.25/5.43 ( ( ( ord_less_int @ I2 @ J2 )
% 5.25/5.43 & ( K = L2 ) )
% 5.25/5.43 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(1)
% 5.25/5.43 thf(fact_727_add__mono__thms__linordered__field_I2_J,axiom,
% 5.25/5.43 ! [I2: real,J2: real,K: real,L2: real] :
% 5.25/5.43 ( ( ( I2 = J2 )
% 5.25/5.43 & ( ord_less_real @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(2)
% 5.25/5.43 thf(fact_728_add__mono__thms__linordered__field_I2_J,axiom,
% 5.25/5.43 ! [I2: rat,J2: rat,K: rat,L2: rat] :
% 5.25/5.43 ( ( ( I2 = J2 )
% 5.25/5.43 & ( ord_less_rat @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(2)
% 5.25/5.43 thf(fact_729_add__mono__thms__linordered__field_I2_J,axiom,
% 5.25/5.43 ! [I2: nat,J2: nat,K: nat,L2: nat] :
% 5.25/5.43 ( ( ( I2 = J2 )
% 5.25/5.43 & ( ord_less_nat @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(2)
% 5.25/5.43 thf(fact_730_add__mono__thms__linordered__field_I2_J,axiom,
% 5.25/5.43 ! [I2: int,J2: int,K: int,L2: int] :
% 5.25/5.43 ( ( ( I2 = J2 )
% 5.25/5.43 & ( ord_less_int @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(2)
% 5.25/5.43 thf(fact_731_add__mono__thms__linordered__field_I5_J,axiom,
% 5.25/5.43 ! [I2: real,J2: real,K: real,L2: real] :
% 5.25/5.43 ( ( ( ord_less_real @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_real @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(5)
% 5.25/5.43 thf(fact_732_add__mono__thms__linordered__field_I5_J,axiom,
% 5.25/5.43 ! [I2: rat,J2: rat,K: rat,L2: rat] :
% 5.25/5.43 ( ( ( ord_less_rat @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_rat @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(5)
% 5.25/5.43 thf(fact_733_add__mono__thms__linordered__field_I5_J,axiom,
% 5.25/5.43 ! [I2: nat,J2: nat,K: nat,L2: nat] :
% 5.25/5.43 ( ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_nat @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(5)
% 5.25/5.43 thf(fact_734_add__mono__thms__linordered__field_I5_J,axiom,
% 5.25/5.43 ! [I2: int,J2: int,K: int,L2: int] :
% 5.25/5.43 ( ( ( ord_less_int @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_int @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(5)
% 5.25/5.43 thf(fact_735_mult_Ocomm__neutral,axiom,
% 5.25/5.43 ! [A: complex] :
% 5.25/5.43 ( ( times_times_complex @ A @ one_one_complex )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % mult.comm_neutral
% 5.25/5.43 thf(fact_736_mult_Ocomm__neutral,axiom,
% 5.25/5.43 ! [A: real] :
% 5.25/5.43 ( ( times_times_real @ A @ one_one_real )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % mult.comm_neutral
% 5.25/5.43 thf(fact_737_mult_Ocomm__neutral,axiom,
% 5.25/5.43 ! [A: rat] :
% 5.25/5.43 ( ( times_times_rat @ A @ one_one_rat )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % mult.comm_neutral
% 5.25/5.43 thf(fact_738_mult_Ocomm__neutral,axiom,
% 5.25/5.43 ! [A: nat] :
% 5.25/5.43 ( ( times_times_nat @ A @ one_one_nat )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % mult.comm_neutral
% 5.25/5.43 thf(fact_739_mult_Ocomm__neutral,axiom,
% 5.25/5.43 ! [A: int] :
% 5.25/5.43 ( ( times_times_int @ A @ one_one_int )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % mult.comm_neutral
% 5.25/5.43 thf(fact_740_comm__monoid__mult__class_Omult__1,axiom,
% 5.25/5.43 ! [A: complex] :
% 5.25/5.43 ( ( times_times_complex @ one_one_complex @ A )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % comm_monoid_mult_class.mult_1
% 5.25/5.43 thf(fact_741_comm__monoid__mult__class_Omult__1,axiom,
% 5.25/5.43 ! [A: real] :
% 5.25/5.43 ( ( times_times_real @ one_one_real @ A )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % comm_monoid_mult_class.mult_1
% 5.25/5.43 thf(fact_742_comm__monoid__mult__class_Omult__1,axiom,
% 5.25/5.43 ! [A: rat] :
% 5.25/5.43 ( ( times_times_rat @ one_one_rat @ A )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % comm_monoid_mult_class.mult_1
% 5.25/5.43 thf(fact_743_comm__monoid__mult__class_Omult__1,axiom,
% 5.25/5.43 ! [A: nat] :
% 5.25/5.43 ( ( times_times_nat @ one_one_nat @ A )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % comm_monoid_mult_class.mult_1
% 5.25/5.43 thf(fact_744_comm__monoid__mult__class_Omult__1,axiom,
% 5.25/5.43 ! [A: int] :
% 5.25/5.43 ( ( times_times_int @ one_one_int @ A )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % comm_monoid_mult_class.mult_1
% 5.25/5.43 thf(fact_745_combine__common__factor,axiom,
% 5.25/5.43 ! [A: real,E: real,B: real,C: real] :
% 5.25/5.43 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 5.25/5.43 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % combine_common_factor
% 5.25/5.43 thf(fact_746_combine__common__factor,axiom,
% 5.25/5.43 ! [A: rat,E: rat,B: rat,C: rat] :
% 5.25/5.43 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 5.25/5.43 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % combine_common_factor
% 5.25/5.43 thf(fact_747_combine__common__factor,axiom,
% 5.25/5.43 ! [A: nat,E: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 5.25/5.43 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % combine_common_factor
% 5.25/5.43 thf(fact_748_combine__common__factor,axiom,
% 5.25/5.43 ! [A: int,E: int,B: int,C: int] :
% 5.25/5.43 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 5.25/5.43 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % combine_common_factor
% 5.25/5.43 thf(fact_749_distrib__right,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real] :
% 5.25/5.43 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % distrib_right
% 5.25/5.43 thf(fact_750_distrib__right,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat] :
% 5.25/5.43 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % distrib_right
% 5.25/5.43 thf(fact_751_distrib__right,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % distrib_right
% 5.25/5.43 thf(fact_752_distrib__right,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % distrib_right
% 5.25/5.43 thf(fact_753_distrib__left,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real] :
% 5.25/5.43 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.25/5.43 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % distrib_left
% 5.25/5.43 thf(fact_754_distrib__left,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat] :
% 5.25/5.43 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.43 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % distrib_left
% 5.25/5.43 thf(fact_755_distrib__left,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.43 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % distrib_left
% 5.25/5.43 thf(fact_756_distrib__left,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.25/5.43 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % distrib_left
% 5.25/5.43 thf(fact_757_comm__semiring__class_Odistrib,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real] :
% 5.25/5.43 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % comm_semiring_class.distrib
% 5.25/5.43 thf(fact_758_comm__semiring__class_Odistrib,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat] :
% 5.25/5.43 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % comm_semiring_class.distrib
% 5.25/5.43 thf(fact_759_comm__semiring__class_Odistrib,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % comm_semiring_class.distrib
% 5.25/5.43 thf(fact_760_comm__semiring__class_Odistrib,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % comm_semiring_class.distrib
% 5.25/5.43 thf(fact_761_ring__class_Oring__distribs_I1_J,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real] :
% 5.25/5.43 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.25/5.43 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % ring_class.ring_distribs(1)
% 5.25/5.43 thf(fact_762_ring__class_Oring__distribs_I1_J,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat] :
% 5.25/5.43 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.43 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % ring_class.ring_distribs(1)
% 5.25/5.43 thf(fact_763_ring__class_Oring__distribs_I1_J,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.25/5.43 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % ring_class.ring_distribs(1)
% 5.25/5.43 thf(fact_764_ring__class_Oring__distribs_I2_J,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real] :
% 5.25/5.43 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % ring_class.ring_distribs(2)
% 5.25/5.43 thf(fact_765_ring__class_Oring__distribs_I2_J,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat] :
% 5.25/5.43 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % ring_class.ring_distribs(2)
% 5.25/5.43 thf(fact_766_ring__class_Oring__distribs_I2_J,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % ring_class.ring_distribs(2)
% 5.25/5.43 thf(fact_767_divide__divide__eq__left_H,axiom,
% 5.25/5.43 ! [A: complex,B: complex,C: complex] :
% 5.25/5.43 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.25/5.43 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % divide_divide_eq_left'
% 5.25/5.43 thf(fact_768_divide__divide__eq__left_H,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real] :
% 5.25/5.43 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.25/5.43 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % divide_divide_eq_left'
% 5.25/5.43 thf(fact_769_divide__divide__eq__left_H,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat] :
% 5.25/5.43 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.25/5.43 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % divide_divide_eq_left'
% 5.25/5.43 thf(fact_770_divide__divide__times__eq,axiom,
% 5.25/5.43 ! [X3: complex,Y: complex,Z: complex,W: complex] :
% 5.25/5.43 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X3 @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.25/5.43 = ( divide1717551699836669952omplex @ ( times_times_complex @ X3 @ W ) @ ( times_times_complex @ Y @ Z ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % divide_divide_times_eq
% 5.25/5.43 thf(fact_771_divide__divide__times__eq,axiom,
% 5.25/5.43 ! [X3: real,Y: real,Z: real,W: real] :
% 5.25/5.43 ( ( divide_divide_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 5.25/5.43 = ( divide_divide_real @ ( times_times_real @ X3 @ W ) @ ( times_times_real @ Y @ Z ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % divide_divide_times_eq
% 5.25/5.43 thf(fact_772_divide__divide__times__eq,axiom,
% 5.25/5.43 ! [X3: rat,Y: rat,Z: rat,W: rat] :
% 5.25/5.43 ( ( divide_divide_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 5.25/5.43 = ( divide_divide_rat @ ( times_times_rat @ X3 @ W ) @ ( times_times_rat @ Y @ Z ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % divide_divide_times_eq
% 5.25/5.43 thf(fact_773_times__divide__times__eq,axiom,
% 5.25/5.43 ! [X3: complex,Y: complex,Z: complex,W: complex] :
% 5.25/5.43 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X3 @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.25/5.43 = ( divide1717551699836669952omplex @ ( times_times_complex @ X3 @ Z ) @ ( times_times_complex @ Y @ W ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % times_divide_times_eq
% 5.25/5.43 thf(fact_774_times__divide__times__eq,axiom,
% 5.25/5.43 ! [X3: real,Y: real,Z: real,W: real] :
% 5.25/5.43 ( ( times_times_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 5.25/5.43 = ( divide_divide_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ Y @ W ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % times_divide_times_eq
% 5.25/5.43 thf(fact_775_times__divide__times__eq,axiom,
% 5.25/5.43 ! [X3: rat,Y: rat,Z: rat,W: rat] :
% 5.25/5.43 ( ( times_times_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 5.25/5.43 = ( divide_divide_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ Y @ W ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % times_divide_times_eq
% 5.25/5.43 thf(fact_776_add__divide__distrib,axiom,
% 5.25/5.43 ! [A: complex,B: complex,C: complex] :
% 5.25/5.43 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_divide_distrib
% 5.25/5.43 thf(fact_777_add__divide__distrib,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real] :
% 5.25/5.43 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_divide_distrib
% 5.25/5.43 thf(fact_778_add__divide__distrib,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat] :
% 5.25/5.43 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.25/5.43 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_divide_distrib
% 5.25/5.43 thf(fact_779_add__less__le__mono,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.43 ( ( ord_less_real @ A @ B )
% 5.25/5.43 => ( ( ord_less_eq_real @ C @ D )
% 5.25/5.43 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_less_le_mono
% 5.25/5.43 thf(fact_780_add__less__le__mono,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.43 ( ( ord_less_rat @ A @ B )
% 5.25/5.43 => ( ( ord_less_eq_rat @ C @ D )
% 5.25/5.43 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_less_le_mono
% 5.25/5.43 thf(fact_781_add__less__le__mono,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.43 ( ( ord_less_nat @ A @ B )
% 5.25/5.43 => ( ( ord_less_eq_nat @ C @ D )
% 5.25/5.43 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_less_le_mono
% 5.25/5.43 thf(fact_782_add__less__le__mono,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.43 ( ( ord_less_int @ A @ B )
% 5.25/5.43 => ( ( ord_less_eq_int @ C @ D )
% 5.25/5.43 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_less_le_mono
% 5.25/5.43 thf(fact_783_add__le__less__mono,axiom,
% 5.25/5.43 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.43 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.43 => ( ( ord_less_real @ C @ D )
% 5.25/5.43 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_le_less_mono
% 5.25/5.43 thf(fact_784_add__le__less__mono,axiom,
% 5.25/5.43 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.43 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.43 => ( ( ord_less_rat @ C @ D )
% 5.25/5.43 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_le_less_mono
% 5.25/5.43 thf(fact_785_add__le__less__mono,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.43 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.43 => ( ( ord_less_nat @ C @ D )
% 5.25/5.43 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_le_less_mono
% 5.25/5.43 thf(fact_786_add__le__less__mono,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.43 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.43 => ( ( ord_less_int @ C @ D )
% 5.25/5.43 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_le_less_mono
% 5.25/5.43 thf(fact_787_add__mono__thms__linordered__field_I3_J,axiom,
% 5.25/5.43 ! [I2: real,J2: real,K: real,L2: real] :
% 5.25/5.43 ( ( ( ord_less_real @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_eq_real @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(3)
% 5.25/5.43 thf(fact_788_add__mono__thms__linordered__field_I3_J,axiom,
% 5.25/5.43 ! [I2: rat,J2: rat,K: rat,L2: rat] :
% 5.25/5.43 ( ( ( ord_less_rat @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(3)
% 5.25/5.43 thf(fact_789_add__mono__thms__linordered__field_I3_J,axiom,
% 5.25/5.43 ! [I2: nat,J2: nat,K: nat,L2: nat] :
% 5.25/5.43 ( ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(3)
% 5.25/5.43 thf(fact_790_add__mono__thms__linordered__field_I3_J,axiom,
% 5.25/5.43 ! [I2: int,J2: int,K: int,L2: int] :
% 5.25/5.43 ( ( ( ord_less_int @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_eq_int @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(3)
% 5.25/5.43 thf(fact_791_add__mono__thms__linordered__field_I4_J,axiom,
% 5.25/5.43 ! [I2: real,J2: real,K: real,L2: real] :
% 5.25/5.43 ( ( ( ord_less_eq_real @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_real @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(4)
% 5.25/5.43 thf(fact_792_add__mono__thms__linordered__field_I4_J,axiom,
% 5.25/5.43 ! [I2: rat,J2: rat,K: rat,L2: rat] :
% 5.25/5.43 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_rat @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(4)
% 5.25/5.43 thf(fact_793_add__mono__thms__linordered__field_I4_J,axiom,
% 5.25/5.43 ! [I2: nat,J2: nat,K: nat,L2: nat] :
% 5.25/5.43 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_nat @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(4)
% 5.25/5.43 thf(fact_794_add__mono__thms__linordered__field_I4_J,axiom,
% 5.25/5.43 ! [I2: int,J2: int,K: int,L2: int] :
% 5.25/5.43 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 5.25/5.43 & ( ord_less_int @ K @ L2 ) )
% 5.25/5.43 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J2 @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono_thms_linordered_field(4)
% 5.25/5.43 thf(fact_795_less__1__mult,axiom,
% 5.25/5.43 ! [M: real,N: real] :
% 5.25/5.43 ( ( ord_less_real @ one_one_real @ M )
% 5.25/5.43 => ( ( ord_less_real @ one_one_real @ N )
% 5.25/5.43 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % less_1_mult
% 5.25/5.43 thf(fact_796_less__1__mult,axiom,
% 5.25/5.43 ! [M: rat,N: rat] :
% 5.25/5.43 ( ( ord_less_rat @ one_one_rat @ M )
% 5.25/5.43 => ( ( ord_less_rat @ one_one_rat @ N )
% 5.25/5.43 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % less_1_mult
% 5.25/5.43 thf(fact_797_less__1__mult,axiom,
% 5.25/5.43 ! [M: nat,N: nat] :
% 5.25/5.43 ( ( ord_less_nat @ one_one_nat @ M )
% 5.25/5.43 => ( ( ord_less_nat @ one_one_nat @ N )
% 5.25/5.43 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % less_1_mult
% 5.25/5.43 thf(fact_798_less__1__mult,axiom,
% 5.25/5.43 ! [M: int,N: int] :
% 5.25/5.43 ( ( ord_less_int @ one_one_int @ M )
% 5.25/5.43 => ( ( ord_less_int @ one_one_int @ N )
% 5.25/5.43 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % less_1_mult
% 5.25/5.43 thf(fact_799_less__add__one,axiom,
% 5.25/5.43 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.25/5.43
% 5.25/5.43 % less_add_one
% 5.25/5.43 thf(fact_800_less__add__one,axiom,
% 5.25/5.43 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.25/5.43
% 5.25/5.43 % less_add_one
% 5.25/5.43 thf(fact_801_less__add__one,axiom,
% 5.25/5.43 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.25/5.43
% 5.25/5.43 % less_add_one
% 5.25/5.43 thf(fact_802_less__add__one,axiom,
% 5.25/5.43 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.25/5.43
% 5.25/5.43 % less_add_one
% 5.25/5.43 thf(fact_803_add__mono1,axiom,
% 5.25/5.43 ! [A: real,B: real] :
% 5.25/5.43 ( ( ord_less_real @ A @ B )
% 5.25/5.43 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono1
% 5.25/5.43 thf(fact_804_add__mono1,axiom,
% 5.25/5.43 ! [A: rat,B: rat] :
% 5.25/5.43 ( ( ord_less_rat @ A @ B )
% 5.25/5.43 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono1
% 5.25/5.43 thf(fact_805_add__mono1,axiom,
% 5.25/5.43 ! [A: nat,B: nat] :
% 5.25/5.43 ( ( ord_less_nat @ A @ B )
% 5.25/5.43 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono1
% 5.25/5.43 thf(fact_806_add__mono1,axiom,
% 5.25/5.43 ! [A: int,B: int] :
% 5.25/5.43 ( ( ord_less_int @ A @ B )
% 5.25/5.43 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_mono1
% 5.25/5.43 thf(fact_807_gt__half__sum,axiom,
% 5.25/5.43 ! [A: real,B: real] :
% 5.25/5.43 ( ( ord_less_real @ A @ B )
% 5.25/5.43 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % gt_half_sum
% 5.25/5.43 thf(fact_808_gt__half__sum,axiom,
% 5.25/5.43 ! [A: rat,B: rat] :
% 5.25/5.43 ( ( ord_less_rat @ A @ B )
% 5.25/5.43 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % gt_half_sum
% 5.25/5.43 thf(fact_809_less__half__sum,axiom,
% 5.25/5.43 ! [A: real,B: real] :
% 5.25/5.43 ( ( ord_less_real @ A @ B )
% 5.25/5.43 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % less_half_sum
% 5.25/5.43 thf(fact_810_less__half__sum,axiom,
% 5.25/5.43 ! [A: rat,B: rat] :
% 5.25/5.43 ( ( ord_less_rat @ A @ B )
% 5.25/5.43 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % less_half_sum
% 5.25/5.43 thf(fact_811_all__set__conv__all__nth,axiom,
% 5.25/5.43 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.25/5.43 ( ( ! [X2: vEBT_VEBT] :
% 5.25/5.43 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.25/5.43 => ( P @ X2 ) ) )
% 5.25/5.43 = ( ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % all_set_conv_all_nth
% 5.25/5.43 thf(fact_812_all__set__conv__all__nth,axiom,
% 5.25/5.43 ! [Xs: list_o,P: $o > $o] :
% 5.25/5.43 ( ( ! [X2: $o] :
% 5.25/5.43 ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 5.25/5.43 => ( P @ X2 ) ) )
% 5.25/5.43 = ( ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_o @ Xs @ I3 ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % all_set_conv_all_nth
% 5.25/5.43 thf(fact_813_all__set__conv__all__nth,axiom,
% 5.25/5.43 ! [Xs: list_nat,P: nat > $o] :
% 5.25/5.43 ( ( ! [X2: nat] :
% 5.25/5.43 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 5.25/5.43 => ( P @ X2 ) ) )
% 5.25/5.43 = ( ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_nat @ Xs @ I3 ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % all_set_conv_all_nth
% 5.25/5.43 thf(fact_814_all__set__conv__all__nth,axiom,
% 5.25/5.43 ! [Xs: list_int,P: int > $o] :
% 5.25/5.43 ( ( ! [X2: int] :
% 5.25/5.43 ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 5.25/5.43 => ( P @ X2 ) ) )
% 5.25/5.43 = ( ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_int @ Xs @ I3 ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % all_set_conv_all_nth
% 5.25/5.43 thf(fact_815_all__nth__imp__all__set,axiom,
% 5.25/5.43 ! [Xs: list_real,P: real > $o,X3: real] :
% 5.25/5.43 ( ! [I4: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_real @ Xs @ I4 ) ) )
% 5.25/5.43 => ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 5.25/5.43 => ( P @ X3 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % all_nth_imp_all_set
% 5.25/5.43 thf(fact_816_all__nth__imp__all__set,axiom,
% 5.25/5.43 ! [Xs: list_complex,P: complex > $o,X3: complex] :
% 5.25/5.43 ( ! [I4: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_complex @ Xs @ I4 ) ) )
% 5.25/5.43 => ( ( member_complex @ X3 @ ( set_complex2 @ Xs ) )
% 5.25/5.43 => ( P @ X3 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % all_nth_imp_all_set
% 5.25/5.43 thf(fact_817_all__nth__imp__all__set,axiom,
% 5.25/5.43 ! [Xs: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,X3: product_prod_nat_nat] :
% 5.25/5.43 ( ! [I4: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ I4 ) ) )
% 5.25/5.43 => ( ( member8440522571783428010at_nat @ X3 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 5.25/5.43 => ( P @ X3 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % all_nth_imp_all_set
% 5.25/5.43 thf(fact_818_all__nth__imp__all__set,axiom,
% 5.25/5.43 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X3: vEBT_VEBT] :
% 5.25/5.43 ( ! [I4: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) )
% 5.25/5.43 => ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.25/5.43 => ( P @ X3 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % all_nth_imp_all_set
% 5.25/5.43 thf(fact_819_all__nth__imp__all__set,axiom,
% 5.25/5.43 ! [Xs: list_o,P: $o > $o,X3: $o] :
% 5.25/5.43 ( ! [I4: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_o @ Xs @ I4 ) ) )
% 5.25/5.43 => ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 5.25/5.43 => ( P @ X3 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % all_nth_imp_all_set
% 5.25/5.43 thf(fact_820_all__nth__imp__all__set,axiom,
% 5.25/5.43 ! [Xs: list_nat,P: nat > $o,X3: nat] :
% 5.25/5.43 ( ! [I4: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_nat @ Xs @ I4 ) ) )
% 5.25/5.43 => ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 5.25/5.43 => ( P @ X3 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % all_nth_imp_all_set
% 5.25/5.43 thf(fact_821_all__nth__imp__all__set,axiom,
% 5.25/5.43 ! [Xs: list_int,P: int > $o,X3: int] :
% 5.25/5.43 ( ! [I4: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_int @ Xs @ I4 ) ) )
% 5.25/5.43 => ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 5.25/5.43 => ( P @ X3 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % all_nth_imp_all_set
% 5.25/5.43 thf(fact_822_in__set__conv__nth,axiom,
% 5.25/5.43 ! [X3: real,Xs: list_real] :
% 5.25/5.43 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 5.25/5.43 = ( ? [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs ) )
% 5.25/5.43 & ( ( nth_real @ Xs @ I3 )
% 5.25/5.43 = X3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % in_set_conv_nth
% 5.25/5.43 thf(fact_823_in__set__conv__nth,axiom,
% 5.25/5.43 ! [X3: complex,Xs: list_complex] :
% 5.25/5.43 ( ( member_complex @ X3 @ ( set_complex2 @ Xs ) )
% 5.25/5.43 = ( ? [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.25/5.43 & ( ( nth_complex @ Xs @ I3 )
% 5.25/5.43 = X3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % in_set_conv_nth
% 5.25/5.43 thf(fact_824_in__set__conv__nth,axiom,
% 5.25/5.43 ! [X3: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 5.25/5.43 ( ( member8440522571783428010at_nat @ X3 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 5.25/5.43 = ( ? [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 5.25/5.43 & ( ( nth_Pr7617993195940197384at_nat @ Xs @ I3 )
% 5.25/5.43 = X3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % in_set_conv_nth
% 5.25/5.43 thf(fact_825_in__set__conv__nth,axiom,
% 5.25/5.43 ! [X3: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.25/5.43 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.25/5.43 = ( ? [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.43 & ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 5.25/5.43 = X3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % in_set_conv_nth
% 5.25/5.43 thf(fact_826_in__set__conv__nth,axiom,
% 5.25/5.43 ! [X3: $o,Xs: list_o] :
% 5.25/5.43 ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 5.25/5.43 = ( ? [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 5.25/5.43 & ( ( nth_o @ Xs @ I3 )
% 5.25/5.43 = X3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % in_set_conv_nth
% 5.25/5.43 thf(fact_827_in__set__conv__nth,axiom,
% 5.25/5.43 ! [X3: nat,Xs: list_nat] :
% 5.25/5.43 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 5.25/5.43 = ( ? [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.43 & ( ( nth_nat @ Xs @ I3 )
% 5.25/5.43 = X3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % in_set_conv_nth
% 5.25/5.43 thf(fact_828_in__set__conv__nth,axiom,
% 5.25/5.43 ! [X3: int,Xs: list_int] :
% 5.25/5.43 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 5.25/5.43 = ( ? [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 5.25/5.43 & ( ( nth_int @ Xs @ I3 )
% 5.25/5.43 = X3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % in_set_conv_nth
% 5.25/5.43 thf(fact_829_list__ball__nth,axiom,
% 5.25/5.43 ! [N: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.25/5.43 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.43 => ( ! [X5: vEBT_VEBT] :
% 5.25/5.43 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.25/5.43 => ( P @ X5 ) )
% 5.25/5.43 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % list_ball_nth
% 5.25/5.43 thf(fact_830_list__ball__nth,axiom,
% 5.25/5.43 ! [N: nat,Xs: list_o,P: $o > $o] :
% 5.25/5.43 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.25/5.43 => ( ! [X5: $o] :
% 5.25/5.43 ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 5.25/5.43 => ( P @ X5 ) )
% 5.25/5.43 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % list_ball_nth
% 5.25/5.43 thf(fact_831_list__ball__nth,axiom,
% 5.25/5.43 ! [N: nat,Xs: list_nat,P: nat > $o] :
% 5.25/5.43 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.25/5.43 => ( ! [X5: nat] :
% 5.25/5.43 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 5.25/5.43 => ( P @ X5 ) )
% 5.25/5.43 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % list_ball_nth
% 5.25/5.43 thf(fact_832_list__ball__nth,axiom,
% 5.25/5.43 ! [N: nat,Xs: list_int,P: int > $o] :
% 5.25/5.43 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.25/5.43 => ( ! [X5: int] :
% 5.25/5.43 ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 5.25/5.43 => ( P @ X5 ) )
% 5.25/5.43 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % list_ball_nth
% 5.25/5.43 thf(fact_833_nth__mem,axiom,
% 5.25/5.43 ! [N: nat,Xs: list_real] :
% 5.25/5.43 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.25/5.43 => ( member_real @ ( nth_real @ Xs @ N ) @ ( set_real2 @ Xs ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % nth_mem
% 5.25/5.43 thf(fact_834_nth__mem,axiom,
% 5.25/5.43 ! [N: nat,Xs: list_complex] :
% 5.25/5.43 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.25/5.43 => ( member_complex @ ( nth_complex @ Xs @ N ) @ ( set_complex2 @ Xs ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % nth_mem
% 5.25/5.43 thf(fact_835_nth__mem,axiom,
% 5.25/5.43 ! [N: nat,Xs: list_P6011104703257516679at_nat] :
% 5.25/5.43 ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs ) )
% 5.25/5.43 => ( member8440522571783428010at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs @ N ) @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % nth_mem
% 5.25/5.43 thf(fact_836_nth__mem,axiom,
% 5.25/5.43 ! [N: nat,Xs: list_VEBT_VEBT] :
% 5.25/5.43 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.43 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % nth_mem
% 5.25/5.43 thf(fact_837_nth__mem,axiom,
% 5.25/5.43 ! [N: nat,Xs: list_o] :
% 5.25/5.43 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.25/5.43 => ( member_o @ ( nth_o @ Xs @ N ) @ ( set_o2 @ Xs ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % nth_mem
% 5.25/5.43 thf(fact_838_nth__mem,axiom,
% 5.25/5.43 ! [N: nat,Xs: list_nat] :
% 5.25/5.43 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.25/5.43 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % nth_mem
% 5.25/5.43 thf(fact_839_nth__mem,axiom,
% 5.25/5.43 ! [N: nat,Xs: list_int] :
% 5.25/5.43 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.25/5.43 => ( member_int @ ( nth_int @ Xs @ N ) @ ( set_int2 @ Xs ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % nth_mem
% 5.25/5.43 thf(fact_840_discrete,axiom,
% 5.25/5.43 ( ord_less_nat
% 5.25/5.43 = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % discrete
% 5.25/5.43 thf(fact_841_discrete,axiom,
% 5.25/5.43 ( ord_less_int
% 5.25/5.43 = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % discrete
% 5.25/5.43 thf(fact_842_low__def,axiom,
% 5.25/5.43 ( vEBT_VEBT_low
% 5.25/5.43 = ( ^ [X2: nat,N2: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % low_def
% 5.25/5.43 thf(fact_843_list__eq__iff__nth__eq,axiom,
% 5.25/5.43 ( ( ^ [Y5: list_VEBT_VEBT,Z3: list_VEBT_VEBT] : ( Y5 = Z3 ) )
% 5.25/5.43 = ( ^ [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.25/5.43 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.25/5.43 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.25/5.43 & ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.25/5.43 => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 5.25/5.43 = ( nth_VEBT_VEBT @ Ys @ I3 ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % list_eq_iff_nth_eq
% 5.25/5.43 thf(fact_844_list__eq__iff__nth__eq,axiom,
% 5.25/5.43 ( ( ^ [Y5: list_o,Z3: list_o] : ( Y5 = Z3 ) )
% 5.25/5.43 = ( ^ [Xs2: list_o,Ys: list_o] :
% 5.25/5.43 ( ( ( size_size_list_o @ Xs2 )
% 5.25/5.43 = ( size_size_list_o @ Ys ) )
% 5.25/5.43 & ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.25/5.43 => ( ( nth_o @ Xs2 @ I3 )
% 5.25/5.43 = ( nth_o @ Ys @ I3 ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % list_eq_iff_nth_eq
% 5.25/5.43 thf(fact_845_list__eq__iff__nth__eq,axiom,
% 5.25/5.43 ( ( ^ [Y5: list_nat,Z3: list_nat] : ( Y5 = Z3 ) )
% 5.25/5.43 = ( ^ [Xs2: list_nat,Ys: list_nat] :
% 5.25/5.43 ( ( ( size_size_list_nat @ Xs2 )
% 5.25/5.43 = ( size_size_list_nat @ Ys ) )
% 5.25/5.43 & ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.25/5.43 => ( ( nth_nat @ Xs2 @ I3 )
% 5.25/5.43 = ( nth_nat @ Ys @ I3 ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % list_eq_iff_nth_eq
% 5.25/5.43 thf(fact_846_list__eq__iff__nth__eq,axiom,
% 5.25/5.43 ( ( ^ [Y5: list_int,Z3: list_int] : ( Y5 = Z3 ) )
% 5.25/5.43 = ( ^ [Xs2: list_int,Ys: list_int] :
% 5.25/5.43 ( ( ( size_size_list_int @ Xs2 )
% 5.25/5.43 = ( size_size_list_int @ Ys ) )
% 5.25/5.43 & ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.25/5.43 => ( ( nth_int @ Xs2 @ I3 )
% 5.25/5.43 = ( nth_int @ Ys @ I3 ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % list_eq_iff_nth_eq
% 5.25/5.43 thf(fact_847_Skolem__list__nth,axiom,
% 5.25/5.43 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.25/5.43 ( ( ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.43 => ? [X4: vEBT_VEBT] : ( P @ I3 @ X4 ) ) )
% 5.25/5.43 = ( ? [Xs2: list_VEBT_VEBT] :
% 5.25/5.43 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.25/5.43 = K )
% 5.25/5.43 & ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.43 => ( P @ I3 @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % Skolem_list_nth
% 5.25/5.43 thf(fact_848_Skolem__list__nth,axiom,
% 5.25/5.43 ! [K: nat,P: nat > $o > $o] :
% 5.25/5.43 ( ( ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.43 => ? [X4: $o] : ( P @ I3 @ X4 ) ) )
% 5.25/5.43 = ( ? [Xs2: list_o] :
% 5.25/5.43 ( ( ( size_size_list_o @ Xs2 )
% 5.25/5.43 = K )
% 5.25/5.43 & ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.43 => ( P @ I3 @ ( nth_o @ Xs2 @ I3 ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % Skolem_list_nth
% 5.25/5.43 thf(fact_849_Skolem__list__nth,axiom,
% 5.25/5.43 ! [K: nat,P: nat > nat > $o] :
% 5.25/5.43 ( ( ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.43 => ? [X4: nat] : ( P @ I3 @ X4 ) ) )
% 5.25/5.43 = ( ? [Xs2: list_nat] :
% 5.25/5.43 ( ( ( size_size_list_nat @ Xs2 )
% 5.25/5.43 = K )
% 5.25/5.43 & ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.43 => ( P @ I3 @ ( nth_nat @ Xs2 @ I3 ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % Skolem_list_nth
% 5.25/5.43 thf(fact_850_Skolem__list__nth,axiom,
% 5.25/5.43 ! [K: nat,P: nat > int > $o] :
% 5.25/5.43 ( ( ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.43 => ? [X4: int] : ( P @ I3 @ X4 ) ) )
% 5.25/5.43 = ( ? [Xs2: list_int] :
% 5.25/5.43 ( ( ( size_size_list_int @ Xs2 )
% 5.25/5.43 = K )
% 5.25/5.43 & ! [I3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.43 => ( P @ I3 @ ( nth_int @ Xs2 @ I3 ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % Skolem_list_nth
% 5.25/5.43 thf(fact_851_nth__equalityI,axiom,
% 5.25/5.43 ! [Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 5.25/5.43 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.25/5.43 = ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 5.25/5.43 => ( ! [I4: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.43 => ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 5.25/5.43 = ( nth_VEBT_VEBT @ Ys2 @ I4 ) ) )
% 5.25/5.43 => ( Xs = Ys2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % nth_equalityI
% 5.25/5.43 thf(fact_852_nth__equalityI,axiom,
% 5.25/5.43 ! [Xs: list_o,Ys2: list_o] :
% 5.25/5.43 ( ( ( size_size_list_o @ Xs )
% 5.25/5.43 = ( size_size_list_o @ Ys2 ) )
% 5.25/5.43 => ( ! [I4: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.25/5.43 => ( ( nth_o @ Xs @ I4 )
% 5.25/5.43 = ( nth_o @ Ys2 @ I4 ) ) )
% 5.25/5.43 => ( Xs = Ys2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % nth_equalityI
% 5.25/5.43 thf(fact_853_nth__equalityI,axiom,
% 5.25/5.43 ! [Xs: list_nat,Ys2: list_nat] :
% 5.25/5.43 ( ( ( size_size_list_nat @ Xs )
% 5.25/5.43 = ( size_size_list_nat @ Ys2 ) )
% 5.25/5.43 => ( ! [I4: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.43 => ( ( nth_nat @ Xs @ I4 )
% 5.25/5.43 = ( nth_nat @ Ys2 @ I4 ) ) )
% 5.25/5.43 => ( Xs = Ys2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % nth_equalityI
% 5.25/5.43 thf(fact_854_nth__equalityI,axiom,
% 5.25/5.43 ! [Xs: list_int,Ys2: list_int] :
% 5.25/5.43 ( ( ( size_size_list_int @ Xs )
% 5.25/5.43 = ( size_size_list_int @ Ys2 ) )
% 5.25/5.43 => ( ! [I4: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 5.25/5.43 => ( ( nth_int @ Xs @ I4 )
% 5.25/5.43 = ( nth_int @ Ys2 @ I4 ) ) )
% 5.25/5.43 => ( Xs = Ys2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % nth_equalityI
% 5.25/5.43 thf(fact_855_zdiv__numeral__Bit0,axiom,
% 5.25/5.43 ! [V: num,W: num] :
% 5.25/5.43 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.25/5.43 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % zdiv_numeral_Bit0
% 5.25/5.43 thf(fact_856_mod__mod__trivial,axiom,
% 5.25/5.43 ! [A: nat,B: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.25/5.43 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mod_trivial
% 5.25/5.43 thf(fact_857_mod__mod__trivial,axiom,
% 5.25/5.43 ! [A: int,B: int] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.25/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mod_trivial
% 5.25/5.43 thf(fact_858_mod__mod__trivial,axiom,
% 5.25/5.43 ! [A: code_integer,B: code_integer] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.25/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mod_trivial
% 5.25/5.43 thf(fact_859_real__divide__square__eq,axiom,
% 5.25/5.43 ! [R2: real,A: real] :
% 5.25/5.43 ( ( divide_divide_real @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ R2 ) )
% 5.25/5.43 = ( divide_divide_real @ A @ R2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % real_divide_square_eq
% 5.25/5.43 thf(fact_860_mod__add__self1,axiom,
% 5.25/5.43 ! [B: nat,A: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.25/5.43 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_self1
% 5.25/5.43 thf(fact_861_mod__add__self1,axiom,
% 5.25/5.43 ! [B: int,A: int] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.25/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_self1
% 5.25/5.43 thf(fact_862_mod__add__self1,axiom,
% 5.25/5.43 ! [B: code_integer,A: code_integer] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.25/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_self1
% 5.25/5.43 thf(fact_863_mod__add__self2,axiom,
% 5.25/5.43 ! [A: nat,B: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.25/5.43 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_self2
% 5.25/5.43 thf(fact_864_mod__add__self2,axiom,
% 5.25/5.43 ! [A: int,B: int] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.25/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_self2
% 5.25/5.43 thf(fact_865_mod__add__self2,axiom,
% 5.25/5.43 ! [A: code_integer,B: code_integer] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.25/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_self2
% 5.25/5.43 thf(fact_866_mod__less,axiom,
% 5.25/5.43 ! [M: nat,N: nat] :
% 5.25/5.43 ( ( ord_less_nat @ M @ N )
% 5.25/5.43 => ( ( modulo_modulo_nat @ M @ N )
% 5.25/5.43 = M ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_less
% 5.25/5.43 thf(fact_867_mod__mult__self4,axiom,
% 5.25/5.43 ! [B: nat,C: nat,A: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.25/5.43 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_self4
% 5.25/5.43 thf(fact_868_mod__mult__self4,axiom,
% 5.25/5.43 ! [B: int,C: int,A: int] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.25/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_self4
% 5.25/5.43 thf(fact_869_mod__mult__self4,axiom,
% 5.25/5.43 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 5.25/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_self4
% 5.25/5.43 thf(fact_870_mod__mult__self3,axiom,
% 5.25/5.43 ! [C: nat,B: nat,A: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.25/5.43 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_self3
% 5.25/5.43 thf(fact_871_mod__mult__self3,axiom,
% 5.25/5.43 ! [C: int,B: int,A: int] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.25/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_self3
% 5.25/5.43 thf(fact_872_mod__mult__self3,axiom,
% 5.25/5.43 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 5.25/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_self3
% 5.25/5.43 thf(fact_873_mod__mult__self2,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.25/5.43 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_self2
% 5.25/5.43 thf(fact_874_mod__mult__self2,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.25/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_self2
% 5.25/5.43 thf(fact_875_mod__mult__self2,axiom,
% 5.25/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 5.25/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_self2
% 5.25/5.43 thf(fact_876_mod__mult__self1,axiom,
% 5.25/5.43 ! [A: nat,C: nat,B: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.25/5.43 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_self1
% 5.25/5.43 thf(fact_877_mod__mult__self1,axiom,
% 5.25/5.43 ! [A: int,C: int,B: int] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.25/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_self1
% 5.25/5.43 thf(fact_878_mod__mult__self1,axiom,
% 5.25/5.43 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 5.25/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_self1
% 5.25/5.43 thf(fact_879_Suc__mod__mult__self4,axiom,
% 5.25/5.43 ! [N: nat,K: nat,M: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 5.25/5.43 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.25/5.43
% 5.25/5.43 % Suc_mod_mult_self4
% 5.25/5.43 thf(fact_880_Suc__mod__mult__self3,axiom,
% 5.25/5.43 ! [K: nat,N: nat,M: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 5.25/5.43 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.25/5.43
% 5.25/5.43 % Suc_mod_mult_self3
% 5.25/5.43 thf(fact_881_Suc__mod__mult__self2,axiom,
% 5.25/5.43 ! [M: nat,N: nat,K: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 5.25/5.43 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.25/5.43
% 5.25/5.43 % Suc_mod_mult_self2
% 5.25/5.43 thf(fact_882_Suc__mod__mult__self1,axiom,
% 5.25/5.43 ! [M: nat,K: nat,N: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 5.25/5.43 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.25/5.43
% 5.25/5.43 % Suc_mod_mult_self1
% 5.25/5.43 thf(fact_883_bits__one__mod__two__eq__one,axiom,
% 5.25/5.43 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.43 = one_one_nat ) ).
% 5.25/5.43
% 5.25/5.43 % bits_one_mod_two_eq_one
% 5.25/5.43 thf(fact_884_bits__one__mod__two__eq__one,axiom,
% 5.25/5.43 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.43 = one_one_int ) ).
% 5.25/5.43
% 5.25/5.43 % bits_one_mod_two_eq_one
% 5.25/5.43 thf(fact_885_bits__one__mod__two__eq__one,axiom,
% 5.25/5.43 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.43 = one_one_Code_integer ) ).
% 5.25/5.43
% 5.25/5.43 % bits_one_mod_two_eq_one
% 5.25/5.43 thf(fact_886_one__mod__two__eq__one,axiom,
% 5.25/5.43 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.43 = one_one_nat ) ).
% 5.25/5.43
% 5.25/5.43 % one_mod_two_eq_one
% 5.25/5.43 thf(fact_887_one__mod__two__eq__one,axiom,
% 5.25/5.43 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.43 = one_one_int ) ).
% 5.25/5.43
% 5.25/5.43 % one_mod_two_eq_one
% 5.25/5.43 thf(fact_888_one__mod__two__eq__one,axiom,
% 5.25/5.43 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.43 = one_one_Code_integer ) ).
% 5.25/5.43
% 5.25/5.43 % one_mod_two_eq_one
% 5.25/5.43 thf(fact_889_mod2__Suc__Suc,axiom,
% 5.25/5.43 ! [M: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.43 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod2_Suc_Suc
% 5.25/5.43 thf(fact_890_Suc__times__numeral__mod__eq,axiom,
% 5.25/5.43 ! [K: num,N: nat] :
% 5.25/5.43 ( ( ( numeral_numeral_nat @ K )
% 5.25/5.43 != one_one_nat )
% 5.25/5.43 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 5.25/5.43 = one_one_nat ) ) ).
% 5.25/5.43
% 5.25/5.43 % Suc_times_numeral_mod_eq
% 5.25/5.43 thf(fact_891_real__arch__pow,axiom,
% 5.25/5.43 ! [X3: real,Y: real] :
% 5.25/5.43 ( ( ord_less_real @ one_one_real @ X3 )
% 5.25/5.43 => ? [N3: nat] : ( ord_less_real @ Y @ ( power_power_real @ X3 @ N3 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % real_arch_pow
% 5.25/5.43 thf(fact_892_less__eq__real__def,axiom,
% 5.25/5.43 ( ord_less_eq_real
% 5.25/5.43 = ( ^ [X2: real,Y6: real] :
% 5.25/5.43 ( ( ord_less_real @ X2 @ Y6 )
% 5.25/5.43 | ( X2 = Y6 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % less_eq_real_def
% 5.25/5.43 thf(fact_893_complete__real,axiom,
% 5.25/5.43 ! [S3: set_real] :
% 5.25/5.43 ( ? [X: real] : ( member_real @ X @ S3 )
% 5.25/5.43 => ( ? [Z4: real] :
% 5.25/5.43 ! [X5: real] :
% 5.25/5.43 ( ( member_real @ X5 @ S3 )
% 5.25/5.43 => ( ord_less_eq_real @ X5 @ Z4 ) )
% 5.25/5.43 => ? [Y3: real] :
% 5.25/5.43 ( ! [X: real] :
% 5.25/5.43 ( ( member_real @ X @ S3 )
% 5.25/5.43 => ( ord_less_eq_real @ X @ Y3 ) )
% 5.25/5.43 & ! [Z4: real] :
% 5.25/5.43 ( ! [X5: real] :
% 5.25/5.43 ( ( member_real @ X5 @ S3 )
% 5.25/5.43 => ( ord_less_eq_real @ X5 @ Z4 ) )
% 5.25/5.43 => ( ord_less_eq_real @ Y3 @ Z4 ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % complete_real
% 5.25/5.43 thf(fact_894_mod__mult__eq,axiom,
% 5.25/5.43 ! [A: nat,C: nat,B: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.25/5.43 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_eq
% 5.25/5.43 thf(fact_895_mod__mult__eq,axiom,
% 5.25/5.43 ! [A: int,C: int,B: int] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.25/5.43 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_eq
% 5.25/5.43 thf(fact_896_mod__mult__eq,axiom,
% 5.25/5.43 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.25/5.43 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_eq
% 5.25/5.43 thf(fact_897_mod__mult__cong,axiom,
% 5.25/5.43 ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 5.25/5.43 ( ( ( modulo_modulo_nat @ A @ C )
% 5.25/5.43 = ( modulo_modulo_nat @ A4 @ C ) )
% 5.25/5.43 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.25/5.43 = ( modulo_modulo_nat @ B4 @ C ) )
% 5.25/5.43 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.43 = ( modulo_modulo_nat @ ( times_times_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_cong
% 5.25/5.43 thf(fact_898_mod__mult__cong,axiom,
% 5.25/5.43 ! [A: int,C: int,A4: int,B: int,B4: int] :
% 5.25/5.43 ( ( ( modulo_modulo_int @ A @ C )
% 5.25/5.43 = ( modulo_modulo_int @ A4 @ C ) )
% 5.25/5.43 => ( ( ( modulo_modulo_int @ B @ C )
% 5.25/5.43 = ( modulo_modulo_int @ B4 @ C ) )
% 5.25/5.43 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.43 = ( modulo_modulo_int @ ( times_times_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_cong
% 5.25/5.43 thf(fact_899_mod__mult__cong,axiom,
% 5.25/5.43 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 5.25/5.43 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.25/5.43 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 5.25/5.43 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.25/5.43 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.25/5.43 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.25/5.43 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_cong
% 5.25/5.43 thf(fact_900_mod__mult__mult2,axiom,
% 5.25/5.43 ! [A: nat,C: nat,B: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.25/5.43 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_mult2
% 5.25/5.43 thf(fact_901_mod__mult__mult2,axiom,
% 5.25/5.43 ! [A: int,C: int,B: int] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.43 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_mult2
% 5.25/5.43 thf(fact_902_mod__mult__mult2,axiom,
% 5.25/5.43 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.25/5.43 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_mult2
% 5.25/5.43 thf(fact_903_mult__mod__right,axiom,
% 5.25/5.43 ! [C: nat,A: nat,B: nat] :
% 5.25/5.43 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.25/5.43 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_mod_right
% 5.25/5.43 thf(fact_904_mult__mod__right,axiom,
% 5.25/5.43 ! [C: int,A: int,B: int] :
% 5.25/5.43 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.25/5.43 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_mod_right
% 5.25/5.43 thf(fact_905_mult__mod__right,axiom,
% 5.25/5.43 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.43 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.25/5.43 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_mod_right
% 5.25/5.43 thf(fact_906_mod__mult__left__eq,axiom,
% 5.25/5.43 ! [A: nat,C: nat,B: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.25/5.43 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_left_eq
% 5.25/5.43 thf(fact_907_mod__mult__left__eq,axiom,
% 5.25/5.43 ! [A: int,C: int,B: int] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.25/5.43 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_left_eq
% 5.25/5.43 thf(fact_908_mod__mult__left__eq,axiom,
% 5.25/5.43 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.25/5.43 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_left_eq
% 5.25/5.43 thf(fact_909_mod__mult__right__eq,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.25/5.43 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_right_eq
% 5.25/5.43 thf(fact_910_mod__mult__right__eq,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.25/5.43 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_right_eq
% 5.25/5.43 thf(fact_911_mod__mult__right__eq,axiom,
% 5.25/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.25/5.43 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_right_eq
% 5.25/5.43 thf(fact_912_mod__add__eq,axiom,
% 5.25/5.43 ! [A: nat,C: nat,B: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.25/5.43 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_eq
% 5.25/5.43 thf(fact_913_mod__add__eq,axiom,
% 5.25/5.43 ! [A: int,C: int,B: int] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.25/5.43 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_eq
% 5.25/5.43 thf(fact_914_mod__add__eq,axiom,
% 5.25/5.43 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.25/5.43 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_eq
% 5.25/5.43 thf(fact_915_mod__add__cong,axiom,
% 5.25/5.43 ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 5.25/5.43 ( ( ( modulo_modulo_nat @ A @ C )
% 5.25/5.43 = ( modulo_modulo_nat @ A4 @ C ) )
% 5.25/5.43 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.25/5.43 = ( modulo_modulo_nat @ B4 @ C ) )
% 5.25/5.43 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.43 = ( modulo_modulo_nat @ ( plus_plus_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_cong
% 5.25/5.43 thf(fact_916_mod__add__cong,axiom,
% 5.25/5.43 ! [A: int,C: int,A4: int,B: int,B4: int] :
% 5.25/5.43 ( ( ( modulo_modulo_int @ A @ C )
% 5.25/5.43 = ( modulo_modulo_int @ A4 @ C ) )
% 5.25/5.43 => ( ( ( modulo_modulo_int @ B @ C )
% 5.25/5.43 = ( modulo_modulo_int @ B4 @ C ) )
% 5.25/5.43 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.43 = ( modulo_modulo_int @ ( plus_plus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_cong
% 5.25/5.43 thf(fact_917_mod__add__cong,axiom,
% 5.25/5.43 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 5.25/5.43 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.25/5.43 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 5.25/5.43 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.25/5.43 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.25/5.43 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.25/5.43 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_cong
% 5.25/5.43 thf(fact_918_mod__add__left__eq,axiom,
% 5.25/5.43 ! [A: nat,C: nat,B: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.25/5.43 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_left_eq
% 5.25/5.43 thf(fact_919_mod__add__left__eq,axiom,
% 5.25/5.43 ! [A: int,C: int,B: int] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.25/5.43 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_left_eq
% 5.25/5.43 thf(fact_920_mod__add__left__eq,axiom,
% 5.25/5.43 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.25/5.43 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_left_eq
% 5.25/5.43 thf(fact_921_mod__add__right__eq,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.25/5.43 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_right_eq
% 5.25/5.43 thf(fact_922_mod__add__right__eq,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.25/5.43 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_right_eq
% 5.25/5.43 thf(fact_923_mod__add__right__eq,axiom,
% 5.25/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.25/5.43 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_add_right_eq
% 5.25/5.43 thf(fact_924_power__mod,axiom,
% 5.25/5.43 ! [A: nat,B: nat,N: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 5.25/5.43 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_mod
% 5.25/5.43 thf(fact_925_power__mod,axiom,
% 5.25/5.43 ! [A: int,B: int,N: nat] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 5.25/5.43 = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_mod
% 5.25/5.43 thf(fact_926_power__mod,axiom,
% 5.25/5.43 ! [A: code_integer,B: code_integer,N: nat] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N ) @ B )
% 5.25/5.43 = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N ) @ B ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_mod
% 5.25/5.43 thf(fact_927_mod__Suc__eq,axiom,
% 5.25/5.43 ! [M: nat,N: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 5.25/5.43 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_Suc_eq
% 5.25/5.43 thf(fact_928_mod__Suc__Suc__eq,axiom,
% 5.25/5.43 ! [M: nat,N: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 5.25/5.43 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_Suc_Suc_eq
% 5.25/5.43 thf(fact_929_mod__less__eq__dividend,axiom,
% 5.25/5.43 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 5.25/5.43
% 5.25/5.43 % mod_less_eq_dividend
% 5.25/5.43 thf(fact_930_cong__exp__iff__simps_I9_J,axiom,
% 5.25/5.43 ! [M: num,Q2: num,N: num] :
% 5.25/5.43 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.25/5.43 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.25/5.43 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.25/5.43 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % cong_exp_iff_simps(9)
% 5.25/5.43 thf(fact_931_cong__exp__iff__simps_I9_J,axiom,
% 5.25/5.43 ! [M: num,Q2: num,N: num] :
% 5.25/5.43 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.25/5.43 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.25/5.43 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.25/5.43 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % cong_exp_iff_simps(9)
% 5.25/5.43 thf(fact_932_cong__exp__iff__simps_I9_J,axiom,
% 5.25/5.43 ! [M: num,Q2: num,N: num] :
% 5.25/5.43 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.25/5.43 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.25/5.43 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.25/5.43 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % cong_exp_iff_simps(9)
% 5.25/5.43 thf(fact_933_cong__exp__iff__simps_I4_J,axiom,
% 5.25/5.43 ! [M: num,N: num] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.25/5.43 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % cong_exp_iff_simps(4)
% 5.25/5.43 thf(fact_934_cong__exp__iff__simps_I4_J,axiom,
% 5.25/5.43 ! [M: num,N: num] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.25/5.43 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % cong_exp_iff_simps(4)
% 5.25/5.43 thf(fact_935_cong__exp__iff__simps_I4_J,axiom,
% 5.25/5.43 ! [M: num,N: num] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 5.25/5.43 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % cong_exp_iff_simps(4)
% 5.25/5.43 thf(fact_936_nat__mod__eq__iff,axiom,
% 5.25/5.43 ! [X3: nat,N: nat,Y: nat] :
% 5.25/5.43 ( ( ( modulo_modulo_nat @ X3 @ N )
% 5.25/5.43 = ( modulo_modulo_nat @ Y @ N ) )
% 5.25/5.43 = ( ? [Q1: nat,Q22: nat] :
% 5.25/5.43 ( ( plus_plus_nat @ X3 @ ( times_times_nat @ N @ Q1 ) )
% 5.25/5.43 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % nat_mod_eq_iff
% 5.25/5.43 thf(fact_937_cong__exp__iff__simps_I8_J,axiom,
% 5.25/5.43 ! [M: num,Q2: num] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.25/5.43 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % cong_exp_iff_simps(8)
% 5.25/5.43 thf(fact_938_cong__exp__iff__simps_I8_J,axiom,
% 5.25/5.43 ! [M: num,Q2: num] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.25/5.43 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % cong_exp_iff_simps(8)
% 5.25/5.43 thf(fact_939_cong__exp__iff__simps_I8_J,axiom,
% 5.25/5.43 ! [M: num,Q2: num] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.25/5.43 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % cong_exp_iff_simps(8)
% 5.25/5.43 thf(fact_940_cong__exp__iff__simps_I6_J,axiom,
% 5.25/5.43 ! [Q2: num,N: num] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.25/5.43 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % cong_exp_iff_simps(6)
% 5.25/5.43 thf(fact_941_cong__exp__iff__simps_I6_J,axiom,
% 5.25/5.43 ! [Q2: num,N: num] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.25/5.43 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % cong_exp_iff_simps(6)
% 5.25/5.43 thf(fact_942_cong__exp__iff__simps_I6_J,axiom,
% 5.25/5.43 ! [Q2: num,N: num] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.25/5.43 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % cong_exp_iff_simps(6)
% 5.25/5.43 thf(fact_943_mod__eqE,axiom,
% 5.25/5.43 ! [A: int,C: int,B: int] :
% 5.25/5.43 ( ( ( modulo_modulo_int @ A @ C )
% 5.25/5.43 = ( modulo_modulo_int @ B @ C ) )
% 5.25/5.43 => ~ ! [D3: int] :
% 5.25/5.43 ( B
% 5.25/5.43 != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_eqE
% 5.25/5.43 thf(fact_944_mod__eqE,axiom,
% 5.25/5.43 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.43 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.25/5.43 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.25/5.43 => ~ ! [D3: code_integer] :
% 5.25/5.43 ( B
% 5.25/5.43 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_eqE
% 5.25/5.43 thf(fact_945_div__add1__eq,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.43 = ( 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 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_add1_eq
% 5.25/5.43 thf(fact_946_div__add1__eq,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.43 = ( 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 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_add1_eq
% 5.25/5.43 thf(fact_947_div__add1__eq,axiom,
% 5.25/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.43 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.25/5.43 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_add1_eq
% 5.25/5.43 thf(fact_948_mod__induct,axiom,
% 5.25/5.43 ! [P: nat > $o,N: nat,P2: nat,M: nat] :
% 5.25/5.43 ( ( P @ N )
% 5.25/5.43 => ( ( ord_less_nat @ N @ P2 )
% 5.25/5.43 => ( ( ord_less_nat @ M @ P2 )
% 5.25/5.43 => ( ! [N3: nat] :
% 5.25/5.43 ( ( ord_less_nat @ N3 @ P2 )
% 5.25/5.43 => ( ( P @ N3 )
% 5.25/5.43 => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P2 ) ) ) )
% 5.25/5.43 => ( P @ M ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_induct
% 5.25/5.43 thf(fact_949_mod__Suc__le__divisor,axiom,
% 5.25/5.43 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 5.25/5.43
% 5.25/5.43 % mod_Suc_le_divisor
% 5.25/5.43 thf(fact_950_nat__mod__eq__lemma,axiom,
% 5.25/5.43 ! [X3: nat,N: nat,Y: nat] :
% 5.25/5.43 ( ( ( modulo_modulo_nat @ X3 @ N )
% 5.25/5.43 = ( modulo_modulo_nat @ Y @ N ) )
% 5.25/5.43 => ( ( ord_less_eq_nat @ Y @ X3 )
% 5.25/5.43 => ? [Q3: nat] :
% 5.25/5.43 ( X3
% 5.25/5.43 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % nat_mod_eq_lemma
% 5.25/5.43 thf(fact_951_mod__eq__nat2E,axiom,
% 5.25/5.43 ! [M: nat,Q2: nat,N: nat] :
% 5.25/5.43 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.25/5.43 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.25/5.43 => ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.43 => ~ ! [S2: nat] :
% 5.25/5.43 ( N
% 5.25/5.43 != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S2 ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_eq_nat2E
% 5.25/5.43 thf(fact_952_mod__eq__nat1E,axiom,
% 5.25/5.43 ! [M: nat,Q2: nat,N: nat] :
% 5.25/5.43 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.25/5.43 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.25/5.43 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.43 => ~ ! [S2: nat] :
% 5.25/5.43 ( M
% 5.25/5.43 != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S2 ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_eq_nat1E
% 5.25/5.43 thf(fact_953_div__mult1__eq,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.43 = ( 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 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_mult1_eq
% 5.25/5.43 thf(fact_954_div__mult1__eq,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.43 = ( 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 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_mult1_eq
% 5.25/5.43 thf(fact_955_div__mult1__eq,axiom,
% 5.25/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.43 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.25/5.43 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_mult1_eq
% 5.25/5.43 thf(fact_956_cancel__div__mod__rules_I2_J,axiom,
% 5.25/5.43 ! [B: nat,A: nat,C: nat] :
% 5.25/5.43 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.25/5.43 = ( plus_plus_nat @ A @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % cancel_div_mod_rules(2)
% 5.25/5.43 thf(fact_957_cancel__div__mod__rules_I2_J,axiom,
% 5.25/5.43 ! [B: int,A: int,C: int] :
% 5.25/5.43 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.25/5.43 = ( plus_plus_int @ A @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % cancel_div_mod_rules(2)
% 5.25/5.43 thf(fact_958_cancel__div__mod__rules_I2_J,axiom,
% 5.25/5.43 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.43 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.25/5.43 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % cancel_div_mod_rules(2)
% 5.25/5.43 thf(fact_959_cancel__div__mod__rules_I1_J,axiom,
% 5.25/5.43 ! [A: nat,B: nat,C: nat] :
% 5.25/5.43 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.25/5.43 = ( plus_plus_nat @ A @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % cancel_div_mod_rules(1)
% 5.25/5.43 thf(fact_960_cancel__div__mod__rules_I1_J,axiom,
% 5.25/5.43 ! [A: int,B: int,C: int] :
% 5.25/5.43 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.25/5.43 = ( plus_plus_int @ A @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % cancel_div_mod_rules(1)
% 5.25/5.43 thf(fact_961_cancel__div__mod__rules_I1_J,axiom,
% 5.25/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.43 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.25/5.43 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.25/5.43
% 5.25/5.43 % cancel_div_mod_rules(1)
% 5.25/5.43 thf(fact_962_mod__div__decomp,axiom,
% 5.25/5.43 ! [A: nat,B: nat] :
% 5.25/5.43 ( A
% 5.25/5.43 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_div_decomp
% 5.25/5.43 thf(fact_963_mod__div__decomp,axiom,
% 5.25/5.43 ! [A: int,B: int] :
% 5.25/5.43 ( A
% 5.25/5.43 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_div_decomp
% 5.25/5.43 thf(fact_964_mod__div__decomp,axiom,
% 5.25/5.43 ! [A: code_integer,B: code_integer] :
% 5.25/5.43 ( A
% 5.25/5.43 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_div_decomp
% 5.25/5.43 thf(fact_965_div__mult__mod__eq,axiom,
% 5.25/5.43 ! [A: nat,B: nat] :
% 5.25/5.43 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % div_mult_mod_eq
% 5.25/5.43 thf(fact_966_div__mult__mod__eq,axiom,
% 5.25/5.43 ! [A: int,B: int] :
% 5.25/5.43 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % div_mult_mod_eq
% 5.25/5.43 thf(fact_967_div__mult__mod__eq,axiom,
% 5.25/5.43 ! [A: code_integer,B: code_integer] :
% 5.25/5.43 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % div_mult_mod_eq
% 5.25/5.43 thf(fact_968_mod__div__mult__eq,axiom,
% 5.25/5.43 ! [A: nat,B: nat] :
% 5.25/5.43 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % mod_div_mult_eq
% 5.25/5.43 thf(fact_969_mod__div__mult__eq,axiom,
% 5.25/5.43 ! [A: int,B: int] :
% 5.25/5.43 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % mod_div_mult_eq
% 5.25/5.43 thf(fact_970_mod__div__mult__eq,axiom,
% 5.25/5.43 ! [A: code_integer,B: code_integer] :
% 5.25/5.43 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % mod_div_mult_eq
% 5.25/5.43 thf(fact_971_mod__mult__div__eq,axiom,
% 5.25/5.43 ! [A: nat,B: nat] :
% 5.25/5.43 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_div_eq
% 5.25/5.43 thf(fact_972_mod__mult__div__eq,axiom,
% 5.25/5.43 ! [A: int,B: int] :
% 5.25/5.43 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_div_eq
% 5.25/5.43 thf(fact_973_mod__mult__div__eq,axiom,
% 5.25/5.43 ! [A: code_integer,B: code_integer] :
% 5.25/5.43 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult_div_eq
% 5.25/5.43 thf(fact_974_mult__div__mod__eq,axiom,
% 5.25/5.43 ! [B: nat,A: nat] :
% 5.25/5.43 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % mult_div_mod_eq
% 5.25/5.43 thf(fact_975_mult__div__mod__eq,axiom,
% 5.25/5.43 ! [B: int,A: int] :
% 5.25/5.43 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % mult_div_mod_eq
% 5.25/5.43 thf(fact_976_mult__div__mod__eq,axiom,
% 5.25/5.43 ! [B: code_integer,A: code_integer] :
% 5.25/5.43 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % mult_div_mod_eq
% 5.25/5.43 thf(fact_977_mod__mult2__eq,axiom,
% 5.25/5.43 ! [M: nat,N: nat,Q2: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.25/5.43 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mod_mult2_eq
% 5.25/5.43 thf(fact_978_bounded__Max__nat,axiom,
% 5.25/5.43 ! [P: nat > $o,X3: nat,M7: nat] :
% 5.25/5.43 ( ( P @ X3 )
% 5.25/5.43 => ( ! [X5: nat] :
% 5.25/5.43 ( ( P @ X5 )
% 5.25/5.43 => ( ord_less_eq_nat @ X5 @ M7 ) )
% 5.25/5.43 => ~ ! [M5: nat] :
% 5.25/5.43 ( ( P @ M5 )
% 5.25/5.43 => ~ ! [X: nat] :
% 5.25/5.43 ( ( P @ X )
% 5.25/5.43 => ( ord_less_eq_nat @ X @ M5 ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % bounded_Max_nat
% 5.25/5.43 thf(fact_979_subset__code_I1_J,axiom,
% 5.25/5.43 ! [Xs: list_real,B3: set_real] :
% 5.25/5.43 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B3 )
% 5.25/5.43 = ( ! [X2: real] :
% 5.25/5.43 ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 5.25/5.43 => ( member_real @ X2 @ B3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % subset_code(1)
% 5.25/5.43 thf(fact_980_subset__code_I1_J,axiom,
% 5.25/5.43 ! [Xs: list_complex,B3: set_complex] :
% 5.25/5.43 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ B3 )
% 5.25/5.43 = ( ! [X2: complex] :
% 5.25/5.43 ( ( member_complex @ X2 @ ( set_complex2 @ Xs ) )
% 5.25/5.43 => ( member_complex @ X2 @ B3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % subset_code(1)
% 5.25/5.43 thf(fact_981_subset__code_I1_J,axiom,
% 5.25/5.43 ! [Xs: list_P6011104703257516679at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.25/5.43 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ B3 )
% 5.25/5.43 = ( ! [X2: product_prod_nat_nat] :
% 5.25/5.43 ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 5.25/5.43 => ( member8440522571783428010at_nat @ X2 @ B3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % subset_code(1)
% 5.25/5.43 thf(fact_982_subset__code_I1_J,axiom,
% 5.25/5.43 ! [Xs: list_VEBT_VEBT,B3: set_VEBT_VEBT] :
% 5.25/5.43 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B3 )
% 5.25/5.43 = ( ! [X2: vEBT_VEBT] :
% 5.25/5.43 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.25/5.43 => ( member_VEBT_VEBT @ X2 @ B3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % subset_code(1)
% 5.25/5.43 thf(fact_983_subset__code_I1_J,axiom,
% 5.25/5.43 ! [Xs: list_nat,B3: set_nat] :
% 5.25/5.43 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B3 )
% 5.25/5.43 = ( ! [X2: nat] :
% 5.25/5.43 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 5.25/5.43 => ( member_nat @ X2 @ B3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % subset_code(1)
% 5.25/5.43 thf(fact_984_subset__code_I1_J,axiom,
% 5.25/5.43 ! [Xs: list_int,B3: set_int] :
% 5.25/5.43 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B3 )
% 5.25/5.43 = ( ! [X2: int] :
% 5.25/5.43 ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 5.25/5.43 => ( member_int @ X2 @ B3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % subset_code(1)
% 5.25/5.43 thf(fact_985_Ex__list__of__length,axiom,
% 5.25/5.43 ! [N: nat] :
% 5.25/5.43 ? [Xs3: list_VEBT_VEBT] :
% 5.25/5.43 ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.25/5.43 = N ) ).
% 5.25/5.43
% 5.25/5.43 % Ex_list_of_length
% 5.25/5.43 thf(fact_986_Ex__list__of__length,axiom,
% 5.25/5.43 ! [N: nat] :
% 5.25/5.43 ? [Xs3: list_o] :
% 5.25/5.43 ( ( size_size_list_o @ Xs3 )
% 5.25/5.43 = N ) ).
% 5.25/5.43
% 5.25/5.43 % Ex_list_of_length
% 5.25/5.43 thf(fact_987_Ex__list__of__length,axiom,
% 5.25/5.43 ! [N: nat] :
% 5.25/5.43 ? [Xs3: list_nat] :
% 5.25/5.43 ( ( size_size_list_nat @ Xs3 )
% 5.25/5.43 = N ) ).
% 5.25/5.43
% 5.25/5.43 % Ex_list_of_length
% 5.25/5.43 thf(fact_988_Ex__list__of__length,axiom,
% 5.25/5.43 ! [N: nat] :
% 5.25/5.43 ? [Xs3: list_int] :
% 5.25/5.43 ( ( size_size_list_int @ Xs3 )
% 5.25/5.43 = N ) ).
% 5.25/5.43
% 5.25/5.43 % Ex_list_of_length
% 5.25/5.43 thf(fact_989_neq__if__length__neq,axiom,
% 5.25/5.43 ! [Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 5.25/5.43 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.25/5.43 != ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 5.25/5.43 => ( Xs != Ys2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % neq_if_length_neq
% 5.25/5.43 thf(fact_990_neq__if__length__neq,axiom,
% 5.25/5.43 ! [Xs: list_o,Ys2: list_o] :
% 5.25/5.43 ( ( ( size_size_list_o @ Xs )
% 5.25/5.43 != ( size_size_list_o @ Ys2 ) )
% 5.25/5.43 => ( Xs != Ys2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % neq_if_length_neq
% 5.25/5.43 thf(fact_991_neq__if__length__neq,axiom,
% 5.25/5.43 ! [Xs: list_nat,Ys2: list_nat] :
% 5.25/5.43 ( ( ( size_size_list_nat @ Xs )
% 5.25/5.43 != ( size_size_list_nat @ Ys2 ) )
% 5.25/5.43 => ( Xs != Ys2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % neq_if_length_neq
% 5.25/5.43 thf(fact_992_neq__if__length__neq,axiom,
% 5.25/5.43 ! [Xs: list_int,Ys2: list_int] :
% 5.25/5.43 ( ( ( size_size_list_int @ Xs )
% 5.25/5.43 != ( size_size_list_int @ Ys2 ) )
% 5.25/5.43 => ( Xs != Ys2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % neq_if_length_neq
% 5.25/5.43 thf(fact_993_div__exp__mod__exp__eq,axiom,
% 5.25/5.43 ! [A: nat,N: nat,M: nat] :
% 5.25/5.43 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.43 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_exp_mod_exp_eq
% 5.25/5.43 thf(fact_994_div__exp__mod__exp__eq,axiom,
% 5.25/5.43 ! [A: int,N: nat,M: nat] :
% 5.25/5.43 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.43 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_exp_mod_exp_eq
% 5.25/5.43 thf(fact_995_div__exp__mod__exp__eq,axiom,
% 5.25/5.43 ! [A: code_integer,N: nat,M: nat] :
% 5.25/5.43 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.43 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_exp_mod_exp_eq
% 5.25/5.43 thf(fact_996_length__induct,axiom,
% 5.25/5.43 ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 5.25/5.43 ( ! [Xs3: list_VEBT_VEBT] :
% 5.25/5.43 ( ! [Ys3: list_VEBT_VEBT] :
% 5.25/5.43 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys3 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.25/5.43 => ( P @ Ys3 ) )
% 5.25/5.43 => ( P @ Xs3 ) )
% 5.25/5.43 => ( P @ Xs ) ) ).
% 5.25/5.43
% 5.25/5.43 % length_induct
% 5.25/5.43 thf(fact_997_length__induct,axiom,
% 5.25/5.43 ! [P: list_o > $o,Xs: list_o] :
% 5.25/5.43 ( ! [Xs3: list_o] :
% 5.25/5.43 ( ! [Ys3: list_o] :
% 5.25/5.43 ( ( ord_less_nat @ ( size_size_list_o @ Ys3 ) @ ( size_size_list_o @ Xs3 ) )
% 5.25/5.43 => ( P @ Ys3 ) )
% 5.25/5.43 => ( P @ Xs3 ) )
% 5.25/5.43 => ( P @ Xs ) ) ).
% 5.25/5.43
% 5.25/5.43 % length_induct
% 5.25/5.43 thf(fact_998_length__induct,axiom,
% 5.25/5.43 ! [P: list_nat > $o,Xs: list_nat] :
% 5.25/5.43 ( ! [Xs3: list_nat] :
% 5.25/5.43 ( ! [Ys3: list_nat] :
% 5.25/5.43 ( ( ord_less_nat @ ( size_size_list_nat @ Ys3 ) @ ( size_size_list_nat @ Xs3 ) )
% 5.25/5.43 => ( P @ Ys3 ) )
% 5.25/5.43 => ( P @ Xs3 ) )
% 5.25/5.43 => ( P @ Xs ) ) ).
% 5.25/5.43
% 5.25/5.43 % length_induct
% 5.25/5.43 thf(fact_999_length__induct,axiom,
% 5.25/5.43 ! [P: list_int > $o,Xs: list_int] :
% 5.25/5.43 ( ! [Xs3: list_int] :
% 5.25/5.43 ( ! [Ys3: list_int] :
% 5.25/5.43 ( ( ord_less_nat @ ( size_size_list_int @ Ys3 ) @ ( size_size_list_int @ Xs3 ) )
% 5.25/5.43 => ( P @ Ys3 ) )
% 5.25/5.43 => ( P @ Xs3 ) )
% 5.25/5.43 => ( P @ Xs ) ) ).
% 5.25/5.43
% 5.25/5.43 % length_induct
% 5.25/5.43 thf(fact_1000_div__mod__decomp,axiom,
% 5.25/5.43 ! [A2: nat,N: nat] :
% 5.25/5.43 ( A2
% 5.25/5.43 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_mod_decomp
% 5.25/5.43 thf(fact_1001_unset__bit__Suc,axiom,
% 5.25/5.43 ! [N: nat,A: code_integer] :
% 5.25/5.43 ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 5.25/5.43 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % unset_bit_Suc
% 5.25/5.43 thf(fact_1002_unset__bit__Suc,axiom,
% 5.25/5.43 ! [N: nat,A: int] :
% 5.25/5.43 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 5.25/5.43 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % unset_bit_Suc
% 5.25/5.43 thf(fact_1003_unset__bit__Suc,axiom,
% 5.25/5.43 ! [N: nat,A: nat] :
% 5.25/5.43 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 5.25/5.43 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % unset_bit_Suc
% 5.25/5.43 thf(fact_1004_flip__bit__Suc,axiom,
% 5.25/5.43 ! [N: nat,A: code_integer] :
% 5.25/5.43 ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 5.25/5.43 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % flip_bit_Suc
% 5.25/5.43 thf(fact_1005_flip__bit__Suc,axiom,
% 5.25/5.43 ! [N: nat,A: int] :
% 5.25/5.43 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 5.25/5.43 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % flip_bit_Suc
% 5.25/5.43 thf(fact_1006_flip__bit__Suc,axiom,
% 5.25/5.43 ! [N: nat,A: nat] :
% 5.25/5.43 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 5.25/5.43 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % flip_bit_Suc
% 5.25/5.43 thf(fact_1007_set__bit__Suc,axiom,
% 5.25/5.43 ! [N: nat,A: code_integer] :
% 5.25/5.43 ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 5.25/5.43 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % set_bit_Suc
% 5.25/5.43 thf(fact_1008_set__bit__Suc,axiom,
% 5.25/5.43 ! [N: nat,A: int] :
% 5.25/5.43 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 5.25/5.43 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % set_bit_Suc
% 5.25/5.43 thf(fact_1009_set__bit__Suc,axiom,
% 5.25/5.43 ! [N: nat,A: nat] :
% 5.25/5.43 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 5.25/5.43 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % set_bit_Suc
% 5.25/5.43 thf(fact_1010_dbl__simps_I3_J,axiom,
% 5.25/5.43 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.25/5.43 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % dbl_simps(3)
% 5.25/5.43 thf(fact_1011_dbl__simps_I3_J,axiom,
% 5.25/5.43 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.25/5.43 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % dbl_simps(3)
% 5.25/5.43 thf(fact_1012_dbl__simps_I3_J,axiom,
% 5.25/5.43 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 5.25/5.43 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % dbl_simps(3)
% 5.25/5.43 thf(fact_1013_dbl__simps_I3_J,axiom,
% 5.25/5.43 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.25/5.43 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % dbl_simps(3)
% 5.25/5.43 thf(fact_1014_divmod__digit__1_I1_J,axiom,
% 5.25/5.43 ! [A: code_integer,B: code_integer] :
% 5.25/5.43 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.43 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.25/5.43 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.25/5.43 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.25/5.43 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % divmod_digit_1(1)
% 5.25/5.43 thf(fact_1015_divmod__digit__1_I1_J,axiom,
% 5.25/5.43 ! [A: nat,B: nat] :
% 5.25/5.43 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.43 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.43 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.25/5.43 => ( ( 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 )
% 5.25/5.43 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % divmod_digit_1(1)
% 5.25/5.43 thf(fact_1016_divmod__digit__1_I1_J,axiom,
% 5.25/5.43 ! [A: int,B: int] :
% 5.25/5.43 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.43 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.43 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.25/5.43 => ( ( 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 )
% 5.25/5.43 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % divmod_digit_1(1)
% 5.25/5.43 thf(fact_1017_signed__take__bit__Suc,axiom,
% 5.25/5.43 ! [N: nat,A: code_integer] :
% 5.25/5.43 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 5.25/5.43 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % signed_take_bit_Suc
% 5.25/5.43 thf(fact_1018_signed__take__bit__Suc,axiom,
% 5.25/5.43 ! [N: nat,A: int] :
% 5.25/5.43 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 5.25/5.43 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % signed_take_bit_Suc
% 5.25/5.43 thf(fact_1019_power__numeral,axiom,
% 5.25/5.43 ! [K: num,L2: num] :
% 5.25/5.43 ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.25/5.43 = ( numera6690914467698888265omplex @ ( pow @ K @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_numeral
% 5.25/5.43 thf(fact_1020_power__numeral,axiom,
% 5.25/5.43 ! [K: num,L2: num] :
% 5.25/5.43 ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.25/5.43 = ( numeral_numeral_real @ ( pow @ K @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_numeral
% 5.25/5.43 thf(fact_1021_power__numeral,axiom,
% 5.25/5.43 ! [K: num,L2: num] :
% 5.25/5.43 ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.25/5.43 = ( numeral_numeral_rat @ ( pow @ K @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_numeral
% 5.25/5.43 thf(fact_1022_power__numeral,axiom,
% 5.25/5.43 ! [K: num,L2: num] :
% 5.25/5.43 ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.25/5.43 = ( numeral_numeral_nat @ ( pow @ K @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_numeral
% 5.25/5.43 thf(fact_1023_power__numeral,axiom,
% 5.25/5.43 ! [K: num,L2: num] :
% 5.25/5.43 ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.25/5.43 = ( numeral_numeral_int @ ( pow @ K @ L2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_numeral
% 5.25/5.43 thf(fact_1024_arith__geo__mean,axiom,
% 5.25/5.43 ! [U: real,X3: real,Y: real] :
% 5.25/5.43 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.43 = ( times_times_real @ X3 @ Y ) )
% 5.25/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.43 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % arith_geo_mean
% 5.25/5.43 thf(fact_1025_arith__geo__mean,axiom,
% 5.25/5.43 ! [U: rat,X3: rat,Y: rat] :
% 5.25/5.43 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.43 = ( times_times_rat @ X3 @ Y ) )
% 5.25/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.25/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.43 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % arith_geo_mean
% 5.25/5.43 thf(fact_1026_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.25/5.43 ! [X3: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.25/5.43 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.25/5.43 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.25/5.43 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.43 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % both_member_options_from_chilf_to_complete_tree
% 5.25/5.43 thf(fact_1027_valid__tree__deg__neq__0,axiom,
% 5.25/5.43 ! [T: vEBT_VEBT] :
% 5.25/5.43 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.25/5.43
% 5.25/5.43 % valid_tree_deg_neq_0
% 5.25/5.43 thf(fact_1028_valid__0__not,axiom,
% 5.25/5.43 ! [T: vEBT_VEBT] :
% 5.25/5.43 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.25/5.43
% 5.25/5.43 % valid_0_not
% 5.25/5.43 thf(fact_1029_deg__not__0,axiom,
% 5.25/5.43 ! [T: vEBT_VEBT,N: nat] :
% 5.25/5.43 ( ( vEBT_invar_vebt @ T @ N )
% 5.25/5.43 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.25/5.43
% 5.25/5.43 % deg_not_0
% 5.25/5.43 thf(fact_1030_verit__eq__simplify_I8_J,axiom,
% 5.25/5.43 ! [X22: num,Y2: num] :
% 5.25/5.43 ( ( ( bit0 @ X22 )
% 5.25/5.43 = ( bit0 @ Y2 ) )
% 5.25/5.43 = ( X22 = Y2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % verit_eq_simplify(8)
% 5.25/5.43 thf(fact_1031_less__nat__zero__code,axiom,
% 5.25/5.43 ! [N: nat] :
% 5.25/5.43 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.25/5.43
% 5.25/5.43 % less_nat_zero_code
% 5.25/5.43 thf(fact_1032_neq0__conv,axiom,
% 5.25/5.43 ! [N: nat] :
% 5.25/5.43 ( ( N != zero_zero_nat )
% 5.25/5.43 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.25/5.43
% 5.25/5.43 % neq0_conv
% 5.25/5.43 thf(fact_1033_bot__nat__0_Onot__eq__extremum,axiom,
% 5.25/5.43 ! [A: nat] :
% 5.25/5.43 ( ( A != zero_zero_nat )
% 5.25/5.43 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.25/5.43
% 5.25/5.43 % bot_nat_0.not_eq_extremum
% 5.25/5.43 thf(fact_1034_le0,axiom,
% 5.25/5.43 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.25/5.43
% 5.25/5.43 % le0
% 5.25/5.43 thf(fact_1035_bot__nat__0_Oextremum,axiom,
% 5.25/5.43 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.25/5.43
% 5.25/5.43 % bot_nat_0.extremum
% 5.25/5.43 thf(fact_1036_Nat_Oadd__0__right,axiom,
% 5.25/5.43 ! [M: nat] :
% 5.25/5.43 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.25/5.43 = M ) ).
% 5.25/5.43
% 5.25/5.43 % Nat.add_0_right
% 5.25/5.43 thf(fact_1037_add__is__0,axiom,
% 5.25/5.43 ! [M: nat,N: nat] :
% 5.25/5.43 ( ( ( plus_plus_nat @ M @ N )
% 5.25/5.43 = zero_zero_nat )
% 5.25/5.43 = ( ( M = zero_zero_nat )
% 5.25/5.43 & ( N = zero_zero_nat ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_is_0
% 5.25/5.43 thf(fact_1038_mult__cancel2,axiom,
% 5.25/5.43 ! [M: nat,K: nat,N: nat] :
% 5.25/5.43 ( ( ( times_times_nat @ M @ K )
% 5.25/5.43 = ( times_times_nat @ N @ K ) )
% 5.25/5.43 = ( ( M = N )
% 5.25/5.43 | ( K = zero_zero_nat ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_cancel2
% 5.25/5.43 thf(fact_1039_mult__cancel1,axiom,
% 5.25/5.43 ! [K: nat,M: nat,N: nat] :
% 5.25/5.43 ( ( ( times_times_nat @ K @ M )
% 5.25/5.43 = ( times_times_nat @ K @ N ) )
% 5.25/5.43 = ( ( M = N )
% 5.25/5.43 | ( K = zero_zero_nat ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_cancel1
% 5.25/5.43 thf(fact_1040_mult__0__right,axiom,
% 5.25/5.43 ! [M: nat] :
% 5.25/5.43 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.25/5.43 = zero_zero_nat ) ).
% 5.25/5.43
% 5.25/5.43 % mult_0_right
% 5.25/5.43 thf(fact_1041_mult__is__0,axiom,
% 5.25/5.43 ! [M: nat,N: nat] :
% 5.25/5.43 ( ( ( times_times_nat @ M @ N )
% 5.25/5.43 = zero_zero_nat )
% 5.25/5.43 = ( ( M = zero_zero_nat )
% 5.25/5.43 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_is_0
% 5.25/5.43 thf(fact_1042_div__pos__pos__trivial,axiom,
% 5.25/5.43 ! [K: int,L2: int] :
% 5.25/5.43 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.43 => ( ( ord_less_int @ K @ L2 )
% 5.25/5.43 => ( ( divide_divide_int @ K @ L2 )
% 5.25/5.43 = zero_zero_int ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_pos_pos_trivial
% 5.25/5.43 thf(fact_1043_div__neg__neg__trivial,axiom,
% 5.25/5.43 ! [K: int,L2: int] :
% 5.25/5.43 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.25/5.43 => ( ( ord_less_int @ L2 @ K )
% 5.25/5.43 => ( ( divide_divide_int @ K @ L2 )
% 5.25/5.43 = zero_zero_int ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_neg_neg_trivial
% 5.25/5.43 thf(fact_1044_i0__less,axiom,
% 5.25/5.43 ! [N: extended_enat] :
% 5.25/5.43 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.25/5.43 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 5.25/5.43
% 5.25/5.43 % i0_less
% 5.25/5.43 thf(fact_1045_mi__eq__ma__no__ch,axiom,
% 5.25/5.43 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.25/5.43 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 5.25/5.43 => ( ( Mi = Ma )
% 5.25/5.43 => ( ! [X: vEBT_VEBT] :
% 5.25/5.43 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.43 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_1 ) )
% 5.25/5.43 & ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mi_eq_ma_no_ch
% 5.25/5.43 thf(fact_1046_le__zero__eq,axiom,
% 5.25/5.43 ! [N: nat] :
% 5.25/5.43 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.25/5.43 = ( N = zero_zero_nat ) ) ).
% 5.25/5.43
% 5.25/5.43 % le_zero_eq
% 5.25/5.43 thf(fact_1047_not__gr__zero,axiom,
% 5.25/5.43 ! [N: nat] :
% 5.25/5.43 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.25/5.43 = ( N = zero_zero_nat ) ) ).
% 5.25/5.43
% 5.25/5.43 % not_gr_zero
% 5.25/5.43 thf(fact_1048_mult__cancel__right,axiom,
% 5.25/5.43 ! [A: complex,C: complex,B: complex] :
% 5.25/5.43 ( ( ( times_times_complex @ A @ C )
% 5.25/5.43 = ( times_times_complex @ B @ C ) )
% 5.25/5.43 = ( ( C = zero_zero_complex )
% 5.25/5.43 | ( A = B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_cancel_right
% 5.25/5.43 thf(fact_1049_mult__cancel__right,axiom,
% 5.25/5.43 ! [A: real,C: real,B: real] :
% 5.25/5.43 ( ( ( times_times_real @ A @ C )
% 5.25/5.43 = ( times_times_real @ B @ C ) )
% 5.25/5.43 = ( ( C = zero_zero_real )
% 5.25/5.43 | ( A = B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_cancel_right
% 5.25/5.43 thf(fact_1050_mult__cancel__right,axiom,
% 5.25/5.43 ! [A: rat,C: rat,B: rat] :
% 5.25/5.43 ( ( ( times_times_rat @ A @ C )
% 5.25/5.43 = ( times_times_rat @ B @ C ) )
% 5.25/5.43 = ( ( C = zero_zero_rat )
% 5.25/5.43 | ( A = B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_cancel_right
% 5.25/5.43 thf(fact_1051_mult__cancel__right,axiom,
% 5.25/5.43 ! [A: nat,C: nat,B: nat] :
% 5.25/5.43 ( ( ( times_times_nat @ A @ C )
% 5.25/5.43 = ( times_times_nat @ B @ C ) )
% 5.25/5.43 = ( ( C = zero_zero_nat )
% 5.25/5.43 | ( A = B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_cancel_right
% 5.25/5.43 thf(fact_1052_mult__cancel__right,axiom,
% 5.25/5.43 ! [A: int,C: int,B: int] :
% 5.25/5.43 ( ( ( times_times_int @ A @ C )
% 5.25/5.43 = ( times_times_int @ B @ C ) )
% 5.25/5.43 = ( ( C = zero_zero_int )
% 5.25/5.43 | ( A = B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_cancel_right
% 5.25/5.43 thf(fact_1053_mult__cancel__left,axiom,
% 5.25/5.43 ! [C: complex,A: complex,B: complex] :
% 5.25/5.43 ( ( ( times_times_complex @ C @ A )
% 5.25/5.43 = ( times_times_complex @ C @ B ) )
% 5.25/5.43 = ( ( C = zero_zero_complex )
% 5.25/5.43 | ( A = B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_cancel_left
% 5.25/5.43 thf(fact_1054_mult__cancel__left,axiom,
% 5.25/5.43 ! [C: real,A: real,B: real] :
% 5.25/5.43 ( ( ( times_times_real @ C @ A )
% 5.25/5.43 = ( times_times_real @ C @ B ) )
% 5.25/5.43 = ( ( C = zero_zero_real )
% 5.25/5.43 | ( A = B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_cancel_left
% 5.25/5.43 thf(fact_1055_mult__cancel__left,axiom,
% 5.25/5.43 ! [C: rat,A: rat,B: rat] :
% 5.25/5.43 ( ( ( times_times_rat @ C @ A )
% 5.25/5.43 = ( times_times_rat @ C @ B ) )
% 5.25/5.43 = ( ( C = zero_zero_rat )
% 5.25/5.43 | ( A = B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_cancel_left
% 5.25/5.43 thf(fact_1056_mult__cancel__left,axiom,
% 5.25/5.43 ! [C: nat,A: nat,B: nat] :
% 5.25/5.43 ( ( ( times_times_nat @ C @ A )
% 5.25/5.43 = ( times_times_nat @ C @ B ) )
% 5.25/5.43 = ( ( C = zero_zero_nat )
% 5.25/5.43 | ( A = B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_cancel_left
% 5.25/5.43 thf(fact_1057_mult__cancel__left,axiom,
% 5.25/5.43 ! [C: int,A: int,B: int] :
% 5.25/5.43 ( ( ( times_times_int @ C @ A )
% 5.25/5.43 = ( times_times_int @ C @ B ) )
% 5.25/5.43 = ( ( C = zero_zero_int )
% 5.25/5.43 | ( A = B ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_cancel_left
% 5.25/5.43 thf(fact_1058_mult__eq__0__iff,axiom,
% 5.25/5.43 ! [A: complex,B: complex] :
% 5.25/5.43 ( ( ( times_times_complex @ A @ B )
% 5.25/5.43 = zero_zero_complex )
% 5.25/5.43 = ( ( A = zero_zero_complex )
% 5.25/5.43 | ( B = zero_zero_complex ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_eq_0_iff
% 5.25/5.43 thf(fact_1059_mult__eq__0__iff,axiom,
% 5.25/5.43 ! [A: real,B: real] :
% 5.25/5.43 ( ( ( times_times_real @ A @ B )
% 5.25/5.43 = zero_zero_real )
% 5.25/5.43 = ( ( A = zero_zero_real )
% 5.25/5.43 | ( B = zero_zero_real ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_eq_0_iff
% 5.25/5.43 thf(fact_1060_mult__eq__0__iff,axiom,
% 5.25/5.43 ! [A: rat,B: rat] :
% 5.25/5.43 ( ( ( times_times_rat @ A @ B )
% 5.25/5.43 = zero_zero_rat )
% 5.25/5.43 = ( ( A = zero_zero_rat )
% 5.25/5.43 | ( B = zero_zero_rat ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_eq_0_iff
% 5.25/5.43 thf(fact_1061_mult__eq__0__iff,axiom,
% 5.25/5.43 ! [A: nat,B: nat] :
% 5.25/5.43 ( ( ( times_times_nat @ A @ B )
% 5.25/5.43 = zero_zero_nat )
% 5.25/5.43 = ( ( A = zero_zero_nat )
% 5.25/5.43 | ( B = zero_zero_nat ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_eq_0_iff
% 5.25/5.43 thf(fact_1062_mult__eq__0__iff,axiom,
% 5.25/5.43 ! [A: int,B: int] :
% 5.25/5.43 ( ( ( times_times_int @ A @ B )
% 5.25/5.43 = zero_zero_int )
% 5.25/5.43 = ( ( A = zero_zero_int )
% 5.25/5.43 | ( B = zero_zero_int ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % mult_eq_0_iff
% 5.25/5.43 thf(fact_1063_mult__zero__right,axiom,
% 5.25/5.43 ! [A: complex] :
% 5.25/5.43 ( ( times_times_complex @ A @ zero_zero_complex )
% 5.25/5.43 = zero_zero_complex ) ).
% 5.25/5.43
% 5.25/5.43 % mult_zero_right
% 5.25/5.43 thf(fact_1064_mult__zero__right,axiom,
% 5.25/5.43 ! [A: real] :
% 5.25/5.43 ( ( times_times_real @ A @ zero_zero_real )
% 5.25/5.43 = zero_zero_real ) ).
% 5.25/5.43
% 5.25/5.43 % mult_zero_right
% 5.25/5.43 thf(fact_1065_mult__zero__right,axiom,
% 5.25/5.43 ! [A: rat] :
% 5.25/5.43 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.25/5.43 = zero_zero_rat ) ).
% 5.25/5.43
% 5.25/5.43 % mult_zero_right
% 5.25/5.43 thf(fact_1066_mult__zero__right,axiom,
% 5.25/5.43 ! [A: nat] :
% 5.25/5.43 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.25/5.43 = zero_zero_nat ) ).
% 5.25/5.43
% 5.25/5.43 % mult_zero_right
% 5.25/5.43 thf(fact_1067_mult__zero__right,axiom,
% 5.25/5.43 ! [A: int] :
% 5.25/5.43 ( ( times_times_int @ A @ zero_zero_int )
% 5.25/5.43 = zero_zero_int ) ).
% 5.25/5.43
% 5.25/5.43 % mult_zero_right
% 5.25/5.43 thf(fact_1068_mult__zero__left,axiom,
% 5.25/5.43 ! [A: complex] :
% 5.25/5.43 ( ( times_times_complex @ zero_zero_complex @ A )
% 5.25/5.43 = zero_zero_complex ) ).
% 5.25/5.43
% 5.25/5.43 % mult_zero_left
% 5.25/5.43 thf(fact_1069_mult__zero__left,axiom,
% 5.25/5.43 ! [A: real] :
% 5.25/5.43 ( ( times_times_real @ zero_zero_real @ A )
% 5.25/5.43 = zero_zero_real ) ).
% 5.25/5.43
% 5.25/5.43 % mult_zero_left
% 5.25/5.43 thf(fact_1070_mult__zero__left,axiom,
% 5.25/5.43 ! [A: rat] :
% 5.25/5.43 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.25/5.43 = zero_zero_rat ) ).
% 5.25/5.43
% 5.25/5.43 % mult_zero_left
% 5.25/5.43 thf(fact_1071_mult__zero__left,axiom,
% 5.25/5.43 ! [A: nat] :
% 5.25/5.43 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.25/5.43 = zero_zero_nat ) ).
% 5.25/5.43
% 5.25/5.43 % mult_zero_left
% 5.25/5.43 thf(fact_1072_mult__zero__left,axiom,
% 5.25/5.43 ! [A: int] :
% 5.25/5.43 ( ( times_times_int @ zero_zero_int @ A )
% 5.25/5.43 = zero_zero_int ) ).
% 5.25/5.43
% 5.25/5.43 % mult_zero_left
% 5.25/5.43 thf(fact_1073_add__0,axiom,
% 5.25/5.43 ! [A: complex] :
% 5.25/5.43 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % add_0
% 5.25/5.43 thf(fact_1074_add__0,axiom,
% 5.25/5.43 ! [A: real] :
% 5.25/5.43 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % add_0
% 5.25/5.43 thf(fact_1075_add__0,axiom,
% 5.25/5.43 ! [A: rat] :
% 5.25/5.43 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % add_0
% 5.25/5.43 thf(fact_1076_add__0,axiom,
% 5.25/5.43 ! [A: nat] :
% 5.25/5.43 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % add_0
% 5.25/5.43 thf(fact_1077_add__0,axiom,
% 5.25/5.43 ! [A: int] :
% 5.25/5.43 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % add_0
% 5.25/5.43 thf(fact_1078_zero__eq__add__iff__both__eq__0,axiom,
% 5.25/5.43 ! [X3: nat,Y: nat] :
% 5.25/5.43 ( ( zero_zero_nat
% 5.25/5.43 = ( plus_plus_nat @ X3 @ Y ) )
% 5.25/5.43 = ( ( X3 = zero_zero_nat )
% 5.25/5.43 & ( Y = zero_zero_nat ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % zero_eq_add_iff_both_eq_0
% 5.25/5.43 thf(fact_1079_add__eq__0__iff__both__eq__0,axiom,
% 5.25/5.43 ! [X3: nat,Y: nat] :
% 5.25/5.43 ( ( ( plus_plus_nat @ X3 @ Y )
% 5.25/5.43 = zero_zero_nat )
% 5.25/5.43 = ( ( X3 = zero_zero_nat )
% 5.25/5.43 & ( Y = zero_zero_nat ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_eq_0_iff_both_eq_0
% 5.25/5.43 thf(fact_1080_add__cancel__right__right,axiom,
% 5.25/5.43 ! [A: complex,B: complex] :
% 5.25/5.43 ( ( A
% 5.25/5.43 = ( plus_plus_complex @ A @ B ) )
% 5.25/5.43 = ( B = zero_zero_complex ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_right_right
% 5.25/5.43 thf(fact_1081_add__cancel__right__right,axiom,
% 5.25/5.43 ! [A: real,B: real] :
% 5.25/5.43 ( ( A
% 5.25/5.43 = ( plus_plus_real @ A @ B ) )
% 5.25/5.43 = ( B = zero_zero_real ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_right_right
% 5.25/5.43 thf(fact_1082_add__cancel__right__right,axiom,
% 5.25/5.43 ! [A: rat,B: rat] :
% 5.25/5.43 ( ( A
% 5.25/5.43 = ( plus_plus_rat @ A @ B ) )
% 5.25/5.43 = ( B = zero_zero_rat ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_right_right
% 5.25/5.43 thf(fact_1083_add__cancel__right__right,axiom,
% 5.25/5.43 ! [A: nat,B: nat] :
% 5.25/5.43 ( ( A
% 5.25/5.43 = ( plus_plus_nat @ A @ B ) )
% 5.25/5.43 = ( B = zero_zero_nat ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_right_right
% 5.25/5.43 thf(fact_1084_add__cancel__right__right,axiom,
% 5.25/5.43 ! [A: int,B: int] :
% 5.25/5.43 ( ( A
% 5.25/5.43 = ( plus_plus_int @ A @ B ) )
% 5.25/5.43 = ( B = zero_zero_int ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_right_right
% 5.25/5.43 thf(fact_1085_add__cancel__right__left,axiom,
% 5.25/5.43 ! [A: complex,B: complex] :
% 5.25/5.43 ( ( A
% 5.25/5.43 = ( plus_plus_complex @ B @ A ) )
% 5.25/5.43 = ( B = zero_zero_complex ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_right_left
% 5.25/5.43 thf(fact_1086_add__cancel__right__left,axiom,
% 5.25/5.43 ! [A: real,B: real] :
% 5.25/5.43 ( ( A
% 5.25/5.43 = ( plus_plus_real @ B @ A ) )
% 5.25/5.43 = ( B = zero_zero_real ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_right_left
% 5.25/5.43 thf(fact_1087_add__cancel__right__left,axiom,
% 5.25/5.43 ! [A: rat,B: rat] :
% 5.25/5.43 ( ( A
% 5.25/5.43 = ( plus_plus_rat @ B @ A ) )
% 5.25/5.43 = ( B = zero_zero_rat ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_right_left
% 5.25/5.43 thf(fact_1088_add__cancel__right__left,axiom,
% 5.25/5.43 ! [A: nat,B: nat] :
% 5.25/5.43 ( ( A
% 5.25/5.43 = ( plus_plus_nat @ B @ A ) )
% 5.25/5.43 = ( B = zero_zero_nat ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_right_left
% 5.25/5.43 thf(fact_1089_add__cancel__right__left,axiom,
% 5.25/5.43 ! [A: int,B: int] :
% 5.25/5.43 ( ( A
% 5.25/5.43 = ( plus_plus_int @ B @ A ) )
% 5.25/5.43 = ( B = zero_zero_int ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_right_left
% 5.25/5.43 thf(fact_1090_add__cancel__left__right,axiom,
% 5.25/5.43 ! [A: complex,B: complex] :
% 5.25/5.43 ( ( ( plus_plus_complex @ A @ B )
% 5.25/5.43 = A )
% 5.25/5.43 = ( B = zero_zero_complex ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_left_right
% 5.25/5.43 thf(fact_1091_add__cancel__left__right,axiom,
% 5.25/5.43 ! [A: real,B: real] :
% 5.25/5.43 ( ( ( plus_plus_real @ A @ B )
% 5.25/5.43 = A )
% 5.25/5.43 = ( B = zero_zero_real ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_left_right
% 5.25/5.43 thf(fact_1092_add__cancel__left__right,axiom,
% 5.25/5.43 ! [A: rat,B: rat] :
% 5.25/5.43 ( ( ( plus_plus_rat @ A @ B )
% 5.25/5.43 = A )
% 5.25/5.43 = ( B = zero_zero_rat ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_left_right
% 5.25/5.43 thf(fact_1093_add__cancel__left__right,axiom,
% 5.25/5.43 ! [A: nat,B: nat] :
% 5.25/5.43 ( ( ( plus_plus_nat @ A @ B )
% 5.25/5.43 = A )
% 5.25/5.43 = ( B = zero_zero_nat ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_left_right
% 5.25/5.43 thf(fact_1094_add__cancel__left__right,axiom,
% 5.25/5.43 ! [A: int,B: int] :
% 5.25/5.43 ( ( ( plus_plus_int @ A @ B )
% 5.25/5.43 = A )
% 5.25/5.43 = ( B = zero_zero_int ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_left_right
% 5.25/5.43 thf(fact_1095_add__cancel__left__left,axiom,
% 5.25/5.43 ! [B: complex,A: complex] :
% 5.25/5.43 ( ( ( plus_plus_complex @ B @ A )
% 5.25/5.43 = A )
% 5.25/5.43 = ( B = zero_zero_complex ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_left_left
% 5.25/5.43 thf(fact_1096_add__cancel__left__left,axiom,
% 5.25/5.43 ! [B: real,A: real] :
% 5.25/5.43 ( ( ( plus_plus_real @ B @ A )
% 5.25/5.43 = A )
% 5.25/5.43 = ( B = zero_zero_real ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_left_left
% 5.25/5.43 thf(fact_1097_add__cancel__left__left,axiom,
% 5.25/5.43 ! [B: rat,A: rat] :
% 5.25/5.43 ( ( ( plus_plus_rat @ B @ A )
% 5.25/5.43 = A )
% 5.25/5.43 = ( B = zero_zero_rat ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_left_left
% 5.25/5.43 thf(fact_1098_add__cancel__left__left,axiom,
% 5.25/5.43 ! [B: nat,A: nat] :
% 5.25/5.43 ( ( ( plus_plus_nat @ B @ A )
% 5.25/5.43 = A )
% 5.25/5.43 = ( B = zero_zero_nat ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_left_left
% 5.25/5.43 thf(fact_1099_add__cancel__left__left,axiom,
% 5.25/5.43 ! [B: int,A: int] :
% 5.25/5.43 ( ( ( plus_plus_int @ B @ A )
% 5.25/5.43 = A )
% 5.25/5.43 = ( B = zero_zero_int ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_cancel_left_left
% 5.25/5.43 thf(fact_1100_double__zero__sym,axiom,
% 5.25/5.43 ! [A: real] :
% 5.25/5.43 ( ( zero_zero_real
% 5.25/5.43 = ( plus_plus_real @ A @ A ) )
% 5.25/5.43 = ( A = zero_zero_real ) ) ).
% 5.25/5.43
% 5.25/5.43 % double_zero_sym
% 5.25/5.43 thf(fact_1101_double__zero__sym,axiom,
% 5.25/5.43 ! [A: rat] :
% 5.25/5.43 ( ( zero_zero_rat
% 5.25/5.43 = ( plus_plus_rat @ A @ A ) )
% 5.25/5.43 = ( A = zero_zero_rat ) ) ).
% 5.25/5.43
% 5.25/5.43 % double_zero_sym
% 5.25/5.43 thf(fact_1102_double__zero__sym,axiom,
% 5.25/5.43 ! [A: int] :
% 5.25/5.43 ( ( zero_zero_int
% 5.25/5.43 = ( plus_plus_int @ A @ A ) )
% 5.25/5.43 = ( A = zero_zero_int ) ) ).
% 5.25/5.43
% 5.25/5.43 % double_zero_sym
% 5.25/5.43 thf(fact_1103_add_Oright__neutral,axiom,
% 5.25/5.43 ! [A: complex] :
% 5.25/5.43 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % add.right_neutral
% 5.25/5.43 thf(fact_1104_add_Oright__neutral,axiom,
% 5.25/5.43 ! [A: real] :
% 5.25/5.43 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % add.right_neutral
% 5.25/5.44 thf(fact_1105_add_Oright__neutral,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % add.right_neutral
% 5.25/5.44 thf(fact_1106_add_Oright__neutral,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % add.right_neutral
% 5.25/5.44 thf(fact_1107_add_Oright__neutral,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % add.right_neutral
% 5.25/5.44 thf(fact_1108_division__ring__divide__zero,axiom,
% 5.25/5.44 ! [A: complex] :
% 5.25/5.44 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.25/5.44 = zero_zero_complex ) ).
% 5.25/5.44
% 5.25/5.44 % division_ring_divide_zero
% 5.25/5.44 thf(fact_1109_division__ring__divide__zero,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.25/5.44 = zero_zero_real ) ).
% 5.25/5.44
% 5.25/5.44 % division_ring_divide_zero
% 5.25/5.44 thf(fact_1110_division__ring__divide__zero,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.25/5.44 = zero_zero_rat ) ).
% 5.25/5.44
% 5.25/5.44 % division_ring_divide_zero
% 5.25/5.44 thf(fact_1111_divide__cancel__right,axiom,
% 5.25/5.44 ! [A: complex,C: complex,B: complex] :
% 5.25/5.44 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.25/5.44 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.44 = ( ( C = zero_zero_complex )
% 5.25/5.44 | ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_cancel_right
% 5.25/5.44 thf(fact_1112_divide__cancel__right,axiom,
% 5.25/5.44 ! [A: real,C: real,B: real] :
% 5.25/5.44 ( ( ( divide_divide_real @ A @ C )
% 5.25/5.44 = ( divide_divide_real @ B @ C ) )
% 5.25/5.44 = ( ( C = zero_zero_real )
% 5.25/5.44 | ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_cancel_right
% 5.25/5.44 thf(fact_1113_divide__cancel__right,axiom,
% 5.25/5.44 ! [A: rat,C: rat,B: rat] :
% 5.25/5.44 ( ( ( divide_divide_rat @ A @ C )
% 5.25/5.44 = ( divide_divide_rat @ B @ C ) )
% 5.25/5.44 = ( ( C = zero_zero_rat )
% 5.25/5.44 | ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_cancel_right
% 5.25/5.44 thf(fact_1114_divide__cancel__left,axiom,
% 5.25/5.44 ! [C: complex,A: complex,B: complex] :
% 5.25/5.44 ( ( ( divide1717551699836669952omplex @ C @ A )
% 5.25/5.44 = ( divide1717551699836669952omplex @ C @ B ) )
% 5.25/5.44 = ( ( C = zero_zero_complex )
% 5.25/5.44 | ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_cancel_left
% 5.25/5.44 thf(fact_1115_divide__cancel__left,axiom,
% 5.25/5.44 ! [C: real,A: real,B: real] :
% 5.25/5.44 ( ( ( divide_divide_real @ C @ A )
% 5.25/5.44 = ( divide_divide_real @ C @ B ) )
% 5.25/5.44 = ( ( C = zero_zero_real )
% 5.25/5.44 | ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_cancel_left
% 5.25/5.44 thf(fact_1116_divide__cancel__left,axiom,
% 5.25/5.44 ! [C: rat,A: rat,B: rat] :
% 5.25/5.44 ( ( ( divide_divide_rat @ C @ A )
% 5.25/5.44 = ( divide_divide_rat @ C @ B ) )
% 5.25/5.44 = ( ( C = zero_zero_rat )
% 5.25/5.44 | ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_cancel_left
% 5.25/5.44 thf(fact_1117_div__by__0,axiom,
% 5.25/5.44 ! [A: complex] :
% 5.25/5.44 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.25/5.44 = zero_zero_complex ) ).
% 5.25/5.44
% 5.25/5.44 % div_by_0
% 5.25/5.44 thf(fact_1118_div__by__0,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.25/5.44 = zero_zero_real ) ).
% 5.25/5.44
% 5.25/5.44 % div_by_0
% 5.25/5.44 thf(fact_1119_div__by__0,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.25/5.44 = zero_zero_rat ) ).
% 5.25/5.44
% 5.25/5.44 % div_by_0
% 5.25/5.44 thf(fact_1120_div__by__0,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % div_by_0
% 5.25/5.44 thf(fact_1121_div__by__0,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % div_by_0
% 5.25/5.44 thf(fact_1122_divide__eq__0__iff,axiom,
% 5.25/5.44 ! [A: complex,B: complex] :
% 5.25/5.44 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.25/5.44 = zero_zero_complex )
% 5.25/5.44 = ( ( A = zero_zero_complex )
% 5.25/5.44 | ( B = zero_zero_complex ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_eq_0_iff
% 5.25/5.44 thf(fact_1123_divide__eq__0__iff,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ( divide_divide_real @ A @ B )
% 5.25/5.44 = zero_zero_real )
% 5.25/5.44 = ( ( A = zero_zero_real )
% 5.25/5.44 | ( B = zero_zero_real ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_eq_0_iff
% 5.25/5.44 thf(fact_1124_divide__eq__0__iff,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ( divide_divide_rat @ A @ B )
% 5.25/5.44 = zero_zero_rat )
% 5.25/5.44 = ( ( A = zero_zero_rat )
% 5.25/5.44 | ( B = zero_zero_rat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_eq_0_iff
% 5.25/5.44 thf(fact_1125_div__0,axiom,
% 5.25/5.44 ! [A: complex] :
% 5.25/5.44 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.25/5.44 = zero_zero_complex ) ).
% 5.25/5.44
% 5.25/5.44 % div_0
% 5.25/5.44 thf(fact_1126_div__0,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.25/5.44 = zero_zero_real ) ).
% 5.25/5.44
% 5.25/5.44 % div_0
% 5.25/5.44 thf(fact_1127_div__0,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 5.25/5.44 = zero_zero_rat ) ).
% 5.25/5.44
% 5.25/5.44 % div_0
% 5.25/5.44 thf(fact_1128_div__0,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % div_0
% 5.25/5.44 thf(fact_1129_div__0,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % div_0
% 5.25/5.44 thf(fact_1130_bits__div__by__0,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % bits_div_by_0
% 5.25/5.44 thf(fact_1131_bits__div__by__0,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % bits_div_by_0
% 5.25/5.44 thf(fact_1132_bits__div__0,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % bits_div_0
% 5.25/5.44 thf(fact_1133_bits__div__0,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % bits_div_0
% 5.25/5.44 thf(fact_1134_power__Suc0__right,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % power_Suc0_right
% 5.25/5.44 thf(fact_1135_power__Suc0__right,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % power_Suc0_right
% 5.25/5.44 thf(fact_1136_power__Suc0__right,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % power_Suc0_right
% 5.25/5.44 thf(fact_1137_power__Suc0__right,axiom,
% 5.25/5.44 ! [A: complex] :
% 5.25/5.44 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % power_Suc0_right
% 5.25/5.44 thf(fact_1138_bits__mod__0,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % bits_mod_0
% 5.25/5.44 thf(fact_1139_bits__mod__0,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % bits_mod_0
% 5.25/5.44 thf(fact_1140_bits__mod__0,axiom,
% 5.25/5.44 ! [A: code_integer] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.44 = zero_z3403309356797280102nteger ) ).
% 5.25/5.44
% 5.25/5.44 % bits_mod_0
% 5.25/5.44 thf(fact_1141_mod__0,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % mod_0
% 5.25/5.44 thf(fact_1142_mod__0,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % mod_0
% 5.25/5.44 thf(fact_1143_mod__0,axiom,
% 5.25/5.44 ! [A: code_integer] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.44 = zero_z3403309356797280102nteger ) ).
% 5.25/5.44
% 5.25/5.44 % mod_0
% 5.25/5.44 thf(fact_1144_mod__by__0,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % mod_by_0
% 5.25/5.44 thf(fact_1145_mod__by__0,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % mod_by_0
% 5.25/5.44 thf(fact_1146_mod__by__0,axiom,
% 5.25/5.44 ! [A: code_integer] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % mod_by_0
% 5.25/5.44 thf(fact_1147_mod__self,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ A @ A )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % mod_self
% 5.25/5.44 thf(fact_1148_mod__self,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( modulo_modulo_int @ A @ A )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % mod_self
% 5.25/5.44 thf(fact_1149_mod__self,axiom,
% 5.25/5.44 ! [A: code_integer] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ A @ A )
% 5.25/5.44 = zero_z3403309356797280102nteger ) ).
% 5.25/5.44
% 5.25/5.44 % mod_self
% 5.25/5.44 thf(fact_1150_zero__less__Suc,axiom,
% 5.25/5.44 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_less_Suc
% 5.25/5.44 thf(fact_1151_less__Suc0,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.25/5.44 = ( N = zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_Suc0
% 5.25/5.44 thf(fact_1152_add__gr__0,axiom,
% 5.25/5.44 ! [M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.44 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.44 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_gr_0
% 5.25/5.44 thf(fact_1153_one__eq__mult__iff,axiom,
% 5.25/5.44 ! [M: nat,N: nat] :
% 5.25/5.44 ( ( ( suc @ zero_zero_nat )
% 5.25/5.44 = ( times_times_nat @ M @ N ) )
% 5.25/5.44 = ( ( M
% 5.25/5.44 = ( suc @ zero_zero_nat ) )
% 5.25/5.44 & ( N
% 5.25/5.44 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_eq_mult_iff
% 5.25/5.44 thf(fact_1154_mult__eq__1__iff,axiom,
% 5.25/5.44 ! [M: nat,N: nat] :
% 5.25/5.44 ( ( ( times_times_nat @ M @ N )
% 5.25/5.44 = ( suc @ zero_zero_nat ) )
% 5.25/5.44 = ( ( M
% 5.25/5.44 = ( suc @ zero_zero_nat ) )
% 5.25/5.44 & ( N
% 5.25/5.44 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_eq_1_iff
% 5.25/5.44 thf(fact_1155_nat__mult__less__cancel__disj,axiom,
% 5.25/5.44 ! [K: nat,M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.25/5.44 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.44 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_mult_less_cancel_disj
% 5.25/5.44 thf(fact_1156_nat__0__less__mult__iff,axiom,
% 5.25/5.44 ! [M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 5.25/5.44 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.44 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_0_less_mult_iff
% 5.25/5.44 thf(fact_1157_mult__less__cancel2,axiom,
% 5.25/5.44 ! [M: nat,K: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.25/5.44 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.44 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_less_cancel2
% 5.25/5.44 thf(fact_1158_insert__simp__mima,axiom,
% 5.25/5.44 ! [X3: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.25/5.44 ( ( ( X3 = Mi )
% 5.25/5.44 | ( X3 = Ma ) )
% 5.25/5.44 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.25/5.44 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X3 )
% 5.25/5.44 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % insert_simp_mima
% 5.25/5.44 thf(fact_1159_not__real__square__gt__zero,axiom,
% 5.25/5.44 ! [X3: real] :
% 5.25/5.44 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X3 @ X3 ) ) )
% 5.25/5.44 = ( X3 = zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % not_real_square_gt_zero
% 5.25/5.44 thf(fact_1160_div__by__Suc__0,axiom,
% 5.25/5.44 ! [M: nat] :
% 5.25/5.44 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.25/5.44 = M ) ).
% 5.25/5.44
% 5.25/5.44 % div_by_Suc_0
% 5.25/5.44 thf(fact_1161_less__one,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ N @ one_one_nat )
% 5.25/5.44 = ( N = zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_one
% 5.25/5.44 thf(fact_1162_div__less,axiom,
% 5.25/5.44 ! [M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M @ N )
% 5.25/5.44 => ( ( divide_divide_nat @ M @ N )
% 5.25/5.44 = zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_less
% 5.25/5.44 thf(fact_1163_power__Suc__0,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.25/5.44 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_Suc_0
% 5.25/5.44 thf(fact_1164_nat__power__eq__Suc__0__iff,axiom,
% 5.25/5.44 ! [X3: nat,M: nat] :
% 5.25/5.44 ( ( ( power_power_nat @ X3 @ M )
% 5.25/5.44 = ( suc @ zero_zero_nat ) )
% 5.25/5.44 = ( ( M = zero_zero_nat )
% 5.25/5.44 | ( X3
% 5.25/5.44 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_power_eq_Suc_0_iff
% 5.25/5.44 thf(fact_1165_nat__zero__less__power__iff,axiom,
% 5.25/5.44 ! [X3: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X3 @ N ) )
% 5.25/5.44 = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 5.25/5.44 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_zero_less_power_iff
% 5.25/5.44 thf(fact_1166_mod__by__Suc__0,axiom,
% 5.25/5.44 ! [M: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % mod_by_Suc_0
% 5.25/5.44 thf(fact_1167_nat__mult__div__cancel__disj,axiom,
% 5.25/5.44 ! [K: nat,M: nat,N: nat] :
% 5.25/5.44 ( ( ( K = zero_zero_nat )
% 5.25/5.44 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.25/5.44 = zero_zero_nat ) )
% 5.25/5.44 & ( ( K != zero_zero_nat )
% 5.25/5.44 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.25/5.44 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_mult_div_cancel_disj
% 5.25/5.44 thf(fact_1168_signed__take__bit__of__0,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % signed_take_bit_of_0
% 5.25/5.44 thf(fact_1169_dbl__simps_I2_J,axiom,
% 5.25/5.44 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 5.25/5.44 = zero_zero_complex ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_simps(2)
% 5.25/5.44 thf(fact_1170_dbl__simps_I2_J,axiom,
% 5.25/5.44 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.25/5.44 = zero_zero_real ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_simps(2)
% 5.25/5.44 thf(fact_1171_dbl__simps_I2_J,axiom,
% 5.25/5.44 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 5.25/5.44 = zero_zero_rat ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_simps(2)
% 5.25/5.44 thf(fact_1172_dbl__simps_I2_J,axiom,
% 5.25/5.44 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_simps(2)
% 5.25/5.44 thf(fact_1173_mi__ma__2__deg,axiom,
% 5.25/5.44 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.25/5.44 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.25/5.44 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.25/5.44 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mi_ma_2_deg
% 5.25/5.44 thf(fact_1174_add__le__same__cancel1,axiom,
% 5.25/5.44 ! [B: real,A: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.25/5.44 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_same_cancel1
% 5.25/5.44 thf(fact_1175_add__le__same__cancel1,axiom,
% 5.25/5.44 ! [B: rat,A: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.25/5.44 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_same_cancel1
% 5.25/5.44 thf(fact_1176_add__le__same__cancel1,axiom,
% 5.25/5.44 ! [B: nat,A: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.25/5.44 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_same_cancel1
% 5.25/5.44 thf(fact_1177_add__le__same__cancel1,axiom,
% 5.25/5.44 ! [B: int,A: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.25/5.44 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_same_cancel1
% 5.25/5.44 thf(fact_1178_add__le__same__cancel2,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.25/5.44 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_same_cancel2
% 5.25/5.44 thf(fact_1179_add__le__same__cancel2,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.25/5.44 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_same_cancel2
% 5.25/5.44 thf(fact_1180_add__le__same__cancel2,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.25/5.44 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_same_cancel2
% 5.25/5.44 thf(fact_1181_add__le__same__cancel2,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.25/5.44 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_same_cancel2
% 5.25/5.44 thf(fact_1182_le__add__same__cancel1,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.25/5.44 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_add_same_cancel1
% 5.25/5.44 thf(fact_1183_le__add__same__cancel1,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.25/5.44 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_add_same_cancel1
% 5.25/5.44 thf(fact_1184_le__add__same__cancel1,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.25/5.44 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_add_same_cancel1
% 5.25/5.44 thf(fact_1185_le__add__same__cancel1,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.25/5.44 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_add_same_cancel1
% 5.25/5.44 thf(fact_1186_le__add__same__cancel2,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.25/5.44 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_add_same_cancel2
% 5.25/5.44 thf(fact_1187_le__add__same__cancel2,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.25/5.44 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_add_same_cancel2
% 5.25/5.44 thf(fact_1188_le__add__same__cancel2,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.25/5.44 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_add_same_cancel2
% 5.25/5.44 thf(fact_1189_le__add__same__cancel2,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.25/5.44 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_add_same_cancel2
% 5.25/5.44 thf(fact_1190_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.25/5.44 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % double_add_le_zero_iff_single_add_le_zero
% 5.25/5.44 thf(fact_1191_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.25/5.44 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % double_add_le_zero_iff_single_add_le_zero
% 5.25/5.44 thf(fact_1192_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.25/5.44 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % double_add_le_zero_iff_single_add_le_zero
% 5.25/5.44 thf(fact_1193_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.25/5.44 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_le_double_add_iff_zero_le_single_add
% 5.25/5.44 thf(fact_1194_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.25/5.44 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_le_double_add_iff_zero_le_single_add
% 5.25/5.44 thf(fact_1195_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.25/5.44 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_le_double_add_iff_zero_le_single_add
% 5.25/5.44 thf(fact_1196_add__less__same__cancel1,axiom,
% 5.25/5.44 ! [B: real,A: real] :
% 5.25/5.44 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.25/5.44 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_same_cancel1
% 5.25/5.44 thf(fact_1197_add__less__same__cancel1,axiom,
% 5.25/5.44 ! [B: rat,A: rat] :
% 5.25/5.44 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.25/5.44 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_same_cancel1
% 5.25/5.44 thf(fact_1198_add__less__same__cancel1,axiom,
% 5.25/5.44 ! [B: nat,A: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.25/5.44 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_same_cancel1
% 5.25/5.44 thf(fact_1199_add__less__same__cancel1,axiom,
% 5.25/5.44 ! [B: int,A: int] :
% 5.25/5.44 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.25/5.44 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_same_cancel1
% 5.25/5.44 thf(fact_1200_add__less__same__cancel2,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.25/5.44 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_same_cancel2
% 5.25/5.44 thf(fact_1201_add__less__same__cancel2,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.25/5.44 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_same_cancel2
% 5.25/5.44 thf(fact_1202_add__less__same__cancel2,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.25/5.44 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_same_cancel2
% 5.25/5.44 thf(fact_1203_add__less__same__cancel2,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.25/5.44 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_same_cancel2
% 5.25/5.44 thf(fact_1204_less__add__same__cancel1,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.25/5.44 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_same_cancel1
% 5.25/5.44 thf(fact_1205_less__add__same__cancel1,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.25/5.44 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_same_cancel1
% 5.25/5.44 thf(fact_1206_less__add__same__cancel1,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.25/5.44 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_same_cancel1
% 5.25/5.44 thf(fact_1207_less__add__same__cancel1,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.25/5.44 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_same_cancel1
% 5.25/5.44 thf(fact_1208_less__add__same__cancel2,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.25/5.44 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_same_cancel2
% 5.25/5.44 thf(fact_1209_less__add__same__cancel2,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.25/5.44 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_same_cancel2
% 5.25/5.44 thf(fact_1210_less__add__same__cancel2,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.25/5.44 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_same_cancel2
% 5.25/5.44 thf(fact_1211_less__add__same__cancel2,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.25/5.44 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_same_cancel2
% 5.25/5.44 thf(fact_1212_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.25/5.44 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % double_add_less_zero_iff_single_add_less_zero
% 5.25/5.44 thf(fact_1213_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.25/5.44 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % double_add_less_zero_iff_single_add_less_zero
% 5.25/5.44 thf(fact_1214_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.25/5.44 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % double_add_less_zero_iff_single_add_less_zero
% 5.25/5.44 thf(fact_1215_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.25/5.44 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_less_double_add_iff_zero_less_single_add
% 5.25/5.44 thf(fact_1216_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.25/5.44 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_less_double_add_iff_zero_less_single_add
% 5.25/5.44 thf(fact_1217_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.25/5.44 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_less_double_add_iff_zero_less_single_add
% 5.25/5.44 thf(fact_1218_mult__cancel__right2,axiom,
% 5.25/5.44 ! [A: complex,C: complex] :
% 5.25/5.44 ( ( ( times_times_complex @ A @ C )
% 5.25/5.44 = C )
% 5.25/5.44 = ( ( C = zero_zero_complex )
% 5.25/5.44 | ( A = one_one_complex ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_right2
% 5.25/5.44 thf(fact_1219_mult__cancel__right2,axiom,
% 5.25/5.44 ! [A: real,C: real] :
% 5.25/5.44 ( ( ( times_times_real @ A @ C )
% 5.25/5.44 = C )
% 5.25/5.44 = ( ( C = zero_zero_real )
% 5.25/5.44 | ( A = one_one_real ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_right2
% 5.25/5.44 thf(fact_1220_mult__cancel__right2,axiom,
% 5.25/5.44 ! [A: rat,C: rat] :
% 5.25/5.44 ( ( ( times_times_rat @ A @ C )
% 5.25/5.44 = C )
% 5.25/5.44 = ( ( C = zero_zero_rat )
% 5.25/5.44 | ( A = one_one_rat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_right2
% 5.25/5.44 thf(fact_1221_mult__cancel__right2,axiom,
% 5.25/5.44 ! [A: int,C: int] :
% 5.25/5.44 ( ( ( times_times_int @ A @ C )
% 5.25/5.44 = C )
% 5.25/5.44 = ( ( C = zero_zero_int )
% 5.25/5.44 | ( A = one_one_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_right2
% 5.25/5.44 thf(fact_1222_mult__cancel__right1,axiom,
% 5.25/5.44 ! [C: complex,B: complex] :
% 5.25/5.44 ( ( C
% 5.25/5.44 = ( times_times_complex @ B @ C ) )
% 5.25/5.44 = ( ( C = zero_zero_complex )
% 5.25/5.44 | ( B = one_one_complex ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_right1
% 5.25/5.44 thf(fact_1223_mult__cancel__right1,axiom,
% 5.25/5.44 ! [C: real,B: real] :
% 5.25/5.44 ( ( C
% 5.25/5.44 = ( times_times_real @ B @ C ) )
% 5.25/5.44 = ( ( C = zero_zero_real )
% 5.25/5.44 | ( B = one_one_real ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_right1
% 5.25/5.44 thf(fact_1224_mult__cancel__right1,axiom,
% 5.25/5.44 ! [C: rat,B: rat] :
% 5.25/5.44 ( ( C
% 5.25/5.44 = ( times_times_rat @ B @ C ) )
% 5.25/5.44 = ( ( C = zero_zero_rat )
% 5.25/5.44 | ( B = one_one_rat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_right1
% 5.25/5.44 thf(fact_1225_mult__cancel__right1,axiom,
% 5.25/5.44 ! [C: int,B: int] :
% 5.25/5.44 ( ( C
% 5.25/5.44 = ( times_times_int @ B @ C ) )
% 5.25/5.44 = ( ( C = zero_zero_int )
% 5.25/5.44 | ( B = one_one_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_right1
% 5.25/5.44 thf(fact_1226_mult__cancel__left2,axiom,
% 5.25/5.44 ! [C: complex,A: complex] :
% 5.25/5.44 ( ( ( times_times_complex @ C @ A )
% 5.25/5.44 = C )
% 5.25/5.44 = ( ( C = zero_zero_complex )
% 5.25/5.44 | ( A = one_one_complex ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_left2
% 5.25/5.44 thf(fact_1227_mult__cancel__left2,axiom,
% 5.25/5.44 ! [C: real,A: real] :
% 5.25/5.44 ( ( ( times_times_real @ C @ A )
% 5.25/5.44 = C )
% 5.25/5.44 = ( ( C = zero_zero_real )
% 5.25/5.44 | ( A = one_one_real ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_left2
% 5.25/5.44 thf(fact_1228_mult__cancel__left2,axiom,
% 5.25/5.44 ! [C: rat,A: rat] :
% 5.25/5.44 ( ( ( times_times_rat @ C @ A )
% 5.25/5.44 = C )
% 5.25/5.44 = ( ( C = zero_zero_rat )
% 5.25/5.44 | ( A = one_one_rat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_left2
% 5.25/5.44 thf(fact_1229_mult__cancel__left2,axiom,
% 5.25/5.44 ! [C: int,A: int] :
% 5.25/5.44 ( ( ( times_times_int @ C @ A )
% 5.25/5.44 = C )
% 5.25/5.44 = ( ( C = zero_zero_int )
% 5.25/5.44 | ( A = one_one_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_left2
% 5.25/5.44 thf(fact_1230_mult__cancel__left1,axiom,
% 5.25/5.44 ! [C: complex,B: complex] :
% 5.25/5.44 ( ( C
% 5.25/5.44 = ( times_times_complex @ C @ B ) )
% 5.25/5.44 = ( ( C = zero_zero_complex )
% 5.25/5.44 | ( B = one_one_complex ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_left1
% 5.25/5.44 thf(fact_1231_mult__cancel__left1,axiom,
% 5.25/5.44 ! [C: real,B: real] :
% 5.25/5.44 ( ( C
% 5.25/5.44 = ( times_times_real @ C @ B ) )
% 5.25/5.44 = ( ( C = zero_zero_real )
% 5.25/5.44 | ( B = one_one_real ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_left1
% 5.25/5.44 thf(fact_1232_mult__cancel__left1,axiom,
% 5.25/5.44 ! [C: rat,B: rat] :
% 5.25/5.44 ( ( C
% 5.25/5.44 = ( times_times_rat @ C @ B ) )
% 5.25/5.44 = ( ( C = zero_zero_rat )
% 5.25/5.44 | ( B = one_one_rat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_left1
% 5.25/5.44 thf(fact_1233_mult__cancel__left1,axiom,
% 5.25/5.44 ! [C: int,B: int] :
% 5.25/5.44 ( ( C
% 5.25/5.44 = ( times_times_int @ C @ B ) )
% 5.25/5.44 = ( ( C = zero_zero_int )
% 5.25/5.44 | ( B = one_one_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_cancel_left1
% 5.25/5.44 thf(fact_1234_sum__squares__eq__zero__iff,axiom,
% 5.25/5.44 ! [X3: real,Y: real] :
% 5.25/5.44 ( ( ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) )
% 5.25/5.44 = zero_zero_real )
% 5.25/5.44 = ( ( X3 = zero_zero_real )
% 5.25/5.44 & ( Y = zero_zero_real ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % sum_squares_eq_zero_iff
% 5.25/5.44 thf(fact_1235_sum__squares__eq__zero__iff,axiom,
% 5.25/5.44 ! [X3: rat,Y: rat] :
% 5.25/5.44 ( ( ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) )
% 5.25/5.44 = zero_zero_rat )
% 5.25/5.44 = ( ( X3 = zero_zero_rat )
% 5.25/5.44 & ( Y = zero_zero_rat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % sum_squares_eq_zero_iff
% 5.25/5.44 thf(fact_1236_sum__squares__eq__zero__iff,axiom,
% 5.25/5.44 ! [X3: int,Y: int] :
% 5.25/5.44 ( ( ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) )
% 5.25/5.44 = zero_zero_int )
% 5.25/5.44 = ( ( X3 = zero_zero_int )
% 5.25/5.44 & ( Y = zero_zero_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % sum_squares_eq_zero_iff
% 5.25/5.44 thf(fact_1237_mult__divide__mult__cancel__left__if,axiom,
% 5.25/5.44 ! [C: complex,A: complex,B: complex] :
% 5.25/5.44 ( ( ( C = zero_zero_complex )
% 5.25/5.44 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.25/5.44 = zero_zero_complex ) )
% 5.25/5.44 & ( ( C != zero_zero_complex )
% 5.25/5.44 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.25/5.44 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_divide_mult_cancel_left_if
% 5.25/5.44 thf(fact_1238_mult__divide__mult__cancel__left__if,axiom,
% 5.25/5.44 ! [C: real,A: real,B: real] :
% 5.25/5.44 ( ( ( C = zero_zero_real )
% 5.25/5.44 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.44 = zero_zero_real ) )
% 5.25/5.44 & ( ( C != zero_zero_real )
% 5.25/5.44 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.44 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_divide_mult_cancel_left_if
% 5.25/5.44 thf(fact_1239_mult__divide__mult__cancel__left__if,axiom,
% 5.25/5.44 ! [C: rat,A: rat,B: rat] :
% 5.25/5.44 ( ( ( C = zero_zero_rat )
% 5.25/5.44 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.44 = zero_zero_rat ) )
% 5.25/5.44 & ( ( C != zero_zero_rat )
% 5.25/5.44 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.44 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_divide_mult_cancel_left_if
% 5.25/5.44 thf(fact_1240_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.25/5.44 ! [C: complex,A: complex,B: complex] :
% 5.25/5.44 ( ( C != zero_zero_complex )
% 5.25/5.44 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.25/5.44 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_divide_mult_cancel_left
% 5.25/5.44 thf(fact_1241_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.25/5.44 ! [C: real,A: real,B: real] :
% 5.25/5.44 ( ( C != zero_zero_real )
% 5.25/5.44 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.44 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_divide_mult_cancel_left
% 5.25/5.44 thf(fact_1242_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.25/5.44 ! [C: rat,A: rat,B: rat] :
% 5.25/5.44 ( ( C != zero_zero_rat )
% 5.25/5.44 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.44 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_divide_mult_cancel_left
% 5.25/5.44 thf(fact_1243_nonzero__mult__div__cancel__left,axiom,
% 5.25/5.44 ! [A: complex,B: complex] :
% 5.25/5.44 ( ( A != zero_zero_complex )
% 5.25/5.44 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 5.25/5.44 = B ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_div_cancel_left
% 5.25/5.44 thf(fact_1244_nonzero__mult__div__cancel__left,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( A != zero_zero_real )
% 5.25/5.44 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 5.25/5.44 = B ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_div_cancel_left
% 5.25/5.44 thf(fact_1245_nonzero__mult__div__cancel__left,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( A != zero_zero_rat )
% 5.25/5.44 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 5.25/5.44 = B ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_div_cancel_left
% 5.25/5.44 thf(fact_1246_nonzero__mult__div__cancel__left,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( A != zero_zero_nat )
% 5.25/5.44 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.25/5.44 = B ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_div_cancel_left
% 5.25/5.44 thf(fact_1247_nonzero__mult__div__cancel__left,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( A != zero_zero_int )
% 5.25/5.44 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.25/5.44 = B ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_div_cancel_left
% 5.25/5.44 thf(fact_1248_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.25/5.44 ! [C: complex,A: complex,B: complex] :
% 5.25/5.44 ( ( C != zero_zero_complex )
% 5.25/5.44 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 5.25/5.44 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_divide_mult_cancel_left2
% 5.25/5.44 thf(fact_1249_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.25/5.44 ! [C: real,A: real,B: real] :
% 5.25/5.44 ( ( C != zero_zero_real )
% 5.25/5.44 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 5.25/5.44 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_divide_mult_cancel_left2
% 5.25/5.44 thf(fact_1250_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.25/5.44 ! [C: rat,A: rat,B: rat] :
% 5.25/5.44 ( ( C != zero_zero_rat )
% 5.25/5.44 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.44 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_divide_mult_cancel_left2
% 5.25/5.44 thf(fact_1251_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.25/5.44 ! [C: complex,A: complex,B: complex] :
% 5.25/5.44 ( ( C != zero_zero_complex )
% 5.25/5.44 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.25/5.44 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_divide_mult_cancel_right
% 5.25/5.44 thf(fact_1252_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.25/5.44 ! [C: real,A: real,B: real] :
% 5.25/5.44 ( ( C != zero_zero_real )
% 5.25/5.44 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.25/5.44 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_divide_mult_cancel_right
% 5.25/5.44 thf(fact_1253_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.25/5.44 ! [C: rat,A: rat,B: rat] :
% 5.25/5.44 ( ( C != zero_zero_rat )
% 5.25/5.44 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.44 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_divide_mult_cancel_right
% 5.25/5.44 thf(fact_1254_nonzero__mult__div__cancel__right,axiom,
% 5.25/5.44 ! [B: complex,A: complex] :
% 5.25/5.44 ( ( B != zero_zero_complex )
% 5.25/5.44 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 5.25/5.44 = A ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_div_cancel_right
% 5.25/5.44 thf(fact_1255_nonzero__mult__div__cancel__right,axiom,
% 5.25/5.44 ! [B: real,A: real] :
% 5.25/5.44 ( ( B != zero_zero_real )
% 5.25/5.44 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 5.25/5.44 = A ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_div_cancel_right
% 5.25/5.44 thf(fact_1256_nonzero__mult__div__cancel__right,axiom,
% 5.25/5.44 ! [B: rat,A: rat] :
% 5.25/5.44 ( ( B != zero_zero_rat )
% 5.25/5.44 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 5.25/5.44 = A ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_div_cancel_right
% 5.25/5.44 thf(fact_1257_nonzero__mult__div__cancel__right,axiom,
% 5.25/5.44 ! [B: nat,A: nat] :
% 5.25/5.44 ( ( B != zero_zero_nat )
% 5.25/5.44 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.25/5.44 = A ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_div_cancel_right
% 5.25/5.44 thf(fact_1258_nonzero__mult__div__cancel__right,axiom,
% 5.25/5.44 ! [B: int,A: int] :
% 5.25/5.44 ( ( B != zero_zero_int )
% 5.25/5.44 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.25/5.44 = A ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_div_cancel_right
% 5.25/5.44 thf(fact_1259_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.25/5.44 ! [C: complex,A: complex,B: complex] :
% 5.25/5.44 ( ( C != zero_zero_complex )
% 5.25/5.44 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 5.25/5.44 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_divide_mult_cancel_right2
% 5.25/5.44 thf(fact_1260_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.25/5.44 ! [C: real,A: real,B: real] :
% 5.25/5.44 ( ( C != zero_zero_real )
% 5.25/5.44 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 5.25/5.44 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_divide_mult_cancel_right2
% 5.25/5.44 thf(fact_1261_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.25/5.44 ! [C: rat,A: rat,B: rat] :
% 5.25/5.44 ( ( C != zero_zero_rat )
% 5.25/5.44 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.44 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_mult_divide_mult_cancel_right2
% 5.25/5.44 thf(fact_1262_div__mult__mult1,axiom,
% 5.25/5.44 ! [C: nat,A: nat,B: nat] :
% 5.25/5.44 ( ( C != zero_zero_nat )
% 5.25/5.44 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.25/5.44 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_mult1
% 5.25/5.44 thf(fact_1263_div__mult__mult1,axiom,
% 5.25/5.44 ! [C: int,A: int,B: int] :
% 5.25/5.44 ( ( C != zero_zero_int )
% 5.25/5.44 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.44 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_mult1
% 5.25/5.44 thf(fact_1264_div__mult__mult2,axiom,
% 5.25/5.44 ! [C: nat,A: nat,B: nat] :
% 5.25/5.44 ( ( C != zero_zero_nat )
% 5.25/5.44 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.25/5.44 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_mult2
% 5.25/5.44 thf(fact_1265_div__mult__mult2,axiom,
% 5.25/5.44 ! [C: int,A: int,B: int] :
% 5.25/5.44 ( ( C != zero_zero_int )
% 5.25/5.44 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.44 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_mult2
% 5.25/5.44 thf(fact_1266_div__mult__mult1__if,axiom,
% 5.25/5.44 ! [C: nat,A: nat,B: nat] :
% 5.25/5.44 ( ( ( C = zero_zero_nat )
% 5.25/5.44 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.25/5.44 = zero_zero_nat ) )
% 5.25/5.44 & ( ( C != zero_zero_nat )
% 5.25/5.44 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.25/5.44 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_mult1_if
% 5.25/5.44 thf(fact_1267_div__mult__mult1__if,axiom,
% 5.25/5.44 ! [C: int,A: int,B: int] :
% 5.25/5.44 ( ( ( C = zero_zero_int )
% 5.25/5.44 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.44 = zero_zero_int ) )
% 5.25/5.44 & ( ( C != zero_zero_int )
% 5.25/5.44 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.44 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_mult1_if
% 5.25/5.44 thf(fact_1268_divide__eq__1__iff,axiom,
% 5.25/5.44 ! [A: complex,B: complex] :
% 5.25/5.44 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.25/5.44 = one_one_complex )
% 5.25/5.44 = ( ( B != zero_zero_complex )
% 5.25/5.44 & ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_eq_1_iff
% 5.25/5.44 thf(fact_1269_divide__eq__1__iff,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ( divide_divide_real @ A @ B )
% 5.25/5.44 = one_one_real )
% 5.25/5.44 = ( ( B != zero_zero_real )
% 5.25/5.44 & ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_eq_1_iff
% 5.25/5.44 thf(fact_1270_divide__eq__1__iff,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ( divide_divide_rat @ A @ B )
% 5.25/5.44 = one_one_rat )
% 5.25/5.44 = ( ( B != zero_zero_rat )
% 5.25/5.44 & ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_eq_1_iff
% 5.25/5.44 thf(fact_1271_div__self,axiom,
% 5.25/5.44 ! [A: complex] :
% 5.25/5.44 ( ( A != zero_zero_complex )
% 5.25/5.44 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.25/5.44 = one_one_complex ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_self
% 5.25/5.44 thf(fact_1272_div__self,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( A != zero_zero_real )
% 5.25/5.44 => ( ( divide_divide_real @ A @ A )
% 5.25/5.44 = one_one_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_self
% 5.25/5.44 thf(fact_1273_div__self,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( A != zero_zero_rat )
% 5.25/5.44 => ( ( divide_divide_rat @ A @ A )
% 5.25/5.44 = one_one_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_self
% 5.25/5.44 thf(fact_1274_div__self,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( A != zero_zero_nat )
% 5.25/5.44 => ( ( divide_divide_nat @ A @ A )
% 5.25/5.44 = one_one_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_self
% 5.25/5.44 thf(fact_1275_div__self,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( A != zero_zero_int )
% 5.25/5.44 => ( ( divide_divide_int @ A @ A )
% 5.25/5.44 = one_one_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_self
% 5.25/5.44 thf(fact_1276_one__eq__divide__iff,axiom,
% 5.25/5.44 ! [A: complex,B: complex] :
% 5.25/5.44 ( ( one_one_complex
% 5.25/5.44 = ( divide1717551699836669952omplex @ A @ B ) )
% 5.25/5.44 = ( ( B != zero_zero_complex )
% 5.25/5.44 & ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_eq_divide_iff
% 5.25/5.44 thf(fact_1277_one__eq__divide__iff,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( one_one_real
% 5.25/5.44 = ( divide_divide_real @ A @ B ) )
% 5.25/5.44 = ( ( B != zero_zero_real )
% 5.25/5.44 & ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_eq_divide_iff
% 5.25/5.44 thf(fact_1278_one__eq__divide__iff,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( one_one_rat
% 5.25/5.44 = ( divide_divide_rat @ A @ B ) )
% 5.25/5.44 = ( ( B != zero_zero_rat )
% 5.25/5.44 & ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_eq_divide_iff
% 5.25/5.44 thf(fact_1279_divide__self,axiom,
% 5.25/5.44 ! [A: complex] :
% 5.25/5.44 ( ( A != zero_zero_complex )
% 5.25/5.44 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.25/5.44 = one_one_complex ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_self
% 5.25/5.44 thf(fact_1280_divide__self,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( A != zero_zero_real )
% 5.25/5.44 => ( ( divide_divide_real @ A @ A )
% 5.25/5.44 = one_one_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_self
% 5.25/5.44 thf(fact_1281_divide__self,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( A != zero_zero_rat )
% 5.25/5.44 => ( ( divide_divide_rat @ A @ A )
% 5.25/5.44 = one_one_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_self
% 5.25/5.44 thf(fact_1282_divide__self__if,axiom,
% 5.25/5.44 ! [A: complex] :
% 5.25/5.44 ( ( ( A = zero_zero_complex )
% 5.25/5.44 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.25/5.44 = zero_zero_complex ) )
% 5.25/5.44 & ( ( A != zero_zero_complex )
% 5.25/5.44 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.25/5.44 = one_one_complex ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_self_if
% 5.25/5.44 thf(fact_1283_divide__self__if,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( ( A = zero_zero_real )
% 5.25/5.44 => ( ( divide_divide_real @ A @ A )
% 5.25/5.44 = zero_zero_real ) )
% 5.25/5.44 & ( ( A != zero_zero_real )
% 5.25/5.44 => ( ( divide_divide_real @ A @ A )
% 5.25/5.44 = one_one_real ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_self_if
% 5.25/5.44 thf(fact_1284_divide__self__if,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( ( A = zero_zero_rat )
% 5.25/5.44 => ( ( divide_divide_rat @ A @ A )
% 5.25/5.44 = zero_zero_rat ) )
% 5.25/5.44 & ( ( A != zero_zero_rat )
% 5.25/5.44 => ( ( divide_divide_rat @ A @ A )
% 5.25/5.44 = one_one_rat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_self_if
% 5.25/5.44 thf(fact_1285_divide__eq__eq__1,axiom,
% 5.25/5.44 ! [B: real,A: real] :
% 5.25/5.44 ( ( ( divide_divide_real @ B @ A )
% 5.25/5.44 = one_one_real )
% 5.25/5.44 = ( ( A != zero_zero_real )
% 5.25/5.44 & ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_eq_eq_1
% 5.25/5.44 thf(fact_1286_divide__eq__eq__1,axiom,
% 5.25/5.44 ! [B: rat,A: rat] :
% 5.25/5.44 ( ( ( divide_divide_rat @ B @ A )
% 5.25/5.44 = one_one_rat )
% 5.25/5.44 = ( ( A != zero_zero_rat )
% 5.25/5.44 & ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_eq_eq_1
% 5.25/5.44 thf(fact_1287_eq__divide__eq__1,axiom,
% 5.25/5.44 ! [B: real,A: real] :
% 5.25/5.44 ( ( one_one_real
% 5.25/5.44 = ( divide_divide_real @ B @ A ) )
% 5.25/5.44 = ( ( A != zero_zero_real )
% 5.25/5.44 & ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % eq_divide_eq_1
% 5.25/5.44 thf(fact_1288_eq__divide__eq__1,axiom,
% 5.25/5.44 ! [B: rat,A: rat] :
% 5.25/5.44 ( ( one_one_rat
% 5.25/5.44 = ( divide_divide_rat @ B @ A ) )
% 5.25/5.44 = ( ( A != zero_zero_rat )
% 5.25/5.44 & ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % eq_divide_eq_1
% 5.25/5.44 thf(fact_1289_one__divide__eq__0__iff,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.25/5.44 = zero_zero_real )
% 5.25/5.44 = ( A = zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_divide_eq_0_iff
% 5.25/5.44 thf(fact_1290_one__divide__eq__0__iff,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 5.25/5.44 = zero_zero_rat )
% 5.25/5.44 = ( A = zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_divide_eq_0_iff
% 5.25/5.44 thf(fact_1291_zero__eq__1__divide__iff,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( zero_zero_real
% 5.25/5.44 = ( divide_divide_real @ one_one_real @ A ) )
% 5.25/5.44 = ( A = zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_eq_1_divide_iff
% 5.25/5.44 thf(fact_1292_zero__eq__1__divide__iff,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( zero_zero_rat
% 5.25/5.44 = ( divide_divide_rat @ one_one_rat @ A ) )
% 5.25/5.44 = ( A = zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_eq_1_divide_iff
% 5.25/5.44 thf(fact_1293_power__0__Suc,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 5.25/5.44 = zero_zero_rat ) ).
% 5.25/5.44
% 5.25/5.44 % power_0_Suc
% 5.25/5.44 thf(fact_1294_power__0__Suc,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % power_0_Suc
% 5.25/5.44 thf(fact_1295_power__0__Suc,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 5.25/5.44 = zero_zero_real ) ).
% 5.25/5.44
% 5.25/5.44 % power_0_Suc
% 5.25/5.44 thf(fact_1296_power__0__Suc,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % power_0_Suc
% 5.25/5.44 thf(fact_1297_power__0__Suc,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 5.25/5.44 = zero_zero_complex ) ).
% 5.25/5.44
% 5.25/5.44 % power_0_Suc
% 5.25/5.44 thf(fact_1298_power__zero__numeral,axiom,
% 5.25/5.44 ! [K: num] :
% 5.25/5.44 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.25/5.44 = zero_zero_rat ) ).
% 5.25/5.44
% 5.25/5.44 % power_zero_numeral
% 5.25/5.44 thf(fact_1299_power__zero__numeral,axiom,
% 5.25/5.44 ! [K: num] :
% 5.25/5.44 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % power_zero_numeral
% 5.25/5.44 thf(fact_1300_power__zero__numeral,axiom,
% 5.25/5.44 ! [K: num] :
% 5.25/5.44 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.25/5.44 = zero_zero_real ) ).
% 5.25/5.44
% 5.25/5.44 % power_zero_numeral
% 5.25/5.44 thf(fact_1301_power__zero__numeral,axiom,
% 5.25/5.44 ! [K: num] :
% 5.25/5.44 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % power_zero_numeral
% 5.25/5.44 thf(fact_1302_power__zero__numeral,axiom,
% 5.25/5.44 ! [K: num] :
% 5.25/5.44 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.25/5.44 = zero_zero_complex ) ).
% 5.25/5.44
% 5.25/5.44 % power_zero_numeral
% 5.25/5.44 thf(fact_1303_power__eq__0__iff,axiom,
% 5.25/5.44 ! [A: rat,N: nat] :
% 5.25/5.44 ( ( ( power_power_rat @ A @ N )
% 5.25/5.44 = zero_zero_rat )
% 5.25/5.44 = ( ( A = zero_zero_rat )
% 5.25/5.44 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_eq_0_iff
% 5.25/5.44 thf(fact_1304_power__eq__0__iff,axiom,
% 5.25/5.44 ! [A: nat,N: nat] :
% 5.25/5.44 ( ( ( power_power_nat @ A @ N )
% 5.25/5.44 = zero_zero_nat )
% 5.25/5.44 = ( ( A = zero_zero_nat )
% 5.25/5.44 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_eq_0_iff
% 5.25/5.44 thf(fact_1305_power__eq__0__iff,axiom,
% 5.25/5.44 ! [A: real,N: nat] :
% 5.25/5.44 ( ( ( power_power_real @ A @ N )
% 5.25/5.44 = zero_zero_real )
% 5.25/5.44 = ( ( A = zero_zero_real )
% 5.25/5.44 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_eq_0_iff
% 5.25/5.44 thf(fact_1306_power__eq__0__iff,axiom,
% 5.25/5.44 ! [A: int,N: nat] :
% 5.25/5.44 ( ( ( power_power_int @ A @ N )
% 5.25/5.44 = zero_zero_int )
% 5.25/5.44 = ( ( A = zero_zero_int )
% 5.25/5.44 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_eq_0_iff
% 5.25/5.44 thf(fact_1307_power__eq__0__iff,axiom,
% 5.25/5.44 ! [A: complex,N: nat] :
% 5.25/5.44 ( ( ( power_power_complex @ A @ N )
% 5.25/5.44 = zero_zero_complex )
% 5.25/5.44 = ( ( A = zero_zero_complex )
% 5.25/5.44 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_eq_0_iff
% 5.25/5.44 thf(fact_1308_mod__mult__self2__is__0,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % mod_mult_self2_is_0
% 5.25/5.44 thf(fact_1309_mod__mult__self2__is__0,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % mod_mult_self2_is_0
% 5.25/5.44 thf(fact_1310_mod__mult__self2__is__0,axiom,
% 5.25/5.44 ! [A: code_integer,B: code_integer] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.25/5.44 = zero_z3403309356797280102nteger ) ).
% 5.25/5.44
% 5.25/5.44 % mod_mult_self2_is_0
% 5.25/5.44 thf(fact_1311_mod__mult__self1__is__0,axiom,
% 5.25/5.44 ! [B: nat,A: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % mod_mult_self1_is_0
% 5.25/5.44 thf(fact_1312_mod__mult__self1__is__0,axiom,
% 5.25/5.44 ! [B: int,A: int] :
% 5.25/5.44 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % mod_mult_self1_is_0
% 5.25/5.44 thf(fact_1313_mod__mult__self1__is__0,axiom,
% 5.25/5.44 ! [B: code_integer,A: code_integer] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 5.25/5.44 = zero_z3403309356797280102nteger ) ).
% 5.25/5.44
% 5.25/5.44 % mod_mult_self1_is_0
% 5.25/5.44 thf(fact_1314_mod__by__1,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % mod_by_1
% 5.25/5.44 thf(fact_1315_mod__by__1,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % mod_by_1
% 5.25/5.44 thf(fact_1316_mod__by__1,axiom,
% 5.25/5.44 ! [A: code_integer] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.25/5.44 = zero_z3403309356797280102nteger ) ).
% 5.25/5.44
% 5.25/5.44 % mod_by_1
% 5.25/5.44 thf(fact_1317_bits__mod__by__1,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % bits_mod_by_1
% 5.25/5.44 thf(fact_1318_bits__mod__by__1,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % bits_mod_by_1
% 5.25/5.44 thf(fact_1319_bits__mod__by__1,axiom,
% 5.25/5.44 ! [A: code_integer] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.25/5.44 = zero_z3403309356797280102nteger ) ).
% 5.25/5.44
% 5.25/5.44 % bits_mod_by_1
% 5.25/5.44 thf(fact_1320_bits__mod__div__trivial,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % bits_mod_div_trivial
% 5.25/5.44 thf(fact_1321_bits__mod__div__trivial,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % bits_mod_div_trivial
% 5.25/5.44 thf(fact_1322_bits__mod__div__trivial,axiom,
% 5.25/5.44 ! [A: code_integer,B: code_integer] :
% 5.25/5.44 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.25/5.44 = zero_z3403309356797280102nteger ) ).
% 5.25/5.44
% 5.25/5.44 % bits_mod_div_trivial
% 5.25/5.44 thf(fact_1323_mod__div__trivial,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % mod_div_trivial
% 5.25/5.44 thf(fact_1324_mod__div__trivial,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % mod_div_trivial
% 5.25/5.44 thf(fact_1325_mod__div__trivial,axiom,
% 5.25/5.44 ! [A: code_integer,B: code_integer] :
% 5.25/5.44 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.25/5.44 = zero_z3403309356797280102nteger ) ).
% 5.25/5.44
% 5.25/5.44 % mod_div_trivial
% 5.25/5.44 thf(fact_1326_zmod__numeral__Bit0,axiom,
% 5.25/5.44 ! [V: num,W: num] :
% 5.25/5.44 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.25/5.44 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % zmod_numeral_Bit0
% 5.25/5.44 thf(fact_1327_one__le__mult__iff,axiom,
% 5.25/5.44 ! [M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 5.25/5.44 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.25/5.44 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_le_mult_iff
% 5.25/5.44 thf(fact_1328_nat__mult__le__cancel__disj,axiom,
% 5.25/5.44 ! [K: nat,M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.25/5.44 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.44 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_mult_le_cancel_disj
% 5.25/5.44 thf(fact_1329_mult__le__cancel2,axiom,
% 5.25/5.44 ! [M: nat,K: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.25/5.44 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.44 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_le_cancel2
% 5.25/5.44 thf(fact_1330_div__mult__self__is__m,axiom,
% 5.25/5.44 ! [N: nat,M: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.44 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 5.25/5.44 = M ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_self_is_m
% 5.25/5.44 thf(fact_1331_div__mult__self1__is__m,axiom,
% 5.25/5.44 ! [N: nat,M: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.44 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 5.25/5.44 = M ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_self1_is_m
% 5.25/5.44 thf(fact_1332_signed__take__bit__Suc__1,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 5.25/5.44 = one_one_int ) ).
% 5.25/5.44
% 5.25/5.44 % signed_take_bit_Suc_1
% 5.25/5.44 thf(fact_1333_signed__take__bit__numeral__of__1,axiom,
% 5.25/5.44 ! [K: num] :
% 5.25/5.44 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.25/5.44 = one_one_int ) ).
% 5.25/5.44
% 5.25/5.44 % signed_take_bit_numeral_of_1
% 5.25/5.44 thf(fact_1334_dbl__simps_I5_J,axiom,
% 5.25/5.44 ! [K: num] :
% 5.25/5.44 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.25/5.44 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_simps(5)
% 5.25/5.44 thf(fact_1335_dbl__simps_I5_J,axiom,
% 5.25/5.44 ! [K: num] :
% 5.25/5.44 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 5.25/5.44 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_simps(5)
% 5.25/5.44 thf(fact_1336_dbl__simps_I5_J,axiom,
% 5.25/5.44 ! [K: num] :
% 5.25/5.44 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 5.25/5.44 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_simps(5)
% 5.25/5.44 thf(fact_1337_dbl__simps_I5_J,axiom,
% 5.25/5.44 ! [K: num] :
% 5.25/5.44 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 5.25/5.44 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_simps(5)
% 5.25/5.44 thf(fact_1338_both__member__options__from__complete__tree__to__child,axiom,
% 5.25/5.44 ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.25/5.44 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X3 )
% 5.25/5.44 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.44 | ( X3 = Mi )
% 5.25/5.44 | ( X3 = Ma ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % both_member_options_from_complete_tree_to_child
% 5.25/5.44 thf(fact_1339_member__inv,axiom,
% 5.25/5.44 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 5.25/5.44 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X3 )
% 5.25/5.44 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.25/5.44 & ( ( X3 = Mi )
% 5.25/5.44 | ( X3 = Ma )
% 5.25/5.44 | ( ( ord_less_nat @ X3 @ Ma )
% 5.25/5.44 & ( ord_less_nat @ Mi @ X3 )
% 5.25/5.44 & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.25/5.44 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % member_inv
% 5.25/5.44 thf(fact_1340_divide__le__0__1__iff,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.25/5.44 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_le_0_1_iff
% 5.25/5.44 thf(fact_1341_divide__le__0__1__iff,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.25/5.44 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_le_0_1_iff
% 5.25/5.44 thf(fact_1342_zero__le__divide__1__iff,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.25/5.44 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_le_divide_1_iff
% 5.25/5.44 thf(fact_1343_zero__le__divide__1__iff,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.25/5.44 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_le_divide_1_iff
% 5.25/5.44 thf(fact_1344_divide__less__0__1__iff,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.25/5.44 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_less_0_1_iff
% 5.25/5.44 thf(fact_1345_divide__less__0__1__iff,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.25/5.44 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_less_0_1_iff
% 5.25/5.44 thf(fact_1346_divide__less__eq__1__neg,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.44 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.25/5.44 = ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_less_eq_1_neg
% 5.25/5.44 thf(fact_1347_divide__less__eq__1__neg,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.44 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.25/5.44 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_less_eq_1_neg
% 5.25/5.44 thf(fact_1348_divide__less__eq__1__pos,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.44 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.25/5.44 = ( ord_less_real @ B @ A ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_less_eq_1_pos
% 5.25/5.44 thf(fact_1349_divide__less__eq__1__pos,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.44 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.25/5.44 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_less_eq_1_pos
% 5.25/5.44 thf(fact_1350_less__divide__eq__1__neg,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.44 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.25/5.44 = ( ord_less_real @ B @ A ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_divide_eq_1_neg
% 5.25/5.44 thf(fact_1351_less__divide__eq__1__neg,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.44 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.25/5.44 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_divide_eq_1_neg
% 5.25/5.44 thf(fact_1352_less__divide__eq__1__pos,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.44 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.25/5.44 = ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_divide_eq_1_pos
% 5.25/5.44 thf(fact_1353_less__divide__eq__1__pos,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.44 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.25/5.44 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_divide_eq_1_pos
% 5.25/5.44 thf(fact_1354_zero__less__divide__1__iff,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.25/5.44 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_less_divide_1_iff
% 5.25/5.44 thf(fact_1355_zero__less__divide__1__iff,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.25/5.44 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_less_divide_1_iff
% 5.25/5.44 thf(fact_1356_divide__eq__eq__numeral1_I1_J,axiom,
% 5.25/5.44 ! [B: complex,W: num,A: complex] :
% 5.25/5.44 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 5.25/5.44 = A )
% 5.25/5.44 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.25/5.44 != zero_zero_complex )
% 5.25/5.44 => ( B
% 5.25/5.44 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.25/5.44 & ( ( ( numera6690914467698888265omplex @ W )
% 5.25/5.44 = zero_zero_complex )
% 5.25/5.44 => ( A = zero_zero_complex ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_eq_eq_numeral1(1)
% 5.25/5.44 thf(fact_1357_divide__eq__eq__numeral1_I1_J,axiom,
% 5.25/5.44 ! [B: real,W: num,A: real] :
% 5.25/5.44 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 5.25/5.44 = A )
% 5.25/5.44 = ( ( ( ( numeral_numeral_real @ W )
% 5.25/5.44 != zero_zero_real )
% 5.25/5.44 => ( B
% 5.25/5.44 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 5.25/5.44 & ( ( ( numeral_numeral_real @ W )
% 5.25/5.44 = zero_zero_real )
% 5.25/5.44 => ( A = zero_zero_real ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_eq_eq_numeral1(1)
% 5.25/5.44 thf(fact_1358_divide__eq__eq__numeral1_I1_J,axiom,
% 5.25/5.44 ! [B: rat,W: num,A: rat] :
% 5.25/5.44 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 5.25/5.44 = A )
% 5.25/5.44 = ( ( ( ( numeral_numeral_rat @ W )
% 5.25/5.44 != zero_zero_rat )
% 5.25/5.44 => ( B
% 5.25/5.44 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 5.25/5.44 & ( ( ( numeral_numeral_rat @ W )
% 5.25/5.44 = zero_zero_rat )
% 5.25/5.44 => ( A = zero_zero_rat ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_eq_eq_numeral1(1)
% 5.25/5.44 thf(fact_1359_eq__divide__eq__numeral1_I1_J,axiom,
% 5.25/5.44 ! [A: complex,B: complex,W: num] :
% 5.25/5.44 ( ( A
% 5.25/5.44 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 5.25/5.44 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.25/5.44 != zero_zero_complex )
% 5.25/5.44 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 5.25/5.44 = B ) )
% 5.25/5.44 & ( ( ( numera6690914467698888265omplex @ W )
% 5.25/5.44 = zero_zero_complex )
% 5.25/5.44 => ( A = zero_zero_complex ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % eq_divide_eq_numeral1(1)
% 5.25/5.44 thf(fact_1360_eq__divide__eq__numeral1_I1_J,axiom,
% 5.25/5.44 ! [A: real,B: real,W: num] :
% 5.25/5.44 ( ( A
% 5.25/5.44 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.44 = ( ( ( ( numeral_numeral_real @ W )
% 5.25/5.44 != zero_zero_real )
% 5.25/5.44 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 5.25/5.44 = B ) )
% 5.25/5.44 & ( ( ( numeral_numeral_real @ W )
% 5.25/5.44 = zero_zero_real )
% 5.25/5.44 => ( A = zero_zero_real ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % eq_divide_eq_numeral1(1)
% 5.25/5.44 thf(fact_1361_eq__divide__eq__numeral1_I1_J,axiom,
% 5.25/5.44 ! [A: rat,B: rat,W: num] :
% 5.25/5.44 ( ( A
% 5.25/5.44 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.25/5.44 = ( ( ( ( numeral_numeral_rat @ W )
% 5.25/5.44 != zero_zero_rat )
% 5.25/5.44 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 5.25/5.44 = B ) )
% 5.25/5.44 & ( ( ( numeral_numeral_rat @ W )
% 5.25/5.44 = zero_zero_rat )
% 5.25/5.44 => ( A = zero_zero_rat ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % eq_divide_eq_numeral1(1)
% 5.25/5.44 thf(fact_1362_nonzero__divide__mult__cancel__left,axiom,
% 5.25/5.44 ! [A: complex,B: complex] :
% 5.25/5.44 ( ( A != zero_zero_complex )
% 5.25/5.44 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 5.25/5.44 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_divide_mult_cancel_left
% 5.25/5.44 thf(fact_1363_nonzero__divide__mult__cancel__left,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( A != zero_zero_real )
% 5.25/5.44 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 5.25/5.44 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_divide_mult_cancel_left
% 5.25/5.44 thf(fact_1364_nonzero__divide__mult__cancel__left,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( A != zero_zero_rat )
% 5.25/5.44 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 5.25/5.44 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_divide_mult_cancel_left
% 5.25/5.44 thf(fact_1365_nonzero__divide__mult__cancel__right,axiom,
% 5.25/5.44 ! [B: complex,A: complex] :
% 5.25/5.44 ( ( B != zero_zero_complex )
% 5.25/5.44 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 5.25/5.44 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_divide_mult_cancel_right
% 5.25/5.44 thf(fact_1366_nonzero__divide__mult__cancel__right,axiom,
% 5.25/5.44 ! [B: real,A: real] :
% 5.25/5.44 ( ( B != zero_zero_real )
% 5.25/5.44 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 5.25/5.44 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_divide_mult_cancel_right
% 5.25/5.44 thf(fact_1367_nonzero__divide__mult__cancel__right,axiom,
% 5.25/5.44 ! [B: rat,A: rat] :
% 5.25/5.44 ( ( B != zero_zero_rat )
% 5.25/5.44 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 5.25/5.44 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonzero_divide_mult_cancel_right
% 5.25/5.44 thf(fact_1368_div__mult__self4,axiom,
% 5.25/5.44 ! [B: nat,C: nat,A: nat] :
% 5.25/5.44 ( ( B != zero_zero_nat )
% 5.25/5.44 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.25/5.44 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_self4
% 5.25/5.44 thf(fact_1369_div__mult__self4,axiom,
% 5.25/5.44 ! [B: int,C: int,A: int] :
% 5.25/5.44 ( ( B != zero_zero_int )
% 5.25/5.44 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.25/5.44 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_self4
% 5.25/5.44 thf(fact_1370_div__mult__self3,axiom,
% 5.25/5.44 ! [B: nat,C: nat,A: nat] :
% 5.25/5.44 ( ( B != zero_zero_nat )
% 5.25/5.44 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.25/5.44 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_self3
% 5.25/5.44 thf(fact_1371_div__mult__self3,axiom,
% 5.25/5.44 ! [B: int,C: int,A: int] :
% 5.25/5.44 ( ( B != zero_zero_int )
% 5.25/5.44 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.25/5.44 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_self3
% 5.25/5.44 thf(fact_1372_div__mult__self2,axiom,
% 5.25/5.44 ! [B: nat,A: nat,C: nat] :
% 5.25/5.44 ( ( B != zero_zero_nat )
% 5.25/5.44 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.25/5.44 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_self2
% 5.25/5.44 thf(fact_1373_div__mult__self2,axiom,
% 5.25/5.44 ! [B: int,A: int,C: int] :
% 5.25/5.44 ( ( B != zero_zero_int )
% 5.25/5.44 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.25/5.44 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_self2
% 5.25/5.44 thf(fact_1374_div__mult__self1,axiom,
% 5.25/5.44 ! [B: nat,A: nat,C: nat] :
% 5.25/5.44 ( ( B != zero_zero_nat )
% 5.25/5.44 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.25/5.44 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_self1
% 5.25/5.44 thf(fact_1375_div__mult__self1,axiom,
% 5.25/5.44 ! [B: int,A: int,C: int] :
% 5.25/5.44 ( ( B != zero_zero_int )
% 5.25/5.44 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.25/5.44 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mult_self1
% 5.25/5.44 thf(fact_1376_power__mono__iff,axiom,
% 5.25/5.44 ! [A: real,B: real,N: nat] :
% 5.25/5.44 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.44 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.44 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.44 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.25/5.44 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_mono_iff
% 5.25/5.44 thf(fact_1377_power__mono__iff,axiom,
% 5.25/5.44 ! [A: rat,B: rat,N: nat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.44 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.44 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.44 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.25/5.44 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_mono_iff
% 5.25/5.44 thf(fact_1378_power__mono__iff,axiom,
% 5.25/5.44 ! [A: nat,B: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.44 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.44 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.44 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.25/5.44 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_mono_iff
% 5.25/5.44 thf(fact_1379_power__mono__iff,axiom,
% 5.25/5.44 ! [A: int,B: int,N: nat] :
% 5.25/5.44 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.44 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.44 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.44 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.25/5.44 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_mono_iff
% 5.25/5.44 thf(fact_1380_signed__take__bit__Suc__bit0,axiom,
% 5.25/5.44 ! [N: nat,K: num] :
% 5.25/5.44 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.25/5.44 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % signed_take_bit_Suc_bit0
% 5.25/5.44 thf(fact_1381_half__negative__int__iff,axiom,
% 5.25/5.44 ! [K: int] :
% 5.25/5.44 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.25/5.44 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % half_negative_int_iff
% 5.25/5.44 thf(fact_1382_half__nonnegative__int__iff,axiom,
% 5.25/5.44 ! [K: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.25/5.44
% 5.25/5.44 % half_nonnegative_int_iff
% 5.25/5.44 thf(fact_1383_le__divide__eq__1__pos,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.44 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.25/5.44 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_divide_eq_1_pos
% 5.25/5.44 thf(fact_1384_le__divide__eq__1__pos,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.44 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.25/5.44 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_divide_eq_1_pos
% 5.25/5.44 thf(fact_1385_le__divide__eq__1__neg,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.44 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.25/5.44 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_divide_eq_1_neg
% 5.25/5.44 thf(fact_1386_le__divide__eq__1__neg,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.44 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.25/5.44 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_divide_eq_1_neg
% 5.25/5.44 thf(fact_1387_divide__le__eq__1__pos,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.44 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.25/5.44 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_le_eq_1_pos
% 5.25/5.44 thf(fact_1388_divide__le__eq__1__pos,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.44 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.25/5.44 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_le_eq_1_pos
% 5.25/5.44 thf(fact_1389_divide__le__eq__1__neg,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.44 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.25/5.44 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_le_eq_1_neg
% 5.25/5.44 thf(fact_1390_divide__le__eq__1__neg,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.44 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.25/5.44 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divide_le_eq_1_neg
% 5.25/5.44 thf(fact_1391_power__strict__decreasing__iff,axiom,
% 5.25/5.44 ! [B: real,M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.44 => ( ( ord_less_real @ B @ one_one_real )
% 5.25/5.44 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.25/5.44 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_strict_decreasing_iff
% 5.25/5.44 thf(fact_1392_power__strict__decreasing__iff,axiom,
% 5.25/5.44 ! [B: rat,M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.25/5.44 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.25/5.44 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.25/5.44 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_strict_decreasing_iff
% 5.25/5.44 thf(fact_1393_power__strict__decreasing__iff,axiom,
% 5.25/5.44 ! [B: nat,M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.44 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.25/5.44 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.25/5.44 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_strict_decreasing_iff
% 5.25/5.44 thf(fact_1394_power__strict__decreasing__iff,axiom,
% 5.25/5.44 ! [B: int,M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.44 => ( ( ord_less_int @ B @ one_one_int )
% 5.25/5.44 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.25/5.44 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_strict_decreasing_iff
% 5.25/5.44 thf(fact_1395_zero__eq__power2,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = zero_zero_rat )
% 5.25/5.44 = ( A = zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_eq_power2
% 5.25/5.44 thf(fact_1396_zero__eq__power2,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = zero_zero_nat )
% 5.25/5.44 = ( A = zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_eq_power2
% 5.25/5.44 thf(fact_1397_zero__eq__power2,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = zero_zero_real )
% 5.25/5.44 = ( A = zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_eq_power2
% 5.25/5.44 thf(fact_1398_zero__eq__power2,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = zero_zero_int )
% 5.25/5.44 = ( A = zero_zero_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_eq_power2
% 5.25/5.44 thf(fact_1399_zero__eq__power2,axiom,
% 5.25/5.44 ! [A: complex] :
% 5.25/5.44 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = zero_zero_complex )
% 5.25/5.44 = ( A = zero_zero_complex ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_eq_power2
% 5.25/5.44 thf(fact_1400_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 != ( suc @ zero_zero_nat ) )
% 5.25/5.44 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % not_mod2_eq_Suc_0_eq_0
% 5.25/5.44 thf(fact_1401_add__self__mod__2,axiom,
% 5.25/5.44 ! [M: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % add_self_mod_2
% 5.25/5.44 thf(fact_1402_one__div__two__eq__zero,axiom,
% 5.25/5.44 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % one_div_two_eq_zero
% 5.25/5.44 thf(fact_1403_one__div__two__eq__zero,axiom,
% 5.25/5.44 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % one_div_two_eq_zero
% 5.25/5.44 thf(fact_1404_bits__1__div__2,axiom,
% 5.25/5.44 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % bits_1_div_2
% 5.25/5.44 thf(fact_1405_bits__1__div__2,axiom,
% 5.25/5.44 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.44 = zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % bits_1_div_2
% 5.25/5.44 thf(fact_1406_power__decreasing__iff,axiom,
% 5.25/5.44 ! [B: real,M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.44 => ( ( ord_less_real @ B @ one_one_real )
% 5.25/5.44 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.25/5.44 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_decreasing_iff
% 5.25/5.44 thf(fact_1407_power__decreasing__iff,axiom,
% 5.25/5.44 ! [B: rat,M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.25/5.44 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.25/5.44 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.25/5.44 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_decreasing_iff
% 5.25/5.44 thf(fact_1408_power__decreasing__iff,axiom,
% 5.25/5.44 ! [B: nat,M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.44 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.25/5.44 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.25/5.44 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_decreasing_iff
% 5.25/5.44 thf(fact_1409_power__decreasing__iff,axiom,
% 5.25/5.44 ! [B: int,M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.44 => ( ( ord_less_int @ B @ one_one_int )
% 5.25/5.44 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.25/5.44 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_decreasing_iff
% 5.25/5.44 thf(fact_1410_power2__eq__iff__nonneg,axiom,
% 5.25/5.44 ! [X3: real,Y: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.44 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.44 => ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = ( X3 = Y ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power2_eq_iff_nonneg
% 5.25/5.44 thf(fact_1411_power2__eq__iff__nonneg,axiom,
% 5.25/5.44 ! [X3: rat,Y: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.25/5.44 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.44 => ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = ( X3 = Y ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power2_eq_iff_nonneg
% 5.25/5.44 thf(fact_1412_power2__eq__iff__nonneg,axiom,
% 5.25/5.44 ! [X3: nat,Y: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 5.25/5.44 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.25/5.44 => ( ( ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = ( X3 = Y ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power2_eq_iff_nonneg
% 5.25/5.44 thf(fact_1413_power2__eq__iff__nonneg,axiom,
% 5.25/5.44 ! [X3: int,Y: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.44 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.44 => ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = ( X3 = Y ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power2_eq_iff_nonneg
% 5.25/5.44 thf(fact_1414_power2__less__eq__zero__iff,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.25/5.44 = ( A = zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % power2_less_eq_zero_iff
% 5.25/5.44 thf(fact_1415_power2__less__eq__zero__iff,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.25/5.44 = ( A = zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % power2_less_eq_zero_iff
% 5.25/5.44 thf(fact_1416_power2__less__eq__zero__iff,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.25/5.44 = ( A = zero_zero_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % power2_less_eq_zero_iff
% 5.25/5.44 thf(fact_1417_zero__less__power2,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = ( A != zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_less_power2
% 5.25/5.44 thf(fact_1418_zero__less__power2,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = ( A != zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_less_power2
% 5.25/5.44 thf(fact_1419_zero__less__power2,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = ( A != zero_zero_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_less_power2
% 5.25/5.44 thf(fact_1420_sum__power2__eq__zero__iff,axiom,
% 5.25/5.44 ! [X3: rat,Y: rat] :
% 5.25/5.44 ( ( ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = zero_zero_rat )
% 5.25/5.44 = ( ( X3 = zero_zero_rat )
% 5.25/5.44 & ( Y = zero_zero_rat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % sum_power2_eq_zero_iff
% 5.25/5.44 thf(fact_1421_sum__power2__eq__zero__iff,axiom,
% 5.25/5.44 ! [X3: real,Y: real] :
% 5.25/5.44 ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = zero_zero_real )
% 5.25/5.44 = ( ( X3 = zero_zero_real )
% 5.25/5.44 & ( Y = zero_zero_real ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % sum_power2_eq_zero_iff
% 5.25/5.44 thf(fact_1422_sum__power2__eq__zero__iff,axiom,
% 5.25/5.44 ! [X3: int,Y: int] :
% 5.25/5.44 ( ( ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = zero_zero_int )
% 5.25/5.44 = ( ( X3 = zero_zero_int )
% 5.25/5.44 & ( Y = zero_zero_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % sum_power2_eq_zero_iff
% 5.25/5.44 thf(fact_1423_not__mod__2__eq__1__eq__0,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 != one_one_nat )
% 5.25/5.44 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % not_mod_2_eq_1_eq_0
% 5.25/5.44 thf(fact_1424_not__mod__2__eq__1__eq__0,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.44 != one_one_int )
% 5.25/5.44 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.44 = zero_zero_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % not_mod_2_eq_1_eq_0
% 5.25/5.44 thf(fact_1425_not__mod__2__eq__1__eq__0,axiom,
% 5.25/5.44 ! [A: code_integer] :
% 5.25/5.44 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.44 != one_one_Code_integer )
% 5.25/5.44 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.44 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.44
% 5.25/5.44 % not_mod_2_eq_1_eq_0
% 5.25/5.44 thf(fact_1426_not__mod__2__eq__0__eq__1,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 != zero_zero_nat )
% 5.25/5.44 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % not_mod_2_eq_0_eq_1
% 5.25/5.44 thf(fact_1427_not__mod__2__eq__0__eq__1,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.44 != zero_zero_int )
% 5.25/5.44 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % not_mod_2_eq_0_eq_1
% 5.25/5.44 thf(fact_1428_not__mod__2__eq__0__eq__1,axiom,
% 5.25/5.44 ! [A: code_integer] :
% 5.25/5.44 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.44 != zero_z3403309356797280102nteger )
% 5.25/5.44 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_Code_integer ) ) ).
% 5.25/5.44
% 5.25/5.44 % not_mod_2_eq_0_eq_1
% 5.25/5.44 thf(fact_1429_unset__bit__0,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.25/5.44 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % unset_bit_0
% 5.25/5.44 thf(fact_1430_unset__bit__0,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.25/5.44 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % unset_bit_0
% 5.25/5.44 thf(fact_1431_mod2__gr__0,axiom,
% 5.25/5.44 ! [M: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod2_gr_0
% 5.25/5.44 thf(fact_1432_set__bit__0,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.25/5.44 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % set_bit_0
% 5.25/5.44 thf(fact_1433_set__bit__0,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.25/5.44 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % set_bit_0
% 5.25/5.44 thf(fact_1434_split__zdiv,axiom,
% 5.25/5.44 ! [P: int > $o,N: int,K: int] :
% 5.25/5.44 ( ( P @ ( divide_divide_int @ N @ K ) )
% 5.25/5.44 = ( ( ( K = zero_zero_int )
% 5.25/5.44 => ( P @ zero_zero_int ) )
% 5.25/5.44 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.44 => ! [I3: int,J3: int] :
% 5.25/5.44 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.25/5.44 & ( ord_less_int @ J3 @ K )
% 5.25/5.44 & ( N
% 5.25/5.44 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.25/5.44 => ( P @ I3 ) ) )
% 5.25/5.44 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.25/5.44 => ! [I3: int,J3: int] :
% 5.25/5.44 ( ( ( ord_less_int @ K @ J3 )
% 5.25/5.44 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.25/5.44 & ( N
% 5.25/5.44 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.25/5.44 => ( P @ I3 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % split_zdiv
% 5.25/5.44 thf(fact_1435_int__div__neg__eq,axiom,
% 5.25/5.44 ! [A: int,B: int,Q2: int,R2: int] :
% 5.25/5.44 ( ( A
% 5.25/5.44 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.25/5.44 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.25/5.44 => ( ( ord_less_int @ B @ R2 )
% 5.25/5.44 => ( ( divide_divide_int @ A @ B )
% 5.25/5.44 = Q2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % int_div_neg_eq
% 5.25/5.44 thf(fact_1436_int__div__pos__eq,axiom,
% 5.25/5.44 ! [A: int,B: int,Q2: int,R2: int] :
% 5.25/5.44 ( ( A
% 5.25/5.44 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.25/5.44 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.25/5.44 => ( ( ord_less_int @ R2 @ B )
% 5.25/5.44 => ( ( divide_divide_int @ A @ B )
% 5.25/5.44 = Q2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % int_div_pos_eq
% 5.25/5.44 thf(fact_1437_split__neg__lemma,axiom,
% 5.25/5.44 ! [K: int,P: int > int > $o,N: int] :
% 5.25/5.44 ( ( ord_less_int @ K @ zero_zero_int )
% 5.25/5.44 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.25/5.44 = ( ! [I3: int,J3: int] :
% 5.25/5.44 ( ( ( ord_less_int @ K @ J3 )
% 5.25/5.44 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.25/5.44 & ( N
% 5.25/5.44 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.25/5.44 => ( P @ I3 @ J3 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % split_neg_lemma
% 5.25/5.44 thf(fact_1438_split__pos__lemma,axiom,
% 5.25/5.44 ! [K: int,P: int > int > $o,N: int] :
% 5.25/5.44 ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.44 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.25/5.44 = ( ! [I3: int,J3: int] :
% 5.25/5.44 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.25/5.44 & ( ord_less_int @ J3 @ K )
% 5.25/5.44 & ( N
% 5.25/5.44 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.25/5.44 => ( P @ I3 @ J3 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % split_pos_lemma
% 5.25/5.44 thf(fact_1439_int__div__less__self,axiom,
% 5.25/5.44 ! [X3: int,K: int] :
% 5.25/5.44 ( ( ord_less_int @ zero_zero_int @ X3 )
% 5.25/5.44 => ( ( ord_less_int @ one_one_int @ K )
% 5.25/5.44 => ( ord_less_int @ ( divide_divide_int @ X3 @ K ) @ X3 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % int_div_less_self
% 5.25/5.44 thf(fact_1440_verit__le__mono__div__int,axiom,
% 5.25/5.44 ! [A2: int,B3: int,N: int] :
% 5.25/5.44 ( ( ord_less_int @ A2 @ B3 )
% 5.25/5.44 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.25/5.44 => ( ord_less_eq_int
% 5.25/5.44 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 5.25/5.44 @ ( if_int
% 5.25/5.44 @ ( ( modulo_modulo_int @ B3 @ N )
% 5.25/5.44 = zero_zero_int )
% 5.25/5.44 @ one_one_int
% 5.25/5.44 @ zero_zero_int ) )
% 5.25/5.44 @ ( divide_divide_int @ B3 @ N ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % verit_le_mono_div_int
% 5.25/5.44 thf(fact_1441_zdiv__zmult2__eq,axiom,
% 5.25/5.44 ! [C: int,A: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.44 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.25/5.44 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % zdiv_zmult2_eq
% 5.25/5.44 thf(fact_1442_zmod__zmult2__eq,axiom,
% 5.25/5.44 ! [C: int,A: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.44 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.25/5.44 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % zmod_zmult2_eq
% 5.25/5.44 thf(fact_1443_div__mod__decomp__int,axiom,
% 5.25/5.44 ! [A2: int,N: int] :
% 5.25/5.44 ( A2
% 5.25/5.44 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_mod_decomp_int
% 5.25/5.44 thf(fact_1444_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.44 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.25/5.44 = ( ( ord_less_eq_int @ B @ A )
% 5.25/5.44 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nonneg1_imp_zdiv_pos_iff
% 5.25/5.44 thf(fact_1445_pos__imp__zdiv__nonneg__iff,axiom,
% 5.25/5.44 ! [B: int,A: int] :
% 5.25/5.44 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.44 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.25/5.44 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % pos_imp_zdiv_nonneg_iff
% 5.25/5.44 thf(fact_1446_neg__imp__zdiv__nonneg__iff,axiom,
% 5.25/5.44 ! [B: int,A: int] :
% 5.25/5.44 ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.44 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.25/5.44 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % neg_imp_zdiv_nonneg_iff
% 5.25/5.44 thf(fact_1447_pos__imp__zdiv__pos__iff,axiom,
% 5.25/5.44 ! [K: int,I2: int] :
% 5.25/5.44 ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.44 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K ) )
% 5.25/5.44 = ( ord_less_eq_int @ K @ I2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % pos_imp_zdiv_pos_iff
% 5.25/5.44 thf(fact_1448_pos__imp__zdiv__neg__iff,axiom,
% 5.25/5.44 ! [B: int,A: int] :
% 5.25/5.44 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.44 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.25/5.44 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % pos_imp_zdiv_neg_iff
% 5.25/5.44 thf(fact_1449_neg__imp__zdiv__neg__iff,axiom,
% 5.25/5.44 ! [B: int,A: int] :
% 5.25/5.44 ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.44 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.25/5.44 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % neg_imp_zdiv_neg_iff
% 5.25/5.44 thf(fact_1450_div__nonpos__pos__le0,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.44 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.44 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_nonpos_pos_le0
% 5.25/5.44 thf(fact_1451_div__nonneg__neg__le0,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.44 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.44 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_nonneg_neg_le0
% 5.25/5.44 thf(fact_1452_div__neg__pos__less0,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.44 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.44 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_neg_pos_less0
% 5.25/5.44 thf(fact_1453_div__positive__int,axiom,
% 5.25/5.44 ! [L2: int,K: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ L2 @ K )
% 5.25/5.44 => ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.25/5.44 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_positive_int
% 5.25/5.44 thf(fact_1454_div__int__pos__iff,axiom,
% 5.25/5.44 ! [K: int,L2: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) )
% 5.25/5.44 = ( ( K = zero_zero_int )
% 5.25/5.44 | ( L2 = zero_zero_int )
% 5.25/5.44 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.44 & ( ord_less_eq_int @ zero_zero_int @ L2 ) )
% 5.25/5.44 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.25/5.44 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_int_pos_iff
% 5.25/5.44 thf(fact_1455_zdiv__mono2__neg,axiom,
% 5.25/5.44 ! [A: int,B4: int,B: int] :
% 5.25/5.44 ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.44 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.25/5.44 => ( ( ord_less_eq_int @ B4 @ B )
% 5.25/5.44 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B4 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % zdiv_mono2_neg
% 5.25/5.44 thf(fact_1456_zdiv__mono1__neg,axiom,
% 5.25/5.44 ! [A: int,A4: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ A @ A4 )
% 5.25/5.44 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.44 => ( ord_less_eq_int @ ( divide_divide_int @ A4 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % zdiv_mono1_neg
% 5.25/5.44 thf(fact_1457_zdiv__eq__0__iff,axiom,
% 5.25/5.44 ! [I2: int,K: int] :
% 5.25/5.44 ( ( ( divide_divide_int @ I2 @ K )
% 5.25/5.44 = zero_zero_int )
% 5.25/5.44 = ( ( K = zero_zero_int )
% 5.25/5.44 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.25/5.44 & ( ord_less_int @ I2 @ K ) )
% 5.25/5.44 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 5.25/5.44 & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % zdiv_eq_0_iff
% 5.25/5.44 thf(fact_1458_zdiv__mono__strict,axiom,
% 5.25/5.44 ! [A2: int,B3: int,N: int] :
% 5.25/5.44 ( ( ord_less_int @ A2 @ B3 )
% 5.25/5.44 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.25/5.44 => ( ( ( modulo_modulo_int @ A2 @ N )
% 5.25/5.44 = zero_zero_int )
% 5.25/5.44 => ( ( ( modulo_modulo_int @ B3 @ N )
% 5.25/5.44 = zero_zero_int )
% 5.25/5.44 => ( ord_less_int @ ( divide_divide_int @ A2 @ N ) @ ( divide_divide_int @ B3 @ N ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % zdiv_mono_strict
% 5.25/5.44 thf(fact_1459_zdiv__mono2,axiom,
% 5.25/5.44 ! [A: int,B4: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.44 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.25/5.44 => ( ( ord_less_eq_int @ B4 @ B )
% 5.25/5.44 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B4 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % zdiv_mono2
% 5.25/5.44 thf(fact_1460_zdiv__mono1,axiom,
% 5.25/5.44 ! [A: int,A4: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ A @ A4 )
% 5.25/5.44 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.44 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A4 @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % zdiv_mono1
% 5.25/5.44 thf(fact_1461_zero__reorient,axiom,
% 5.25/5.44 ! [X3: complex] :
% 5.25/5.44 ( ( zero_zero_complex = X3 )
% 5.25/5.44 = ( X3 = zero_zero_complex ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_reorient
% 5.25/5.44 thf(fact_1462_zero__reorient,axiom,
% 5.25/5.44 ! [X3: real] :
% 5.25/5.44 ( ( zero_zero_real = X3 )
% 5.25/5.44 = ( X3 = zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_reorient
% 5.25/5.44 thf(fact_1463_zero__reorient,axiom,
% 5.25/5.44 ! [X3: rat] :
% 5.25/5.44 ( ( zero_zero_rat = X3 )
% 5.25/5.44 = ( X3 = zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_reorient
% 5.25/5.44 thf(fact_1464_zero__reorient,axiom,
% 5.25/5.44 ! [X3: nat] :
% 5.25/5.44 ( ( zero_zero_nat = X3 )
% 5.25/5.44 = ( X3 = zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_reorient
% 5.25/5.44 thf(fact_1465_zero__reorient,axiom,
% 5.25/5.44 ! [X3: int] :
% 5.25/5.44 ( ( zero_zero_int = X3 )
% 5.25/5.44 = ( X3 = zero_zero_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_reorient
% 5.25/5.44 thf(fact_1466_verit__sum__simplify,axiom,
% 5.25/5.44 ! [A: complex] :
% 5.25/5.44 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % verit_sum_simplify
% 5.25/5.44 thf(fact_1467_verit__sum__simplify,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % verit_sum_simplify
% 5.25/5.44 thf(fact_1468_verit__sum__simplify,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % verit_sum_simplify
% 5.25/5.44 thf(fact_1469_verit__sum__simplify,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % verit_sum_simplify
% 5.25/5.44 thf(fact_1470_verit__sum__simplify,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % verit_sum_simplify
% 5.25/5.44 thf(fact_1471_pos__zmod__mult__2,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.44 => ( ( 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 ) )
% 5.25/5.44 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % pos_zmod_mult_2
% 5.25/5.44 thf(fact_1472_power__0__left,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( ( N = zero_zero_nat )
% 5.25/5.44 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.25/5.44 = one_one_rat ) )
% 5.25/5.44 & ( ( N != zero_zero_nat )
% 5.25/5.44 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.25/5.44 = zero_zero_rat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_0_left
% 5.25/5.44 thf(fact_1473_power__0__left,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( ( N = zero_zero_nat )
% 5.25/5.44 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.25/5.44 = one_one_nat ) )
% 5.25/5.44 & ( ( N != zero_zero_nat )
% 5.25/5.44 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.25/5.44 = zero_zero_nat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_0_left
% 5.25/5.44 thf(fact_1474_power__0__left,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( ( N = zero_zero_nat )
% 5.25/5.44 => ( ( power_power_real @ zero_zero_real @ N )
% 5.25/5.44 = one_one_real ) )
% 5.25/5.44 & ( ( N != zero_zero_nat )
% 5.25/5.44 => ( ( power_power_real @ zero_zero_real @ N )
% 5.25/5.44 = zero_zero_real ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_0_left
% 5.25/5.44 thf(fact_1475_power__0__left,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( ( N = zero_zero_nat )
% 5.25/5.44 => ( ( power_power_int @ zero_zero_int @ N )
% 5.25/5.44 = one_one_int ) )
% 5.25/5.44 & ( ( N != zero_zero_nat )
% 5.25/5.44 => ( ( power_power_int @ zero_zero_int @ N )
% 5.25/5.44 = zero_zero_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_0_left
% 5.25/5.44 thf(fact_1476_power__0__left,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( ( N = zero_zero_nat )
% 5.25/5.44 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.25/5.44 = one_one_complex ) )
% 5.25/5.44 & ( ( N != zero_zero_nat )
% 5.25/5.44 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.25/5.44 = zero_zero_complex ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_0_left
% 5.25/5.44 thf(fact_1477_zero__power,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.44 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.25/5.44 = zero_zero_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_power
% 5.25/5.44 thf(fact_1478_zero__power,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.44 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.25/5.44 = zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_power
% 5.25/5.44 thf(fact_1479_zero__power,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.44 => ( ( power_power_real @ zero_zero_real @ N )
% 5.25/5.44 = zero_zero_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_power
% 5.25/5.44 thf(fact_1480_zero__power,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.44 => ( ( power_power_int @ zero_zero_int @ N )
% 5.25/5.44 = zero_zero_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_power
% 5.25/5.44 thf(fact_1481_zero__power,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.44 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.25/5.44 = zero_zero_complex ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_power
% 5.25/5.44 thf(fact_1482_realpow__pos__nth,axiom,
% 5.25/5.44 ! [N: nat,A: real] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.44 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.44 => ? [R3: real] :
% 5.25/5.44 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.25/5.44 & ( ( power_power_real @ R3 @ N )
% 5.25/5.44 = A ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % realpow_pos_nth
% 5.25/5.44 thf(fact_1483_realpow__pos__nth__unique,axiom,
% 5.25/5.44 ! [N: nat,A: real] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.44 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.44 => ? [X5: real] :
% 5.25/5.44 ( ( ord_less_real @ zero_zero_real @ X5 )
% 5.25/5.44 & ( ( power_power_real @ X5 @ N )
% 5.25/5.44 = A )
% 5.25/5.44 & ! [Y4: real] :
% 5.25/5.44 ( ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.25/5.44 & ( ( power_power_real @ Y4 @ N )
% 5.25/5.44 = A ) )
% 5.25/5.44 => ( Y4 = X5 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % realpow_pos_nth_unique
% 5.25/5.44 thf(fact_1484_zero__le,axiom,
% 5.25/5.44 ! [X3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X3 ) ).
% 5.25/5.44
% 5.25/5.44 % zero_le
% 5.25/5.44 thf(fact_1485_le__numeral__extra_I3_J,axiom,
% 5.25/5.44 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.25/5.44
% 5.25/5.44 % le_numeral_extra(3)
% 5.25/5.44 thf(fact_1486_le__numeral__extra_I3_J,axiom,
% 5.25/5.44 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.25/5.44
% 5.25/5.44 % le_numeral_extra(3)
% 5.25/5.44 thf(fact_1487_le__numeral__extra_I3_J,axiom,
% 5.25/5.44 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.25/5.44
% 5.25/5.44 % le_numeral_extra(3)
% 5.25/5.44 thf(fact_1488_le__numeral__extra_I3_J,axiom,
% 5.25/5.44 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.25/5.44
% 5.25/5.44 % le_numeral_extra(3)
% 5.25/5.44 thf(fact_1489_zero__less__iff__neq__zero,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.44 = ( N != zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_less_iff_neq_zero
% 5.25/5.44 thf(fact_1490_gr__implies__not__zero,axiom,
% 5.25/5.44 ! [M: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M @ N )
% 5.25/5.44 => ( N != zero_zero_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % gr_implies_not_zero
% 5.25/5.44 thf(fact_1491_not__less__zero,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % not_less_zero
% 5.25/5.44 thf(fact_1492_gr__zeroI,axiom,
% 5.25/5.44 ! [N: nat] :
% 5.25/5.44 ( ( N != zero_zero_nat )
% 5.25/5.44 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.25/5.44
% 5.25/5.44 % gr_zeroI
% 5.25/5.44 thf(fact_1493_less__numeral__extra_I3_J,axiom,
% 5.25/5.44 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.25/5.44
% 5.25/5.44 % less_numeral_extra(3)
% 5.25/5.44 thf(fact_1494_less__numeral__extra_I3_J,axiom,
% 5.25/5.44 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.25/5.44
% 5.25/5.44 % less_numeral_extra(3)
% 5.25/5.44 thf(fact_1495_less__numeral__extra_I3_J,axiom,
% 5.25/5.44 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.25/5.44
% 5.25/5.44 % less_numeral_extra(3)
% 5.25/5.44 thf(fact_1496_less__numeral__extra_I3_J,axiom,
% 5.25/5.44 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.25/5.44
% 5.25/5.44 % less_numeral_extra(3)
% 5.25/5.44 thf(fact_1497_field__lbound__gt__zero,axiom,
% 5.25/5.44 ! [D1: real,D22: real] :
% 5.25/5.44 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.25/5.44 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.25/5.44 => ? [E2: real] :
% 5.25/5.44 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.25/5.44 & ( ord_less_real @ E2 @ D1 )
% 5.25/5.44 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % field_lbound_gt_zero
% 5.25/5.44 thf(fact_1498_field__lbound__gt__zero,axiom,
% 5.25/5.44 ! [D1: rat,D22: rat] :
% 5.25/5.44 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.25/5.44 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 5.25/5.44 => ? [E2: rat] :
% 5.25/5.44 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.25/5.44 & ( ord_less_rat @ E2 @ D1 )
% 5.25/5.44 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % field_lbound_gt_zero
% 5.25/5.44 thf(fact_1499_zero__neq__numeral,axiom,
% 5.25/5.44 ! [N: num] :
% 5.25/5.44 ( zero_zero_complex
% 5.25/5.44 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_neq_numeral
% 5.25/5.44 thf(fact_1500_zero__neq__numeral,axiom,
% 5.25/5.44 ! [N: num] :
% 5.25/5.44 ( zero_zero_real
% 5.25/5.44 != ( numeral_numeral_real @ N ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_neq_numeral
% 5.25/5.44 thf(fact_1501_zero__neq__numeral,axiom,
% 5.25/5.44 ! [N: num] :
% 5.25/5.44 ( zero_zero_rat
% 5.25/5.44 != ( numeral_numeral_rat @ N ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_neq_numeral
% 5.25/5.44 thf(fact_1502_zero__neq__numeral,axiom,
% 5.25/5.44 ! [N: num] :
% 5.25/5.44 ( zero_zero_nat
% 5.25/5.44 != ( numeral_numeral_nat @ N ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_neq_numeral
% 5.25/5.44 thf(fact_1503_zero__neq__numeral,axiom,
% 5.25/5.44 ! [N: num] :
% 5.25/5.44 ( zero_zero_int
% 5.25/5.44 != ( numeral_numeral_int @ N ) ) ).
% 5.25/5.44
% 5.25/5.44 % zero_neq_numeral
% 5.25/5.44 thf(fact_1504_mult__right__cancel,axiom,
% 5.25/5.44 ! [C: complex,A: complex,B: complex] :
% 5.25/5.44 ( ( C != zero_zero_complex )
% 5.25/5.44 => ( ( ( times_times_complex @ A @ C )
% 5.25/5.44 = ( times_times_complex @ B @ C ) )
% 5.25/5.44 = ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_right_cancel
% 5.25/5.44 thf(fact_1505_mult__right__cancel,axiom,
% 5.25/5.44 ! [C: real,A: real,B: real] :
% 5.25/5.44 ( ( C != zero_zero_real )
% 5.25/5.44 => ( ( ( times_times_real @ A @ C )
% 5.25/5.44 = ( times_times_real @ B @ C ) )
% 5.25/5.44 = ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_right_cancel
% 5.25/5.44 thf(fact_1506_mult__right__cancel,axiom,
% 5.25/5.44 ! [C: rat,A: rat,B: rat] :
% 5.25/5.44 ( ( C != zero_zero_rat )
% 5.25/5.44 => ( ( ( times_times_rat @ A @ C )
% 5.25/5.44 = ( times_times_rat @ B @ C ) )
% 5.25/5.44 = ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_right_cancel
% 5.25/5.44 thf(fact_1507_mult__right__cancel,axiom,
% 5.25/5.44 ! [C: nat,A: nat,B: nat] :
% 5.25/5.44 ( ( C != zero_zero_nat )
% 5.25/5.44 => ( ( ( times_times_nat @ A @ C )
% 5.25/5.44 = ( times_times_nat @ B @ C ) )
% 5.25/5.44 = ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_right_cancel
% 5.25/5.44 thf(fact_1508_mult__right__cancel,axiom,
% 5.25/5.44 ! [C: int,A: int,B: int] :
% 5.25/5.44 ( ( C != zero_zero_int )
% 5.25/5.44 => ( ( ( times_times_int @ A @ C )
% 5.25/5.44 = ( times_times_int @ B @ C ) )
% 5.25/5.44 = ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_right_cancel
% 5.25/5.44 thf(fact_1509_mult__left__cancel,axiom,
% 5.25/5.44 ! [C: complex,A: complex,B: complex] :
% 5.25/5.44 ( ( C != zero_zero_complex )
% 5.25/5.44 => ( ( ( times_times_complex @ C @ A )
% 5.25/5.44 = ( times_times_complex @ C @ B ) )
% 5.25/5.44 = ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_left_cancel
% 5.25/5.44 thf(fact_1510_mult__left__cancel,axiom,
% 5.25/5.44 ! [C: real,A: real,B: real] :
% 5.25/5.44 ( ( C != zero_zero_real )
% 5.25/5.44 => ( ( ( times_times_real @ C @ A )
% 5.25/5.44 = ( times_times_real @ C @ B ) )
% 5.25/5.44 = ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_left_cancel
% 5.25/5.44 thf(fact_1511_mult__left__cancel,axiom,
% 5.25/5.44 ! [C: rat,A: rat,B: rat] :
% 5.25/5.44 ( ( C != zero_zero_rat )
% 5.25/5.44 => ( ( ( times_times_rat @ C @ A )
% 5.25/5.44 = ( times_times_rat @ C @ B ) )
% 5.25/5.44 = ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_left_cancel
% 5.25/5.44 thf(fact_1512_mult__left__cancel,axiom,
% 5.25/5.44 ! [C: nat,A: nat,B: nat] :
% 5.25/5.44 ( ( C != zero_zero_nat )
% 5.25/5.44 => ( ( ( times_times_nat @ C @ A )
% 5.25/5.44 = ( times_times_nat @ C @ B ) )
% 5.25/5.44 = ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_left_cancel
% 5.25/5.44 thf(fact_1513_mult__left__cancel,axiom,
% 5.25/5.44 ! [C: int,A: int,B: int] :
% 5.25/5.44 ( ( C != zero_zero_int )
% 5.25/5.44 => ( ( ( times_times_int @ C @ A )
% 5.25/5.44 = ( times_times_int @ C @ B ) )
% 5.25/5.44 = ( A = B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_left_cancel
% 5.25/5.44 thf(fact_1514_no__zero__divisors,axiom,
% 5.25/5.44 ! [A: complex,B: complex] :
% 5.25/5.44 ( ( A != zero_zero_complex )
% 5.25/5.44 => ( ( B != zero_zero_complex )
% 5.25/5.44 => ( ( times_times_complex @ A @ B )
% 5.25/5.44 != zero_zero_complex ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % no_zero_divisors
% 5.25/5.44 thf(fact_1515_no__zero__divisors,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( A != zero_zero_real )
% 5.25/5.44 => ( ( B != zero_zero_real )
% 5.25/5.44 => ( ( times_times_real @ A @ B )
% 5.25/5.44 != zero_zero_real ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % no_zero_divisors
% 5.25/5.44 thf(fact_1516_no__zero__divisors,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( A != zero_zero_rat )
% 5.25/5.44 => ( ( B != zero_zero_rat )
% 5.25/5.44 => ( ( times_times_rat @ A @ B )
% 5.25/5.44 != zero_zero_rat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % no_zero_divisors
% 5.25/5.44 thf(fact_1517_no__zero__divisors,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( A != zero_zero_nat )
% 5.25/5.44 => ( ( B != zero_zero_nat )
% 5.25/5.44 => ( ( times_times_nat @ A @ B )
% 5.25/5.44 != zero_zero_nat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % no_zero_divisors
% 5.25/5.44 thf(fact_1518_no__zero__divisors,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( A != zero_zero_int )
% 5.25/5.44 => ( ( B != zero_zero_int )
% 5.25/5.44 => ( ( times_times_int @ A @ B )
% 5.25/5.44 != zero_zero_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % no_zero_divisors
% 5.25/5.44 thf(fact_1519_divisors__zero,axiom,
% 5.25/5.44 ! [A: complex,B: complex] :
% 5.25/5.44 ( ( ( times_times_complex @ A @ B )
% 5.25/5.44 = zero_zero_complex )
% 5.25/5.44 => ( ( A = zero_zero_complex )
% 5.25/5.44 | ( B = zero_zero_complex ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divisors_zero
% 5.25/5.44 thf(fact_1520_divisors__zero,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ( times_times_real @ A @ B )
% 5.25/5.44 = zero_zero_real )
% 5.25/5.44 => ( ( A = zero_zero_real )
% 5.25/5.44 | ( B = zero_zero_real ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divisors_zero
% 5.25/5.44 thf(fact_1521_divisors__zero,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ( times_times_rat @ A @ B )
% 5.25/5.44 = zero_zero_rat )
% 5.25/5.44 => ( ( A = zero_zero_rat )
% 5.25/5.44 | ( B = zero_zero_rat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divisors_zero
% 5.25/5.44 thf(fact_1522_divisors__zero,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( ( times_times_nat @ A @ B )
% 5.25/5.44 = zero_zero_nat )
% 5.25/5.44 => ( ( A = zero_zero_nat )
% 5.25/5.44 | ( B = zero_zero_nat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divisors_zero
% 5.25/5.44 thf(fact_1523_divisors__zero,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( ( times_times_int @ A @ B )
% 5.25/5.44 = zero_zero_int )
% 5.25/5.44 => ( ( A = zero_zero_int )
% 5.25/5.44 | ( B = zero_zero_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % divisors_zero
% 5.25/5.44 thf(fact_1524_mult__not__zero,axiom,
% 5.25/5.44 ! [A: complex,B: complex] :
% 5.25/5.44 ( ( ( times_times_complex @ A @ B )
% 5.25/5.44 != zero_zero_complex )
% 5.25/5.44 => ( ( A != zero_zero_complex )
% 5.25/5.44 & ( B != zero_zero_complex ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_not_zero
% 5.25/5.44 thf(fact_1525_mult__not__zero,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ( times_times_real @ A @ B )
% 5.25/5.44 != zero_zero_real )
% 5.25/5.44 => ( ( A != zero_zero_real )
% 5.25/5.44 & ( B != zero_zero_real ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_not_zero
% 5.25/5.44 thf(fact_1526_mult__not__zero,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ( times_times_rat @ A @ B )
% 5.25/5.44 != zero_zero_rat )
% 5.25/5.44 => ( ( A != zero_zero_rat )
% 5.25/5.44 & ( B != zero_zero_rat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_not_zero
% 5.25/5.44 thf(fact_1527_mult__not__zero,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( ( times_times_nat @ A @ B )
% 5.25/5.44 != zero_zero_nat )
% 5.25/5.44 => ( ( A != zero_zero_nat )
% 5.25/5.44 & ( B != zero_zero_nat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_not_zero
% 5.25/5.44 thf(fact_1528_mult__not__zero,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( ( times_times_int @ A @ B )
% 5.25/5.44 != zero_zero_int )
% 5.25/5.44 => ( ( A != zero_zero_int )
% 5.25/5.44 & ( B != zero_zero_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mult_not_zero
% 5.25/5.44 thf(fact_1529_zero__neq__one,axiom,
% 5.25/5.44 zero_zero_complex != one_one_complex ).
% 5.25/5.44
% 5.25/5.44 % zero_neq_one
% 5.25/5.44 thf(fact_1530_zero__neq__one,axiom,
% 5.25/5.44 zero_zero_real != one_one_real ).
% 5.25/5.44
% 5.25/5.44 % zero_neq_one
% 5.25/5.44 thf(fact_1531_zero__neq__one,axiom,
% 5.25/5.44 zero_zero_rat != one_one_rat ).
% 5.25/5.44
% 5.25/5.44 % zero_neq_one
% 5.25/5.44 thf(fact_1532_zero__neq__one,axiom,
% 5.25/5.44 zero_zero_nat != one_one_nat ).
% 5.25/5.44
% 5.25/5.44 % zero_neq_one
% 5.25/5.44 thf(fact_1533_zero__neq__one,axiom,
% 5.25/5.44 zero_zero_int != one_one_int ).
% 5.25/5.44
% 5.25/5.44 % zero_neq_one
% 5.25/5.44 thf(fact_1534_add_Ogroup__left__neutral,axiom,
% 5.25/5.44 ! [A: complex] :
% 5.25/5.44 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % add.group_left_neutral
% 5.25/5.44 thf(fact_1535_add_Ogroup__left__neutral,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % add.group_left_neutral
% 5.25/5.44 thf(fact_1536_add_Ogroup__left__neutral,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % add.group_left_neutral
% 5.25/5.44 thf(fact_1537_add_Ogroup__left__neutral,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % add.group_left_neutral
% 5.25/5.44 thf(fact_1538_add_Ocomm__neutral,axiom,
% 5.25/5.44 ! [A: complex] :
% 5.25/5.44 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % add.comm_neutral
% 5.25/5.44 thf(fact_1539_add_Ocomm__neutral,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % add.comm_neutral
% 5.25/5.44 thf(fact_1540_add_Ocomm__neutral,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % add.comm_neutral
% 5.25/5.44 thf(fact_1541_add_Ocomm__neutral,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % add.comm_neutral
% 5.25/5.44 thf(fact_1542_add_Ocomm__neutral,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % add.comm_neutral
% 5.25/5.44 thf(fact_1543_comm__monoid__add__class_Oadd__0,axiom,
% 5.25/5.44 ! [A: complex] :
% 5.25/5.44 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % comm_monoid_add_class.add_0
% 5.25/5.44 thf(fact_1544_comm__monoid__add__class_Oadd__0,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % comm_monoid_add_class.add_0
% 5.25/5.44 thf(fact_1545_comm__monoid__add__class_Oadd__0,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % comm_monoid_add_class.add_0
% 5.25/5.44 thf(fact_1546_comm__monoid__add__class_Oadd__0,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % comm_monoid_add_class.add_0
% 5.25/5.44 thf(fact_1547_comm__monoid__add__class_Oadd__0,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % comm_monoid_add_class.add_0
% 5.25/5.45 thf(fact_1548_power__not__zero,axiom,
% 5.25/5.45 ! [A: rat,N: nat] :
% 5.25/5.45 ( ( A != zero_zero_rat )
% 5.25/5.45 => ( ( power_power_rat @ A @ N )
% 5.25/5.45 != zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_not_zero
% 5.25/5.45 thf(fact_1549_power__not__zero,axiom,
% 5.25/5.45 ! [A: nat,N: nat] :
% 5.25/5.45 ( ( A != zero_zero_nat )
% 5.25/5.45 => ( ( power_power_nat @ A @ N )
% 5.25/5.45 != zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_not_zero
% 5.25/5.45 thf(fact_1550_power__not__zero,axiom,
% 5.25/5.45 ! [A: real,N: nat] :
% 5.25/5.45 ( ( A != zero_zero_real )
% 5.25/5.45 => ( ( power_power_real @ A @ N )
% 5.25/5.45 != zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_not_zero
% 5.25/5.45 thf(fact_1551_power__not__zero,axiom,
% 5.25/5.45 ! [A: int,N: nat] :
% 5.25/5.45 ( ( A != zero_zero_int )
% 5.25/5.45 => ( ( power_power_int @ A @ N )
% 5.25/5.45 != zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_not_zero
% 5.25/5.45 thf(fact_1552_power__not__zero,axiom,
% 5.25/5.45 ! [A: complex,N: nat] :
% 5.25/5.45 ( ( A != zero_zero_complex )
% 5.25/5.45 => ( ( power_power_complex @ A @ N )
% 5.25/5.45 != zero_zero_complex ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_not_zero
% 5.25/5.45 thf(fact_1553_num_Osize_I4_J,axiom,
% 5.25/5.45 ( ( size_size_num @ one )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % num.size(4)
% 5.25/5.45 thf(fact_1554_not0__implies__Suc,axiom,
% 5.25/5.45 ! [N: nat] :
% 5.25/5.45 ( ( N != zero_zero_nat )
% 5.25/5.45 => ? [M5: nat] :
% 5.25/5.45 ( N
% 5.25/5.45 = ( suc @ M5 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % not0_implies_Suc
% 5.25/5.45 thf(fact_1555_Zero__not__Suc,axiom,
% 5.25/5.45 ! [M: nat] :
% 5.25/5.45 ( zero_zero_nat
% 5.25/5.45 != ( suc @ M ) ) ).
% 5.25/5.45
% 5.25/5.45 % Zero_not_Suc
% 5.25/5.45 thf(fact_1556_Zero__neq__Suc,axiom,
% 5.25/5.45 ! [M: nat] :
% 5.25/5.45 ( zero_zero_nat
% 5.25/5.45 != ( suc @ M ) ) ).
% 5.25/5.45
% 5.25/5.45 % Zero_neq_Suc
% 5.25/5.45 thf(fact_1557_Suc__neq__Zero,axiom,
% 5.25/5.45 ! [M: nat] :
% 5.25/5.45 ( ( suc @ M )
% 5.25/5.45 != zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % Suc_neq_Zero
% 5.25/5.45 thf(fact_1558_zero__induct,axiom,
% 5.25/5.45 ! [P: nat > $o,K: nat] :
% 5.25/5.45 ( ( P @ K )
% 5.25/5.45 => ( ! [N3: nat] :
% 5.25/5.45 ( ( P @ ( suc @ N3 ) )
% 5.25/5.45 => ( P @ N3 ) )
% 5.25/5.45 => ( P @ zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_induct
% 5.25/5.45 thf(fact_1559_diff__induct,axiom,
% 5.25/5.45 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.25/5.45 ( ! [X5: nat] : ( P @ X5 @ zero_zero_nat )
% 5.25/5.45 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 5.25/5.45 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.45 ( ( P @ X5 @ Y3 )
% 5.25/5.45 => ( P @ ( suc @ X5 ) @ ( suc @ Y3 ) ) )
% 5.25/5.45 => ( P @ M @ N ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % diff_induct
% 5.25/5.45 thf(fact_1560_nat__induct,axiom,
% 5.25/5.45 ! [P: nat > $o,N: nat] :
% 5.25/5.45 ( ( P @ zero_zero_nat )
% 5.25/5.45 => ( ! [N3: nat] :
% 5.25/5.45 ( ( P @ N3 )
% 5.25/5.45 => ( P @ ( suc @ N3 ) ) )
% 5.25/5.45 => ( P @ N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nat_induct
% 5.25/5.45 thf(fact_1561_old_Onat_Oexhaust,axiom,
% 5.25/5.45 ! [Y: nat] :
% 5.25/5.45 ( ( Y != zero_zero_nat )
% 5.25/5.45 => ~ ! [Nat3: nat] :
% 5.25/5.45 ( Y
% 5.25/5.45 != ( suc @ Nat3 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % old.nat.exhaust
% 5.25/5.45 thf(fact_1562_nat_OdiscI,axiom,
% 5.25/5.45 ! [Nat: nat,X22: nat] :
% 5.25/5.45 ( ( Nat
% 5.25/5.45 = ( suc @ X22 ) )
% 5.25/5.45 => ( Nat != zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % nat.discI
% 5.25/5.45 thf(fact_1563_old_Onat_Odistinct_I1_J,axiom,
% 5.25/5.45 ! [Nat2: nat] :
% 5.25/5.45 ( zero_zero_nat
% 5.25/5.45 != ( suc @ Nat2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % old.nat.distinct(1)
% 5.25/5.45 thf(fact_1564_old_Onat_Odistinct_I2_J,axiom,
% 5.25/5.45 ! [Nat2: nat] :
% 5.25/5.45 ( ( suc @ Nat2 )
% 5.25/5.45 != zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % old.nat.distinct(2)
% 5.25/5.45 thf(fact_1565_nat_Odistinct_I1_J,axiom,
% 5.25/5.45 ! [X22: nat] :
% 5.25/5.45 ( zero_zero_nat
% 5.25/5.45 != ( suc @ X22 ) ) ).
% 5.25/5.45
% 5.25/5.45 % nat.distinct(1)
% 5.25/5.45 thf(fact_1566_infinite__descent0,axiom,
% 5.25/5.45 ! [P: nat > $o,N: nat] :
% 5.25/5.45 ( ( P @ zero_zero_nat )
% 5.25/5.45 => ( ! [N3: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.25/5.45 => ( ~ ( P @ N3 )
% 5.25/5.45 => ? [M2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ M2 @ N3 )
% 5.25/5.45 & ~ ( P @ M2 ) ) ) )
% 5.25/5.45 => ( P @ N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % infinite_descent0
% 5.25/5.45 thf(fact_1567_gr__implies__not0,axiom,
% 5.25/5.45 ! [M: nat,N: nat] :
% 5.25/5.45 ( ( ord_less_nat @ M @ N )
% 5.25/5.45 => ( N != zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % gr_implies_not0
% 5.25/5.45 thf(fact_1568_less__zeroE,axiom,
% 5.25/5.45 ! [N: nat] :
% 5.25/5.45 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % less_zeroE
% 5.25/5.45 thf(fact_1569_not__less0,axiom,
% 5.25/5.45 ! [N: nat] :
% 5.25/5.45 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % not_less0
% 5.25/5.45 thf(fact_1570_not__gr0,axiom,
% 5.25/5.45 ! [N: nat] :
% 5.25/5.45 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.25/5.45 = ( N = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % not_gr0
% 5.25/5.45 thf(fact_1571_gr0I,axiom,
% 5.25/5.45 ! [N: nat] :
% 5.25/5.45 ( ( N != zero_zero_nat )
% 5.25/5.45 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.25/5.45
% 5.25/5.45 % gr0I
% 5.25/5.45 thf(fact_1572_bot__nat__0_Oextremum__strict,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % bot_nat_0.extremum_strict
% 5.25/5.45 thf(fact_1573_le__0__eq,axiom,
% 5.25/5.45 ! [N: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.25/5.45 = ( N = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_0_eq
% 5.25/5.45 thf(fact_1574_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.25/5.45 => ( A = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % bot_nat_0.extremum_uniqueI
% 5.25/5.45 thf(fact_1575_bot__nat__0_Oextremum__unique,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.25/5.45 = ( A = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % bot_nat_0.extremum_unique
% 5.25/5.45 thf(fact_1576_less__eq__nat_Osimps_I1_J,axiom,
% 5.25/5.45 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.25/5.45
% 5.25/5.45 % less_eq_nat.simps(1)
% 5.25/5.45 thf(fact_1577_add__eq__self__zero,axiom,
% 5.25/5.45 ! [M: nat,N: nat] :
% 5.25/5.45 ( ( ( plus_plus_nat @ M @ N )
% 5.25/5.45 = M )
% 5.25/5.45 => ( N = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_eq_self_zero
% 5.25/5.45 thf(fact_1578_plus__nat_Oadd__0,axiom,
% 5.25/5.45 ! [N: nat] :
% 5.25/5.45 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 5.25/5.45 = N ) ).
% 5.25/5.45
% 5.25/5.45 % plus_nat.add_0
% 5.25/5.45 thf(fact_1579_mult__0,axiom,
% 5.25/5.45 ! [N: nat] :
% 5.25/5.45 ( ( times_times_nat @ zero_zero_nat @ N )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % mult_0
% 5.25/5.45 thf(fact_1580_nat__mult__eq__cancel__disj,axiom,
% 5.25/5.45 ! [K: nat,M: nat,N: nat] :
% 5.25/5.45 ( ( ( times_times_nat @ K @ M )
% 5.25/5.45 = ( times_times_nat @ K @ N ) )
% 5.25/5.45 = ( ( K = zero_zero_nat )
% 5.25/5.45 | ( M = N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nat_mult_eq_cancel_disj
% 5.25/5.45 thf(fact_1581_enat__0__less__mult__iff,axiom,
% 5.25/5.45 ! [M: extended_enat,N: extended_enat] :
% 5.25/5.45 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 5.25/5.45 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.25/5.45 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % enat_0_less_mult_iff
% 5.25/5.45 thf(fact_1582_not__iless0,axiom,
% 5.25/5.45 ! [N: extended_enat] :
% 5.25/5.45 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 5.25/5.45
% 5.25/5.45 % not_iless0
% 5.25/5.45 thf(fact_1583_ile0__eq,axiom,
% 5.25/5.45 ! [N: extended_enat] :
% 5.25/5.45 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.25/5.45 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.25/5.45
% 5.25/5.45 % ile0_eq
% 5.25/5.45 thf(fact_1584_i0__lb,axiom,
% 5.25/5.45 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 5.25/5.45
% 5.25/5.45 % i0_lb
% 5.25/5.45 thf(fact_1585_power__eq__imp__eq__base,axiom,
% 5.25/5.45 ! [A: real,N: nat,B: real] :
% 5.25/5.45 ( ( ( power_power_real @ A @ N )
% 5.25/5.45 = ( power_power_real @ B @ N ) )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ( A = B ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_eq_imp_eq_base
% 5.25/5.45 thf(fact_1586_power__eq__imp__eq__base,axiom,
% 5.25/5.45 ! [A: rat,N: nat,B: rat] :
% 5.25/5.45 ( ( ( power_power_rat @ A @ N )
% 5.25/5.45 = ( power_power_rat @ B @ N ) )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ( A = B ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_eq_imp_eq_base
% 5.25/5.45 thf(fact_1587_power__eq__imp__eq__base,axiom,
% 5.25/5.45 ! [A: nat,N: nat,B: nat] :
% 5.25/5.45 ( ( ( power_power_nat @ A @ N )
% 5.25/5.45 = ( power_power_nat @ B @ N ) )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ( A = B ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_eq_imp_eq_base
% 5.25/5.45 thf(fact_1588_power__eq__imp__eq__base,axiom,
% 5.25/5.45 ! [A: int,N: nat,B: int] :
% 5.25/5.45 ( ( ( power_power_int @ A @ N )
% 5.25/5.45 = ( power_power_int @ B @ N ) )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ( A = B ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_eq_imp_eq_base
% 5.25/5.45 thf(fact_1589_power__eq__iff__eq__base,axiom,
% 5.25/5.45 ! [N: nat,A: real,B: real] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.45 => ( ( ( power_power_real @ A @ N )
% 5.25/5.45 = ( power_power_real @ B @ N ) )
% 5.25/5.45 = ( A = B ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_eq_iff_eq_base
% 5.25/5.45 thf(fact_1590_power__eq__iff__eq__base,axiom,
% 5.25/5.45 ! [N: nat,A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.45 => ( ( ( power_power_rat @ A @ N )
% 5.25/5.45 = ( power_power_rat @ B @ N ) )
% 5.25/5.45 = ( A = B ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_eq_iff_eq_base
% 5.25/5.45 thf(fact_1591_power__eq__iff__eq__base,axiom,
% 5.25/5.45 ! [N: nat,A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.45 => ( ( ( power_power_nat @ A @ N )
% 5.25/5.45 = ( power_power_nat @ B @ N ) )
% 5.25/5.45 = ( A = B ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_eq_iff_eq_base
% 5.25/5.45 thf(fact_1592_power__eq__iff__eq__base,axiom,
% 5.25/5.45 ! [N: nat,A: int,B: int] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.45 => ( ( ( power_power_int @ A @ N )
% 5.25/5.45 = ( power_power_int @ B @ N ) )
% 5.25/5.45 = ( A = B ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_eq_iff_eq_base
% 5.25/5.45 thf(fact_1593_signed__take__bit__int__less__exp,axiom,
% 5.25/5.45 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.45
% 5.25/5.45 % signed_take_bit_int_less_exp
% 5.25/5.45 thf(fact_1594_signed__take__bit__int__less__self__iff,axiom,
% 5.25/5.45 ! [N: nat,K: int] :
% 5.25/5.45 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.25/5.45 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.25/5.45
% 5.25/5.45 % signed_take_bit_int_less_self_iff
% 5.25/5.45 thf(fact_1595_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.25/5.45 ! [K: int,N: nat] :
% 5.25/5.45 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.25/5.45 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % signed_take_bit_int_greater_eq_self_iff
% 5.25/5.45 thf(fact_1596_power__strict__mono,axiom,
% 5.25/5.45 ! [A: real,B: real,N: nat] :
% 5.25/5.45 ( ( ord_less_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_strict_mono
% 5.25/5.45 thf(fact_1597_power__strict__mono,axiom,
% 5.25/5.45 ! [A: rat,B: rat,N: nat] :
% 5.25/5.45 ( ( ord_less_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_strict_mono
% 5.25/5.45 thf(fact_1598_power__strict__mono,axiom,
% 5.25/5.45 ! [A: nat,B: nat,N: nat] :
% 5.25/5.45 ( ( ord_less_nat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_strict_mono
% 5.25/5.45 thf(fact_1599_power__strict__mono,axiom,
% 5.25/5.45 ! [A: int,B: int,N: nat] :
% 5.25/5.45 ( ( ord_less_int @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_strict_mono
% 5.25/5.45 thf(fact_1600_dbl__def,axiom,
% 5.25/5.45 ( neg_numeral_dbl_real
% 5.25/5.45 = ( ^ [X2: real] : ( plus_plus_real @ X2 @ X2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % dbl_def
% 5.25/5.45 thf(fact_1601_dbl__def,axiom,
% 5.25/5.45 ( neg_numeral_dbl_rat
% 5.25/5.45 = ( ^ [X2: rat] : ( plus_plus_rat @ X2 @ X2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % dbl_def
% 5.25/5.45 thf(fact_1602_dbl__def,axiom,
% 5.25/5.45 ( neg_numeral_dbl_int
% 5.25/5.45 = ( ^ [X2: int] : ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % dbl_def
% 5.25/5.45 thf(fact_1603_not__numeral__le__zero,axiom,
% 5.25/5.45 ! [N: num] :
% 5.25/5.45 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_le_zero
% 5.25/5.45 thf(fact_1604_not__numeral__le__zero,axiom,
% 5.25/5.45 ! [N: num] :
% 5.25/5.45 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_le_zero
% 5.25/5.45 thf(fact_1605_not__numeral__le__zero,axiom,
% 5.25/5.45 ! [N: num] :
% 5.25/5.45 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_le_zero
% 5.25/5.45 thf(fact_1606_not__numeral__le__zero,axiom,
% 5.25/5.45 ! [N: num] :
% 5.25/5.45 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_le_zero
% 5.25/5.45 thf(fact_1607_zero__le__numeral,axiom,
% 5.25/5.45 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_numeral
% 5.25/5.45 thf(fact_1608_zero__le__numeral,axiom,
% 5.25/5.45 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_numeral
% 5.25/5.45 thf(fact_1609_zero__le__numeral,axiom,
% 5.25/5.45 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_numeral
% 5.25/5.45 thf(fact_1610_zero__le__numeral,axiom,
% 5.25/5.45 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_numeral
% 5.25/5.45 thf(fact_1611_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.25/5.45 thf(fact_1612_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.25/5.45 thf(fact_1613_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.25/5.45 ! [A: nat,B: nat,C: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.25/5.45 thf(fact_1614_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.25/5.45 ! [A: int,B: int,C: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.25/5.45 thf(fact_1615_zero__le__mult__iff,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.25/5.45 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.25/5.45 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.45 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_mult_iff
% 5.25/5.45 thf(fact_1616_zero__le__mult__iff,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.45 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.25/5.45 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.45 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_mult_iff
% 5.25/5.45 thf(fact_1617_zero__le__mult__iff,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.25/5.45 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.25/5.45 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.45 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_mult_iff
% 5.25/5.45 thf(fact_1618_mult__nonneg__nonpos2,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.25/5.45 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonneg_nonpos2
% 5.25/5.45 thf(fact_1619_mult__nonneg__nonpos2,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonneg_nonpos2
% 5.25/5.45 thf(fact_1620_mult__nonneg__nonpos2,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.25/5.45 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonneg_nonpos2
% 5.25/5.45 thf(fact_1621_mult__nonneg__nonpos2,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.25/5.45 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonneg_nonpos2
% 5.25/5.45 thf(fact_1622_mult__nonpos__nonneg,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.45 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonpos_nonneg
% 5.25/5.45 thf(fact_1623_mult__nonpos__nonneg,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.45 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonpos_nonneg
% 5.25/5.45 thf(fact_1624_mult__nonpos__nonneg,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.45 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonpos_nonneg
% 5.25/5.45 thf(fact_1625_mult__nonpos__nonneg,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.45 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonpos_nonneg
% 5.25/5.45 thf(fact_1626_mult__nonneg__nonpos,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.25/5.45 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonneg_nonpos
% 5.25/5.45 thf(fact_1627_mult__nonneg__nonpos,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonneg_nonpos
% 5.25/5.45 thf(fact_1628_mult__nonneg__nonpos,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.25/5.45 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonneg_nonpos
% 5.25/5.45 thf(fact_1629_mult__nonneg__nonpos,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.25/5.45 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonneg_nonpos
% 5.25/5.45 thf(fact_1630_mult__nonneg__nonneg,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.45 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonneg_nonneg
% 5.25/5.45 thf(fact_1631_mult__nonneg__nonneg,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.45 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonneg_nonneg
% 5.25/5.45 thf(fact_1632_mult__nonneg__nonneg,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.45 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonneg_nonneg
% 5.25/5.45 thf(fact_1633_mult__nonneg__nonneg,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.45 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonneg_nonneg
% 5.25/5.45 thf(fact_1634_split__mult__neg__le,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.25/5.45 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.45 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.25/5.45 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % split_mult_neg_le
% 5.25/5.45 thf(fact_1635_split__mult__neg__le,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.25/5.45 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.45 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.25/5.45 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % split_mult_neg_le
% 5.25/5.45 thf(fact_1636_split__mult__neg__le,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.25/5.45 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.25/5.45 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.25/5.45 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % split_mult_neg_le
% 5.25/5.45 thf(fact_1637_split__mult__neg__le,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.25/5.45 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.45 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.25/5.45 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % split_mult_neg_le
% 5.25/5.45 thf(fact_1638_mult__le__0__iff,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.25/5.45 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.25/5.45 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.45 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_le_0_iff
% 5.25/5.45 thf(fact_1639_mult__le__0__iff,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.25/5.45 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.25/5.45 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.45 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_le_0_iff
% 5.25/5.45 thf(fact_1640_mult__le__0__iff,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.25/5.45 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.25/5.45 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.45 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_le_0_iff
% 5.25/5.45 thf(fact_1641_mult__right__mono,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_mono
% 5.25/5.45 thf(fact_1642_mult__right__mono,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_mono
% 5.25/5.45 thf(fact_1643_mult__right__mono,axiom,
% 5.25/5.45 ! [A: nat,B: nat,C: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_mono
% 5.25/5.45 thf(fact_1644_mult__right__mono,axiom,
% 5.25/5.45 ! [A: int,B: int,C: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_mono
% 5.25/5.45 thf(fact_1645_mult__right__mono__neg,axiom,
% 5.25/5.45 ! [B: real,A: real,C: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ B @ A )
% 5.25/5.45 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.45 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_mono_neg
% 5.25/5.45 thf(fact_1646_mult__right__mono__neg,axiom,
% 5.25/5.45 ! [B: rat,A: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.45 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_mono_neg
% 5.25/5.45 thf(fact_1647_mult__right__mono__neg,axiom,
% 5.25/5.45 ! [B: int,A: int,C: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.45 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.45 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_mono_neg
% 5.25/5.45 thf(fact_1648_mult__left__mono,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_left_mono
% 5.25/5.45 thf(fact_1649_mult__left__mono,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_left_mono
% 5.25/5.45 thf(fact_1650_mult__left__mono,axiom,
% 5.25/5.45 ! [A: nat,B: nat,C: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_left_mono
% 5.25/5.45 thf(fact_1651_mult__left__mono,axiom,
% 5.25/5.45 ! [A: int,B: int,C: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_left_mono
% 5.25/5.45 thf(fact_1652_mult__nonpos__nonpos,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.25/5.45 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonpos_nonpos
% 5.25/5.45 thf(fact_1653_mult__nonpos__nonpos,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonpos_nonpos
% 5.25/5.45 thf(fact_1654_mult__nonpos__nonpos,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.45 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.25/5.45 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_nonpos_nonpos
% 5.25/5.45 thf(fact_1655_mult__left__mono__neg,axiom,
% 5.25/5.45 ! [B: real,A: real,C: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ B @ A )
% 5.25/5.45 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.45 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_left_mono_neg
% 5.25/5.45 thf(fact_1656_mult__left__mono__neg,axiom,
% 5.25/5.45 ! [B: rat,A: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.45 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_left_mono_neg
% 5.25/5.45 thf(fact_1657_mult__left__mono__neg,axiom,
% 5.25/5.45 ! [B: int,A: int,C: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.45 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.45 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_left_mono_neg
% 5.25/5.45 thf(fact_1658_split__mult__pos__le,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.25/5.45 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.45 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.25/5.45 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % split_mult_pos_le
% 5.25/5.45 thf(fact_1659_split__mult__pos__le,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.25/5.45 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.45 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.25/5.45 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % split_mult_pos_le
% 5.25/5.45 thf(fact_1660_split__mult__pos__le,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.25/5.45 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.45 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.25/5.45 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % split_mult_pos_le
% 5.25/5.45 thf(fact_1661_zero__le__square,axiom,
% 5.25/5.45 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_square
% 5.25/5.45 thf(fact_1662_zero__le__square,axiom,
% 5.25/5.45 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_square
% 5.25/5.45 thf(fact_1663_zero__le__square,axiom,
% 5.25/5.45 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_square
% 5.25/5.45 thf(fact_1664_mult__mono_H,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_real @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_mono'
% 5.25/5.45 thf(fact_1665_mult__mono_H,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_rat @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_mono'
% 5.25/5.45 thf(fact_1666_mult__mono_H,axiom,
% 5.25/5.45 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_nat @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_mono'
% 5.25/5.45 thf(fact_1667_mult__mono_H,axiom,
% 5.25/5.45 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_int @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_mono'
% 5.25/5.45 thf(fact_1668_mult__mono,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_real @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_mono
% 5.25/5.45 thf(fact_1669_mult__mono,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_rat @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_mono
% 5.25/5.45 thf(fact_1670_mult__mono,axiom,
% 5.25/5.45 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_nat @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_mono
% 5.25/5.45 thf(fact_1671_mult__mono,axiom,
% 5.25/5.45 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_int @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_mono
% 5.25/5.45 thf(fact_1672_not__numeral__less__zero,axiom,
% 5.25/5.45 ! [N: num] :
% 5.25/5.45 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_less_zero
% 5.25/5.45 thf(fact_1673_not__numeral__less__zero,axiom,
% 5.25/5.45 ! [N: num] :
% 5.25/5.45 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_less_zero
% 5.25/5.45 thf(fact_1674_not__numeral__less__zero,axiom,
% 5.25/5.45 ! [N: num] :
% 5.25/5.45 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_less_zero
% 5.25/5.45 thf(fact_1675_not__numeral__less__zero,axiom,
% 5.25/5.45 ! [N: num] :
% 5.25/5.45 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_less_zero
% 5.25/5.45 thf(fact_1676_zero__less__numeral,axiom,
% 5.25/5.45 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_numeral
% 5.25/5.45 thf(fact_1677_zero__less__numeral,axiom,
% 5.25/5.45 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_numeral
% 5.25/5.45 thf(fact_1678_zero__less__numeral,axiom,
% 5.25/5.45 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_numeral
% 5.25/5.45 thf(fact_1679_zero__less__numeral,axiom,
% 5.25/5.45 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_numeral
% 5.25/5.45 thf(fact_1680_not__one__le__zero,axiom,
% 5.25/5.45 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.25/5.45
% 5.25/5.45 % not_one_le_zero
% 5.25/5.45 thf(fact_1681_not__one__le__zero,axiom,
% 5.25/5.45 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.25/5.45
% 5.25/5.45 % not_one_le_zero
% 5.25/5.45 thf(fact_1682_not__one__le__zero,axiom,
% 5.25/5.45 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % not_one_le_zero
% 5.25/5.45 thf(fact_1683_not__one__le__zero,axiom,
% 5.25/5.45 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % not_one_le_zero
% 5.25/5.45 thf(fact_1684_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.25/5.45 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.25/5.45
% 5.25/5.45 % linordered_nonzero_semiring_class.zero_le_one
% 5.25/5.45 thf(fact_1685_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.25/5.45 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.25/5.45
% 5.25/5.45 % linordered_nonzero_semiring_class.zero_le_one
% 5.25/5.45 thf(fact_1686_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.25/5.45 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.25/5.45
% 5.25/5.45 % linordered_nonzero_semiring_class.zero_le_one
% 5.25/5.45 thf(fact_1687_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.25/5.45 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.25/5.45
% 5.25/5.45 % linordered_nonzero_semiring_class.zero_le_one
% 5.25/5.45 thf(fact_1688_zero__less__one__class_Ozero__le__one,axiom,
% 5.25/5.45 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.25/5.45
% 5.25/5.45 % zero_less_one_class.zero_le_one
% 5.25/5.45 thf(fact_1689_zero__less__one__class_Ozero__le__one,axiom,
% 5.25/5.45 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.25/5.45
% 5.25/5.45 % zero_less_one_class.zero_le_one
% 5.25/5.45 thf(fact_1690_zero__less__one__class_Ozero__le__one,axiom,
% 5.25/5.45 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.25/5.45
% 5.25/5.45 % zero_less_one_class.zero_le_one
% 5.25/5.45 thf(fact_1691_zero__less__one__class_Ozero__le__one,axiom,
% 5.25/5.45 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.25/5.45
% 5.25/5.45 % zero_less_one_class.zero_le_one
% 5.25/5.45 thf(fact_1692_add__decreasing,axiom,
% 5.25/5.45 ! [A: real,C: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_eq_real @ C @ B )
% 5.25/5.45 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_decreasing
% 5.25/5.45 thf(fact_1693_add__decreasing,axiom,
% 5.25/5.45 ! [A: rat,C: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_eq_rat @ C @ B )
% 5.25/5.45 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_decreasing
% 5.25/5.45 thf(fact_1694_add__decreasing,axiom,
% 5.25/5.45 ! [A: nat,C: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.25/5.45 => ( ( ord_less_eq_nat @ C @ B )
% 5.25/5.45 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_decreasing
% 5.25/5.45 thf(fact_1695_add__decreasing,axiom,
% 5.25/5.45 ! [A: int,C: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.45 => ( ( ord_less_eq_int @ C @ B )
% 5.25/5.45 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_decreasing
% 5.25/5.45 thf(fact_1696_add__increasing,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_eq_real @ B @ C )
% 5.25/5.45 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_increasing
% 5.25/5.45 thf(fact_1697_add__increasing,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.45 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_increasing
% 5.25/5.45 thf(fact_1698_add__increasing,axiom,
% 5.25/5.45 ! [A: nat,B: nat,C: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.45 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_increasing
% 5.25/5.45 thf(fact_1699_add__increasing,axiom,
% 5.25/5.45 ! [A: int,B: int,C: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_eq_int @ B @ C )
% 5.25/5.45 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_increasing
% 5.25/5.45 thf(fact_1700_add__decreasing2,axiom,
% 5.25/5.45 ! [C: real,A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_eq_real @ A @ B )
% 5.25/5.45 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_decreasing2
% 5.25/5.45 thf(fact_1701_add__decreasing2,axiom,
% 5.25/5.45 ! [C: rat,A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_decreasing2
% 5.25/5.45 thf(fact_1702_add__decreasing2,axiom,
% 5.25/5.45 ! [C: nat,A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.25/5.45 => ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.45 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_decreasing2
% 5.25/5.45 thf(fact_1703_add__decreasing2,axiom,
% 5.25/5.45 ! [C: int,A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.45 => ( ( ord_less_eq_int @ A @ B )
% 5.25/5.45 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_decreasing2
% 5.25/5.45 thf(fact_1704_add__increasing2,axiom,
% 5.25/5.45 ! [C: real,B: real,A: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ( ord_less_eq_real @ B @ A )
% 5.25/5.45 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_increasing2
% 5.25/5.45 thf(fact_1705_add__increasing2,axiom,
% 5.25/5.45 ! [C: rat,B: rat,A: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.45 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_increasing2
% 5.25/5.45 thf(fact_1706_add__increasing2,axiom,
% 5.25/5.45 ! [C: nat,B: nat,A: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.45 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_increasing2
% 5.25/5.45 thf(fact_1707_add__increasing2,axiom,
% 5.25/5.45 ! [C: int,B: int,A: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ( ord_less_eq_int @ B @ A )
% 5.25/5.45 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_increasing2
% 5.25/5.45 thf(fact_1708_add__nonneg__nonneg,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.45 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonneg_nonneg
% 5.25/5.45 thf(fact_1709_add__nonneg__nonneg,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.45 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonneg_nonneg
% 5.25/5.45 thf(fact_1710_add__nonneg__nonneg,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.45 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonneg_nonneg
% 5.25/5.45 thf(fact_1711_add__nonneg__nonneg,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.45 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonneg_nonneg
% 5.25/5.45 thf(fact_1712_add__nonpos__nonpos,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.25/5.45 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonpos_nonpos
% 5.25/5.45 thf(fact_1713_add__nonpos__nonpos,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonpos_nonpos
% 5.25/5.45 thf(fact_1714_add__nonpos__nonpos,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.25/5.45 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.25/5.45 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonpos_nonpos
% 5.25/5.45 thf(fact_1715_add__nonpos__nonpos,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.45 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.25/5.45 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonpos_nonpos
% 5.25/5.45 thf(fact_1716_add__nonneg__eq__0__iff,axiom,
% 5.25/5.45 ! [X3: real,Y: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.45 => ( ( ( plus_plus_real @ X3 @ Y )
% 5.25/5.45 = zero_zero_real )
% 5.25/5.45 = ( ( X3 = zero_zero_real )
% 5.25/5.45 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonneg_eq_0_iff
% 5.25/5.45 thf(fact_1717_add__nonneg__eq__0__iff,axiom,
% 5.25/5.45 ! [X3: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.45 => ( ( ( plus_plus_rat @ X3 @ Y )
% 5.25/5.45 = zero_zero_rat )
% 5.25/5.45 = ( ( X3 = zero_zero_rat )
% 5.25/5.45 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonneg_eq_0_iff
% 5.25/5.45 thf(fact_1718_add__nonneg__eq__0__iff,axiom,
% 5.25/5.45 ! [X3: nat,Y: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.25/5.45 => ( ( ( plus_plus_nat @ X3 @ Y )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 = ( ( X3 = zero_zero_nat )
% 5.25/5.45 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonneg_eq_0_iff
% 5.25/5.45 thf(fact_1719_add__nonneg__eq__0__iff,axiom,
% 5.25/5.45 ! [X3: int,Y: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.45 => ( ( ( plus_plus_int @ X3 @ Y )
% 5.25/5.45 = zero_zero_int )
% 5.25/5.45 = ( ( X3 = zero_zero_int )
% 5.25/5.45 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonneg_eq_0_iff
% 5.25/5.45 thf(fact_1720_add__nonpos__eq__0__iff,axiom,
% 5.25/5.45 ! [X3: real,Y: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.25/5.45 => ( ( ( plus_plus_real @ X3 @ Y )
% 5.25/5.45 = zero_zero_real )
% 5.25/5.45 = ( ( X3 = zero_zero_real )
% 5.25/5.45 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonpos_eq_0_iff
% 5.25/5.45 thf(fact_1721_add__nonpos__eq__0__iff,axiom,
% 5.25/5.45 ! [X3: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.25/5.45 => ( ( ( plus_plus_rat @ X3 @ Y )
% 5.25/5.45 = zero_zero_rat )
% 5.25/5.45 = ( ( X3 = zero_zero_rat )
% 5.25/5.45 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonpos_eq_0_iff
% 5.25/5.45 thf(fact_1722_add__nonpos__eq__0__iff,axiom,
% 5.25/5.45 ! [X3: nat,Y: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ X3 @ zero_zero_nat )
% 5.25/5.45 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 5.25/5.45 => ( ( ( plus_plus_nat @ X3 @ Y )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 = ( ( X3 = zero_zero_nat )
% 5.25/5.45 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonpos_eq_0_iff
% 5.25/5.45 thf(fact_1723_add__nonpos__eq__0__iff,axiom,
% 5.25/5.45 ! [X3: int,Y: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ X3 @ zero_zero_int )
% 5.25/5.45 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.25/5.45 => ( ( ( plus_plus_int @ X3 @ Y )
% 5.25/5.45 = zero_zero_int )
% 5.25/5.45 = ( ( X3 = zero_zero_int )
% 5.25/5.45 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_nonpos_eq_0_iff
% 5.25/5.45 thf(fact_1724_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real] :
% 5.25/5.45 ( ( ord_less_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.25/5.45 thf(fact_1725_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.25/5.45 thf(fact_1726_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.25/5.45 ! [A: nat,B: nat,C: nat] :
% 5.25/5.45 ( ( ord_less_nat @ A @ B )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.25/5.45 thf(fact_1727_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.25/5.45 ! [A: int,B: int,C: int] :
% 5.25/5.45 ( ( ord_less_int @ A @ B )
% 5.25/5.45 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.25/5.45 thf(fact_1728_mult__less__cancel__right__disj,axiom,
% 5.25/5.45 ! [A: real,C: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.25/5.45 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.45 & ( ord_less_real @ A @ B ) )
% 5.25/5.45 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.45 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_right_disj
% 5.25/5.45 thf(fact_1729_mult__less__cancel__right__disj,axiom,
% 5.25/5.45 ! [A: rat,C: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.45 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.45 & ( ord_less_rat @ A @ B ) )
% 5.25/5.45 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.45 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_right_disj
% 5.25/5.45 thf(fact_1730_mult__less__cancel__right__disj,axiom,
% 5.25/5.45 ! [A: int,C: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.45 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.45 & ( ord_less_int @ A @ B ) )
% 5.25/5.45 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.45 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_right_disj
% 5.25/5.45 thf(fact_1731_mult__strict__right__mono,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real] :
% 5.25/5.45 ( ( ord_less_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_right_mono
% 5.25/5.45 thf(fact_1732_mult__strict__right__mono,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_right_mono
% 5.25/5.45 thf(fact_1733_mult__strict__right__mono,axiom,
% 5.25/5.45 ! [A: nat,B: nat,C: nat] :
% 5.25/5.45 ( ( ord_less_nat @ A @ B )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_right_mono
% 5.25/5.45 thf(fact_1734_mult__strict__right__mono,axiom,
% 5.25/5.45 ! [A: int,B: int,C: int] :
% 5.25/5.45 ( ( ord_less_int @ A @ B )
% 5.25/5.45 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_right_mono
% 5.25/5.45 thf(fact_1735_mult__strict__right__mono__neg,axiom,
% 5.25/5.45 ! [B: real,A: real,C: real] :
% 5.25/5.45 ( ( ord_less_real @ B @ A )
% 5.25/5.45 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.45 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_right_mono_neg
% 5.25/5.45 thf(fact_1736_mult__strict__right__mono__neg,axiom,
% 5.25/5.45 ! [B: rat,A: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_rat @ B @ A )
% 5.25/5.45 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_right_mono_neg
% 5.25/5.45 thf(fact_1737_mult__strict__right__mono__neg,axiom,
% 5.25/5.45 ! [B: int,A: int,C: int] :
% 5.25/5.45 ( ( ord_less_int @ B @ A )
% 5.25/5.45 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.45 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_right_mono_neg
% 5.25/5.45 thf(fact_1738_mult__less__cancel__left__disj,axiom,
% 5.25/5.45 ! [C: real,A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.45 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.45 & ( ord_less_real @ A @ B ) )
% 5.25/5.45 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.45 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_left_disj
% 5.25/5.45 thf(fact_1739_mult__less__cancel__left__disj,axiom,
% 5.25/5.45 ! [C: rat,A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.45 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.45 & ( ord_less_rat @ A @ B ) )
% 5.25/5.45 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.45 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_left_disj
% 5.25/5.45 thf(fact_1740_mult__less__cancel__left__disj,axiom,
% 5.25/5.45 ! [C: int,A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.45 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.45 & ( ord_less_int @ A @ B ) )
% 5.25/5.45 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.45 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_left_disj
% 5.25/5.45 thf(fact_1741_mult__strict__left__mono,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real] :
% 5.25/5.45 ( ( ord_less_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_left_mono
% 5.25/5.45 thf(fact_1742_mult__strict__left__mono,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_left_mono
% 5.25/5.45 thf(fact_1743_mult__strict__left__mono,axiom,
% 5.25/5.45 ! [A: nat,B: nat,C: nat] :
% 5.25/5.45 ( ( ord_less_nat @ A @ B )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_left_mono
% 5.25/5.45 thf(fact_1744_mult__strict__left__mono,axiom,
% 5.25/5.45 ! [A: int,B: int,C: int] :
% 5.25/5.45 ( ( ord_less_int @ A @ B )
% 5.25/5.45 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_left_mono
% 5.25/5.45 thf(fact_1745_mult__strict__left__mono__neg,axiom,
% 5.25/5.45 ! [B: real,A: real,C: real] :
% 5.25/5.45 ( ( ord_less_real @ B @ A )
% 5.25/5.45 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.45 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_left_mono_neg
% 5.25/5.45 thf(fact_1746_mult__strict__left__mono__neg,axiom,
% 5.25/5.45 ! [B: rat,A: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_rat @ B @ A )
% 5.25/5.45 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_left_mono_neg
% 5.25/5.45 thf(fact_1747_mult__strict__left__mono__neg,axiom,
% 5.25/5.45 ! [B: int,A: int,C: int] :
% 5.25/5.45 ( ( ord_less_int @ B @ A )
% 5.25/5.45 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.45 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_left_mono_neg
% 5.25/5.45 thf(fact_1748_mult__less__cancel__left__pos,axiom,
% 5.25/5.45 ! [C: real,A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.45 = ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_left_pos
% 5.25/5.45 thf(fact_1749_mult__less__cancel__left__pos,axiom,
% 5.25/5.45 ! [C: rat,A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.45 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_left_pos
% 5.25/5.45 thf(fact_1750_mult__less__cancel__left__pos,axiom,
% 5.25/5.45 ! [C: int,A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.45 = ( ord_less_int @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_left_pos
% 5.25/5.45 thf(fact_1751_mult__less__cancel__left__neg,axiom,
% 5.25/5.45 ! [C: real,A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.45 = ( ord_less_real @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_left_neg
% 5.25/5.45 thf(fact_1752_mult__less__cancel__left__neg,axiom,
% 5.25/5.45 ! [C: rat,A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.45 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_left_neg
% 5.25/5.45 thf(fact_1753_mult__less__cancel__left__neg,axiom,
% 5.25/5.45 ! [C: int,A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.45 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.45 = ( ord_less_int @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_left_neg
% 5.25/5.45 thf(fact_1754_zero__less__mult__pos2,axiom,
% 5.25/5.45 ! [B: real,A: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_mult_pos2
% 5.25/5.45 thf(fact_1755_zero__less__mult__pos2,axiom,
% 5.25/5.45 ! [B: rat,A: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_mult_pos2
% 5.25/5.45 thf(fact_1756_zero__less__mult__pos2,axiom,
% 5.25/5.45 ! [B: nat,A: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_mult_pos2
% 5.25/5.45 thf(fact_1757_zero__less__mult__pos2,axiom,
% 5.25/5.45 ! [B: int,A: int] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.25/5.45 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_mult_pos2
% 5.25/5.45 thf(fact_1758_zero__less__mult__pos,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_mult_pos
% 5.25/5.45 thf(fact_1759_zero__less__mult__pos,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_mult_pos
% 5.25/5.45 thf(fact_1760_zero__less__mult__pos,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_mult_pos
% 5.25/5.45 thf(fact_1761_zero__less__mult__pos,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.25/5.45 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_mult_pos
% 5.25/5.45 thf(fact_1762_zero__less__mult__iff,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.25/5.45 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.45 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.25/5.45 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.45 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_mult_iff
% 5.25/5.45 thf(fact_1763_zero__less__mult__iff,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.45 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.45 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.25/5.45 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.45 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_mult_iff
% 5.25/5.45 thf(fact_1764_zero__less__mult__iff,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.25/5.45 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.45 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.25/5.45 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.45 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_mult_iff
% 5.25/5.45 thf(fact_1765_mult__pos__neg2,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.25/5.45 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_pos_neg2
% 5.25/5.45 thf(fact_1766_mult__pos__neg2,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_pos_neg2
% 5.25/5.45 thf(fact_1767_mult__pos__neg2,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.25/5.45 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_pos_neg2
% 5.25/5.45 thf(fact_1768_mult__pos__neg2,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.45 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_pos_neg2
% 5.25/5.45 thf(fact_1769_mult__pos__pos,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.45 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_pos_pos
% 5.25/5.45 thf(fact_1770_mult__pos__pos,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.25/5.45 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_pos_pos
% 5.25/5.45 thf(fact_1771_mult__pos__pos,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.45 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_pos_pos
% 5.25/5.45 thf(fact_1772_mult__pos__pos,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.45 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_pos_pos
% 5.25/5.45 thf(fact_1773_mult__pos__neg,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.25/5.45 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_pos_neg
% 5.25/5.45 thf(fact_1774_mult__pos__neg,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_pos_neg
% 5.25/5.45 thf(fact_1775_mult__pos__neg,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.25/5.45 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_pos_neg
% 5.25/5.45 thf(fact_1776_mult__pos__neg,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.45 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_pos_neg
% 5.25/5.45 thf(fact_1777_mult__neg__pos,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.45 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_neg_pos
% 5.25/5.45 thf(fact_1778_mult__neg__pos,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.25/5.45 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_neg_pos
% 5.25/5.45 thf(fact_1779_mult__neg__pos,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.45 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_neg_pos
% 5.25/5.45 thf(fact_1780_mult__neg__pos,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.45 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.45 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_neg_pos
% 5.25/5.45 thf(fact_1781_mult__less__0__iff,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.25/5.45 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.45 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.25/5.45 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.45 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_0_iff
% 5.25/5.45 thf(fact_1782_mult__less__0__iff,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.25/5.45 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.45 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.25/5.45 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.45 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_0_iff
% 5.25/5.45 thf(fact_1783_mult__less__0__iff,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.25/5.45 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.45 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.25/5.45 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.45 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_0_iff
% 5.25/5.45 thf(fact_1784_not__square__less__zero,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.25/5.45
% 5.25/5.45 % not_square_less_zero
% 5.25/5.45 thf(fact_1785_not__square__less__zero,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.25/5.45
% 5.25/5.45 % not_square_less_zero
% 5.25/5.45 thf(fact_1786_not__square__less__zero,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % not_square_less_zero
% 5.25/5.45 thf(fact_1787_mult__neg__neg,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.25/5.45 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_neg_neg
% 5.25/5.45 thf(fact_1788_mult__neg__neg,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_neg_neg
% 5.25/5.45 thf(fact_1789_mult__neg__neg,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.45 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.45 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_neg_neg
% 5.25/5.45 thf(fact_1790_not__one__less__zero,axiom,
% 5.25/5.45 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.25/5.45
% 5.25/5.45 % not_one_less_zero
% 5.25/5.45 thf(fact_1791_not__one__less__zero,axiom,
% 5.25/5.45 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.25/5.45
% 5.25/5.45 % not_one_less_zero
% 5.25/5.45 thf(fact_1792_not__one__less__zero,axiom,
% 5.25/5.45 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % not_one_less_zero
% 5.25/5.45 thf(fact_1793_not__one__less__zero,axiom,
% 5.25/5.45 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % not_one_less_zero
% 5.25/5.45 thf(fact_1794_zero__less__one,axiom,
% 5.25/5.45 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.25/5.45
% 5.25/5.45 % zero_less_one
% 5.25/5.45 thf(fact_1795_zero__less__one,axiom,
% 5.25/5.45 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.25/5.45
% 5.25/5.45 % zero_less_one
% 5.25/5.45 thf(fact_1796_zero__less__one,axiom,
% 5.25/5.45 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.25/5.45
% 5.25/5.45 % zero_less_one
% 5.25/5.45 thf(fact_1797_zero__less__one,axiom,
% 5.25/5.45 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.25/5.45
% 5.25/5.45 % zero_less_one
% 5.25/5.45 thf(fact_1798_less__numeral__extra_I1_J,axiom,
% 5.25/5.45 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.25/5.45
% 5.25/5.45 % less_numeral_extra(1)
% 5.25/5.45 thf(fact_1799_less__numeral__extra_I1_J,axiom,
% 5.25/5.45 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.25/5.45
% 5.25/5.45 % less_numeral_extra(1)
% 5.25/5.45 thf(fact_1800_less__numeral__extra_I1_J,axiom,
% 5.25/5.45 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.25/5.45
% 5.25/5.45 % less_numeral_extra(1)
% 5.25/5.45 thf(fact_1801_less__numeral__extra_I1_J,axiom,
% 5.25/5.45 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.25/5.45
% 5.25/5.45 % less_numeral_extra(1)
% 5.25/5.45 thf(fact_1802_add__less__zeroD,axiom,
% 5.25/5.45 ! [X3: real,Y: real] :
% 5.25/5.45 ( ( ord_less_real @ ( plus_plus_real @ X3 @ Y ) @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_real @ X3 @ zero_zero_real )
% 5.25/5.45 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_less_zeroD
% 5.25/5.45 thf(fact_1803_add__less__zeroD,axiom,
% 5.25/5.45 ! [X3: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_rat @ ( plus_plus_rat @ X3 @ Y ) @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 5.25/5.45 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_less_zeroD
% 5.25/5.45 thf(fact_1804_add__less__zeroD,axiom,
% 5.25/5.45 ! [X3: int,Y: int] :
% 5.25/5.45 ( ( ord_less_int @ ( plus_plus_int @ X3 @ Y ) @ zero_zero_int )
% 5.25/5.45 => ( ( ord_less_int @ X3 @ zero_zero_int )
% 5.25/5.45 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_less_zeroD
% 5.25/5.45 thf(fact_1805_add__neg__neg,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.25/5.45 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_neg_neg
% 5.25/5.45 thf(fact_1806_add__neg__neg,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_neg_neg
% 5.25/5.45 thf(fact_1807_add__neg__neg,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.25/5.45 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.25/5.45 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_neg_neg
% 5.25/5.45 thf(fact_1808_add__neg__neg,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.45 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.45 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_neg_neg
% 5.25/5.45 thf(fact_1809_add__pos__pos,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.45 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_pos_pos
% 5.25/5.45 thf(fact_1810_add__pos__pos,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.25/5.45 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_pos_pos
% 5.25/5.45 thf(fact_1811_add__pos__pos,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.45 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_pos_pos
% 5.25/5.45 thf(fact_1812_add__pos__pos,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.45 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_pos_pos
% 5.25/5.45 thf(fact_1813_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_nat @ A @ B )
% 5.25/5.45 => ~ ! [C3: nat] :
% 5.25/5.45 ( ( B
% 5.25/5.45 = ( plus_plus_nat @ A @ C3 ) )
% 5.25/5.45 => ( C3 = zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % canonically_ordered_monoid_add_class.lessE
% 5.25/5.45 thf(fact_1814_pos__add__strict,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_real @ B @ C )
% 5.25/5.45 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % pos_add_strict
% 5.25/5.45 thf(fact_1815_pos__add__strict,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_rat @ B @ C )
% 5.25/5.45 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % pos_add_strict
% 5.25/5.45 thf(fact_1816_pos__add__strict,axiom,
% 5.25/5.45 ! [A: nat,B: nat,C: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_nat @ B @ C )
% 5.25/5.45 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % pos_add_strict
% 5.25/5.45 thf(fact_1817_pos__add__strict,axiom,
% 5.25/5.45 ! [A: int,B: int,C: int] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_int @ B @ C )
% 5.25/5.45 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % pos_add_strict
% 5.25/5.45 thf(fact_1818_divide__le__0__iff,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.25/5.45 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.25/5.45 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.45 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_le_0_iff
% 5.25/5.45 thf(fact_1819_divide__le__0__iff,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.25/5.45 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.25/5.45 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.45 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_le_0_iff
% 5.25/5.45 thf(fact_1820_divide__right__mono,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_right_mono
% 5.25/5.45 thf(fact_1821_divide__right__mono,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_right_mono
% 5.25/5.45 thf(fact_1822_zero__le__divide__iff,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.25/5.45 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.25/5.45 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.45 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_divide_iff
% 5.25/5.45 thf(fact_1823_zero__le__divide__iff,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.25/5.45 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.25/5.45 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.45 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_divide_iff
% 5.25/5.45 thf(fact_1824_divide__nonneg__nonneg,axiom,
% 5.25/5.45 ! [X3: real,Y: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.45 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonneg_nonneg
% 5.25/5.45 thf(fact_1825_divide__nonneg__nonneg,axiom,
% 5.25/5.45 ! [X3: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.45 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonneg_nonneg
% 5.25/5.45 thf(fact_1826_divide__nonneg__nonpos,axiom,
% 5.25/5.45 ! [X3: real,Y: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.45 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.25/5.45 => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonneg_nonpos
% 5.25/5.45 thf(fact_1827_divide__nonneg__nonpos,axiom,
% 5.25/5.45 ! [X3: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.25/5.45 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonneg_nonpos
% 5.25/5.45 thf(fact_1828_divide__nonpos__nonneg,axiom,
% 5.25/5.45 ! [X3: real,Y: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.45 => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonpos_nonneg
% 5.25/5.45 thf(fact_1829_divide__nonpos__nonneg,axiom,
% 5.25/5.45 ! [X3: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.45 => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonpos_nonneg
% 5.25/5.45 thf(fact_1830_divide__nonpos__nonpos,axiom,
% 5.25/5.45 ! [X3: real,Y: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.25/5.45 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonpos_nonpos
% 5.25/5.45 thf(fact_1831_divide__nonpos__nonpos,axiom,
% 5.25/5.45 ! [X3: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonpos_nonpos
% 5.25/5.45 thf(fact_1832_divide__right__mono__neg,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.45 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_right_mono_neg
% 5.25/5.45 thf(fact_1833_divide__right__mono__neg,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_right_mono_neg
% 5.25/5.45 thf(fact_1834_divide__neg__neg,axiom,
% 5.25/5.45 ! [X3: real,Y: real] :
% 5.25/5.45 ( ( ord_less_real @ X3 @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.25/5.45 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_neg_neg
% 5.25/5.45 thf(fact_1835_divide__neg__neg,axiom,
% 5.25/5.45 ! [X3: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_neg_neg
% 5.25/5.45 thf(fact_1836_divide__neg__pos,axiom,
% 5.25/5.45 ! [X3: real,Y: real] :
% 5.25/5.45 ( ( ord_less_real @ X3 @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.45 => ( ord_less_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_neg_pos
% 5.25/5.45 thf(fact_1837_divide__neg__pos,axiom,
% 5.25/5.45 ! [X3: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_rat @ X3 @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.45 => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_neg_pos
% 5.25/5.45 thf(fact_1838_divide__pos__neg,axiom,
% 5.25/5.45 ! [X3: real,Y: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.45 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.25/5.45 => ( ord_less_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_pos_neg
% 5.25/5.45 thf(fact_1839_divide__pos__neg,axiom,
% 5.25/5.45 ! [X3: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 5.25/5.45 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_pos_neg
% 5.25/5.45 thf(fact_1840_divide__pos__pos,axiom,
% 5.25/5.45 ! [X3: real,Y: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.45 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_pos_pos
% 5.25/5.45 thf(fact_1841_divide__pos__pos,axiom,
% 5.25/5.45 ! [X3: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.45 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_pos_pos
% 5.25/5.45 thf(fact_1842_divide__less__0__iff,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.25/5.45 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.45 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.25/5.45 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.45 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_less_0_iff
% 5.25/5.45 thf(fact_1843_divide__less__0__iff,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.25/5.45 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.45 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.25/5.45 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.45 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_less_0_iff
% 5.25/5.45 thf(fact_1844_divide__less__cancel,axiom,
% 5.25/5.45 ! [A: real,C: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.25/5.45 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_real @ A @ B ) )
% 5.25/5.45 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.45 => ( ord_less_real @ B @ A ) )
% 5.25/5.45 & ( C != zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_less_cancel
% 5.25/5.45 thf(fact_1845_divide__less__cancel,axiom,
% 5.25/5.45 ! [A: rat,C: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.45 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_rat @ A @ B ) )
% 5.25/5.45 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_rat @ B @ A ) )
% 5.25/5.45 & ( C != zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_less_cancel
% 5.25/5.45 thf(fact_1846_zero__less__divide__iff,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.25/5.45 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.45 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.25/5.45 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.45 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_divide_iff
% 5.25/5.45 thf(fact_1847_zero__less__divide__iff,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.25/5.45 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.45 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.25/5.45 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.45 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_divide_iff
% 5.25/5.45 thf(fact_1848_divide__strict__right__mono,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real] :
% 5.25/5.45 ( ( ord_less_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_strict_right_mono
% 5.25/5.45 thf(fact_1849_divide__strict__right__mono,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_strict_right_mono
% 5.25/5.45 thf(fact_1850_divide__strict__right__mono__neg,axiom,
% 5.25/5.45 ! [B: real,A: real,C: real] :
% 5.25/5.45 ( ( ord_less_real @ B @ A )
% 5.25/5.45 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.45 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_strict_right_mono_neg
% 5.25/5.45 thf(fact_1851_divide__strict__right__mono__neg,axiom,
% 5.25/5.45 ! [B: rat,A: rat,C: rat] :
% 5.25/5.45 ( ( ord_less_rat @ B @ A )
% 5.25/5.45 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_strict_right_mono_neg
% 5.25/5.45 thf(fact_1852_zero__le__power,axiom,
% 5.25/5.45 ! [A: real,N: nat] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_power
% 5.25/5.45 thf(fact_1853_zero__le__power,axiom,
% 5.25/5.45 ! [A: rat,N: nat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_power
% 5.25/5.45 thf(fact_1854_zero__le__power,axiom,
% 5.25/5.45 ! [A: nat,N: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_power
% 5.25/5.45 thf(fact_1855_zero__le__power,axiom,
% 5.25/5.45 ! [A: int,N: nat] :
% 5.25/5.45 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_power
% 5.25/5.45 thf(fact_1856_power__mono,axiom,
% 5.25/5.45 ! [A: real,B: real,N: nat] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_mono
% 5.25/5.45 thf(fact_1857_power__mono,axiom,
% 5.25/5.45 ! [A: rat,B: rat,N: nat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_mono
% 5.25/5.45 thf(fact_1858_power__mono,axiom,
% 5.25/5.45 ! [A: nat,B: nat,N: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_mono
% 5.25/5.45 thf(fact_1859_power__mono,axiom,
% 5.25/5.45 ! [A: int,B: int,N: nat] :
% 5.25/5.45 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_mono
% 5.25/5.45 thf(fact_1860_zero__less__power,axiom,
% 5.25/5.45 ! [A: real,N: nat] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_power
% 5.25/5.45 thf(fact_1861_zero__less__power,axiom,
% 5.25/5.45 ! [A: rat,N: nat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_power
% 5.25/5.45 thf(fact_1862_zero__less__power,axiom,
% 5.25/5.45 ! [A: nat,N: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_power
% 5.25/5.45 thf(fact_1863_zero__less__power,axiom,
% 5.25/5.45 ! [A: int,N: nat] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_power
% 5.25/5.45 thf(fact_1864_frac__eq__eq,axiom,
% 5.25/5.45 ! [Y: complex,Z: complex,X3: complex,W: complex] :
% 5.25/5.45 ( ( Y != zero_zero_complex )
% 5.25/5.45 => ( ( Z != zero_zero_complex )
% 5.25/5.45 => ( ( ( divide1717551699836669952omplex @ X3 @ Y )
% 5.25/5.45 = ( divide1717551699836669952omplex @ W @ Z ) )
% 5.25/5.45 = ( ( times_times_complex @ X3 @ Z )
% 5.25/5.45 = ( times_times_complex @ W @ Y ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % frac_eq_eq
% 5.25/5.45 thf(fact_1865_frac__eq__eq,axiom,
% 5.25/5.45 ! [Y: real,Z: real,X3: real,W: real] :
% 5.25/5.45 ( ( Y != zero_zero_real )
% 5.25/5.45 => ( ( Z != zero_zero_real )
% 5.25/5.45 => ( ( ( divide_divide_real @ X3 @ Y )
% 5.25/5.45 = ( divide_divide_real @ W @ Z ) )
% 5.25/5.45 = ( ( times_times_real @ X3 @ Z )
% 5.25/5.45 = ( times_times_real @ W @ Y ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % frac_eq_eq
% 5.25/5.45 thf(fact_1866_frac__eq__eq,axiom,
% 5.25/5.45 ! [Y: rat,Z: rat,X3: rat,W: rat] :
% 5.25/5.45 ( ( Y != zero_zero_rat )
% 5.25/5.45 => ( ( Z != zero_zero_rat )
% 5.25/5.45 => ( ( ( divide_divide_rat @ X3 @ Y )
% 5.25/5.45 = ( divide_divide_rat @ W @ Z ) )
% 5.25/5.45 = ( ( times_times_rat @ X3 @ Z )
% 5.25/5.45 = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % frac_eq_eq
% 5.25/5.45 thf(fact_1867_divide__eq__eq,axiom,
% 5.25/5.45 ! [B: complex,C: complex,A: complex] :
% 5.25/5.45 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.25/5.45 = A )
% 5.25/5.45 = ( ( ( C != zero_zero_complex )
% 5.25/5.45 => ( B
% 5.25/5.45 = ( times_times_complex @ A @ C ) ) )
% 5.25/5.45 & ( ( C = zero_zero_complex )
% 5.25/5.45 => ( A = zero_zero_complex ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_eq_eq
% 5.25/5.45 thf(fact_1868_divide__eq__eq,axiom,
% 5.25/5.45 ! [B: real,C: real,A: real] :
% 5.25/5.45 ( ( ( divide_divide_real @ B @ C )
% 5.25/5.45 = A )
% 5.25/5.45 = ( ( ( C != zero_zero_real )
% 5.25/5.45 => ( B
% 5.25/5.45 = ( times_times_real @ A @ C ) ) )
% 5.25/5.45 & ( ( C = zero_zero_real )
% 5.25/5.45 => ( A = zero_zero_real ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_eq_eq
% 5.25/5.45 thf(fact_1869_divide__eq__eq,axiom,
% 5.25/5.45 ! [B: rat,C: rat,A: rat] :
% 5.25/5.45 ( ( ( divide_divide_rat @ B @ C )
% 5.25/5.45 = A )
% 5.25/5.45 = ( ( ( C != zero_zero_rat )
% 5.25/5.45 => ( B
% 5.25/5.45 = ( times_times_rat @ A @ C ) ) )
% 5.25/5.45 & ( ( C = zero_zero_rat )
% 5.25/5.45 => ( A = zero_zero_rat ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_eq_eq
% 5.25/5.45 thf(fact_1870_eq__divide__eq,axiom,
% 5.25/5.45 ! [A: complex,B: complex,C: complex] :
% 5.25/5.45 ( ( A
% 5.25/5.45 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.45 = ( ( ( C != zero_zero_complex )
% 5.25/5.45 => ( ( times_times_complex @ A @ C )
% 5.25/5.45 = B ) )
% 5.25/5.45 & ( ( C = zero_zero_complex )
% 5.25/5.45 => ( A = zero_zero_complex ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % eq_divide_eq
% 5.25/5.45 thf(fact_1871_eq__divide__eq,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real] :
% 5.25/5.45 ( ( A
% 5.25/5.45 = ( divide_divide_real @ B @ C ) )
% 5.25/5.45 = ( ( ( C != zero_zero_real )
% 5.25/5.45 => ( ( times_times_real @ A @ C )
% 5.25/5.45 = B ) )
% 5.25/5.45 & ( ( C = zero_zero_real )
% 5.25/5.45 => ( A = zero_zero_real ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % eq_divide_eq
% 5.25/5.45 thf(fact_1872_eq__divide__eq,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat] :
% 5.25/5.45 ( ( A
% 5.25/5.45 = ( divide_divide_rat @ B @ C ) )
% 5.25/5.45 = ( ( ( C != zero_zero_rat )
% 5.25/5.45 => ( ( times_times_rat @ A @ C )
% 5.25/5.45 = B ) )
% 5.25/5.45 & ( ( C = zero_zero_rat )
% 5.25/5.45 => ( A = zero_zero_rat ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % eq_divide_eq
% 5.25/5.45 thf(fact_1873_divide__eq__imp,axiom,
% 5.25/5.45 ! [C: complex,B: complex,A: complex] :
% 5.25/5.45 ( ( C != zero_zero_complex )
% 5.25/5.45 => ( ( B
% 5.25/5.45 = ( times_times_complex @ A @ C ) )
% 5.25/5.45 => ( ( divide1717551699836669952omplex @ B @ C )
% 5.25/5.45 = A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_eq_imp
% 5.25/5.45 thf(fact_1874_divide__eq__imp,axiom,
% 5.25/5.45 ! [C: real,B: real,A: real] :
% 5.25/5.45 ( ( C != zero_zero_real )
% 5.25/5.45 => ( ( B
% 5.25/5.45 = ( times_times_real @ A @ C ) )
% 5.25/5.45 => ( ( divide_divide_real @ B @ C )
% 5.25/5.45 = A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_eq_imp
% 5.25/5.45 thf(fact_1875_divide__eq__imp,axiom,
% 5.25/5.45 ! [C: rat,B: rat,A: rat] :
% 5.25/5.45 ( ( C != zero_zero_rat )
% 5.25/5.45 => ( ( B
% 5.25/5.45 = ( times_times_rat @ A @ C ) )
% 5.25/5.45 => ( ( divide_divide_rat @ B @ C )
% 5.25/5.45 = A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_eq_imp
% 5.25/5.45 thf(fact_1876_eq__divide__imp,axiom,
% 5.25/5.45 ! [C: complex,A: complex,B: complex] :
% 5.25/5.45 ( ( C != zero_zero_complex )
% 5.25/5.45 => ( ( ( times_times_complex @ A @ C )
% 5.25/5.45 = B )
% 5.25/5.45 => ( A
% 5.25/5.45 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % eq_divide_imp
% 5.25/5.45 thf(fact_1877_eq__divide__imp,axiom,
% 5.25/5.45 ! [C: real,A: real,B: real] :
% 5.25/5.45 ( ( C != zero_zero_real )
% 5.25/5.45 => ( ( ( times_times_real @ A @ C )
% 5.25/5.45 = B )
% 5.25/5.45 => ( A
% 5.25/5.45 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % eq_divide_imp
% 5.25/5.45 thf(fact_1878_eq__divide__imp,axiom,
% 5.25/5.45 ! [C: rat,A: rat,B: rat] :
% 5.25/5.45 ( ( C != zero_zero_rat )
% 5.25/5.45 => ( ( ( times_times_rat @ A @ C )
% 5.25/5.45 = B )
% 5.25/5.45 => ( A
% 5.25/5.45 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % eq_divide_imp
% 5.25/5.45 thf(fact_1879_nonzero__divide__eq__eq,axiom,
% 5.25/5.45 ! [C: complex,B: complex,A: complex] :
% 5.25/5.45 ( ( C != zero_zero_complex )
% 5.25/5.45 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.25/5.45 = A )
% 5.25/5.45 = ( B
% 5.25/5.45 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nonzero_divide_eq_eq
% 5.25/5.45 thf(fact_1880_nonzero__divide__eq__eq,axiom,
% 5.25/5.45 ! [C: real,B: real,A: real] :
% 5.25/5.45 ( ( C != zero_zero_real )
% 5.25/5.45 => ( ( ( divide_divide_real @ B @ C )
% 5.25/5.45 = A )
% 5.25/5.45 = ( B
% 5.25/5.45 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nonzero_divide_eq_eq
% 5.25/5.45 thf(fact_1881_nonzero__divide__eq__eq,axiom,
% 5.25/5.45 ! [C: rat,B: rat,A: rat] :
% 5.25/5.45 ( ( C != zero_zero_rat )
% 5.25/5.45 => ( ( ( divide_divide_rat @ B @ C )
% 5.25/5.45 = A )
% 5.25/5.45 = ( B
% 5.25/5.45 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nonzero_divide_eq_eq
% 5.25/5.45 thf(fact_1882_nonzero__eq__divide__eq,axiom,
% 5.25/5.45 ! [C: complex,A: complex,B: complex] :
% 5.25/5.45 ( ( C != zero_zero_complex )
% 5.25/5.45 => ( ( A
% 5.25/5.45 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.45 = ( ( times_times_complex @ A @ C )
% 5.25/5.45 = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nonzero_eq_divide_eq
% 5.25/5.45 thf(fact_1883_nonzero__eq__divide__eq,axiom,
% 5.25/5.45 ! [C: real,A: real,B: real] :
% 5.25/5.45 ( ( C != zero_zero_real )
% 5.25/5.45 => ( ( A
% 5.25/5.45 = ( divide_divide_real @ B @ C ) )
% 5.25/5.45 = ( ( times_times_real @ A @ C )
% 5.25/5.45 = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nonzero_eq_divide_eq
% 5.25/5.45 thf(fact_1884_nonzero__eq__divide__eq,axiom,
% 5.25/5.45 ! [C: rat,A: rat,B: rat] :
% 5.25/5.45 ( ( C != zero_zero_rat )
% 5.25/5.45 => ( ( A
% 5.25/5.45 = ( divide_divide_rat @ B @ C ) )
% 5.25/5.45 = ( ( times_times_rat @ A @ C )
% 5.25/5.45 = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nonzero_eq_divide_eq
% 5.25/5.45 thf(fact_1885_right__inverse__eq,axiom,
% 5.25/5.45 ! [B: complex,A: complex] :
% 5.25/5.45 ( ( B != zero_zero_complex )
% 5.25/5.45 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.25/5.45 = one_one_complex )
% 5.25/5.45 = ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % right_inverse_eq
% 5.25/5.45 thf(fact_1886_right__inverse__eq,axiom,
% 5.25/5.45 ! [B: real,A: real] :
% 5.25/5.45 ( ( B != zero_zero_real )
% 5.25/5.45 => ( ( ( divide_divide_real @ A @ B )
% 5.25/5.45 = one_one_real )
% 5.25/5.45 = ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % right_inverse_eq
% 5.25/5.45 thf(fact_1887_right__inverse__eq,axiom,
% 5.25/5.45 ! [B: rat,A: rat] :
% 5.25/5.45 ( ( B != zero_zero_rat )
% 5.25/5.45 => ( ( ( divide_divide_rat @ A @ B )
% 5.25/5.45 = one_one_rat )
% 5.25/5.45 = ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % right_inverse_eq
% 5.25/5.45 thf(fact_1888_not__exp__less__eq__0__int,axiom,
% 5.25/5.45 ! [N: nat] :
% 5.25/5.45 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % not_exp_less_eq_0_int
% 5.25/5.45 thf(fact_1889_pos__zdiv__mult__2,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( 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 ) )
% 5.25/5.45 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % pos_zdiv_mult_2
% 5.25/5.45 thf(fact_1890_neg__zdiv__mult__2,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.45 => ( ( 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 ) )
% 5.25/5.45 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % neg_zdiv_mult_2
% 5.25/5.45 thf(fact_1891_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.25/5.45 ! [A: code_integer,B: code_integer] :
% 5.25/5.45 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.45 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.25/5.45 thf(fact_1892_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.25/5.45 thf(fact_1893_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.25/5.45 thf(fact_1894_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.25/5.45 ! [B: nat,A: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.45 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.25/5.45 thf(fact_1895_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.25/5.45 ! [B: int,A: int] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.45 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.25/5.45 thf(fact_1896_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.25/5.45 ! [B: code_integer,A: code_integer] :
% 5.25/5.45 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.25/5.45 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.25/5.45 thf(fact_1897_power__0,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( power_power_rat @ A @ zero_zero_nat )
% 5.25/5.45 = one_one_rat ) ).
% 5.25/5.45
% 5.25/5.45 % power_0
% 5.25/5.45 thf(fact_1898_power__0,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.25/5.45 = one_one_nat ) ).
% 5.25/5.45
% 5.25/5.45 % power_0
% 5.25/5.45 thf(fact_1899_power__0,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( power_power_real @ A @ zero_zero_nat )
% 5.25/5.45 = one_one_real ) ).
% 5.25/5.45
% 5.25/5.45 % power_0
% 5.25/5.45 thf(fact_1900_power__0,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( power_power_int @ A @ zero_zero_nat )
% 5.25/5.45 = one_one_int ) ).
% 5.25/5.45
% 5.25/5.45 % power_0
% 5.25/5.45 thf(fact_1901_power__0,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.25/5.45 = one_one_complex ) ).
% 5.25/5.45
% 5.25/5.45 % power_0
% 5.25/5.45 thf(fact_1902_mod__eq__self__iff__div__eq__0,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ( modulo_modulo_nat @ A @ B )
% 5.25/5.45 = A )
% 5.25/5.45 = ( ( divide_divide_nat @ A @ B )
% 5.25/5.45 = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % mod_eq_self_iff_div_eq_0
% 5.25/5.45 thf(fact_1903_mod__eq__self__iff__div__eq__0,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ( modulo_modulo_int @ A @ B )
% 5.25/5.45 = A )
% 5.25/5.45 = ( ( divide_divide_int @ A @ B )
% 5.25/5.45 = zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % mod_eq_self_iff_div_eq_0
% 5.25/5.45 thf(fact_1904_mod__eq__self__iff__div__eq__0,axiom,
% 5.25/5.45 ! [A: code_integer,B: code_integer] :
% 5.25/5.45 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.25/5.45 = A )
% 5.25/5.45 = ( ( divide6298287555418463151nteger @ A @ B )
% 5.25/5.45 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.45
% 5.25/5.45 % mod_eq_self_iff_div_eq_0
% 5.25/5.45 thf(fact_1905_less__Suc__eq__0__disj,axiom,
% 5.25/5.45 ! [M: nat,N: nat] :
% 5.25/5.45 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.25/5.45 = ( ( M = zero_zero_nat )
% 5.25/5.45 | ? [J3: nat] :
% 5.25/5.45 ( ( M
% 5.25/5.45 = ( suc @ J3 ) )
% 5.25/5.45 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_Suc_eq_0_disj
% 5.25/5.45 thf(fact_1906_gr0__implies__Suc,axiom,
% 5.25/5.45 ! [N: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ? [M5: nat] :
% 5.25/5.45 ( N
% 5.25/5.45 = ( suc @ M5 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % gr0_implies_Suc
% 5.25/5.45 thf(fact_1907_All__less__Suc2,axiom,
% 5.25/5.45 ! [N: nat,P: nat > $o] :
% 5.25/5.45 ( ( ! [I3: nat] :
% 5.25/5.45 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 5.25/5.45 => ( P @ I3 ) ) )
% 5.25/5.45 = ( ( P @ zero_zero_nat )
% 5.25/5.45 & ! [I3: nat] :
% 5.25/5.45 ( ( ord_less_nat @ I3 @ N )
% 5.25/5.45 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % All_less_Suc2
% 5.25/5.45 thf(fact_1908_gr0__conv__Suc,axiom,
% 5.25/5.45 ! [N: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 = ( ? [M6: nat] :
% 5.25/5.45 ( N
% 5.25/5.45 = ( suc @ M6 ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % gr0_conv_Suc
% 5.25/5.45 thf(fact_1909_Ex__less__Suc2,axiom,
% 5.25/5.45 ! [N: nat,P: nat > $o] :
% 5.25/5.45 ( ( ? [I3: nat] :
% 5.25/5.45 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 5.25/5.45 & ( P @ I3 ) ) )
% 5.25/5.45 = ( ( P @ zero_zero_nat )
% 5.25/5.45 | ? [I3: nat] :
% 5.25/5.45 ( ( ord_less_nat @ I3 @ N )
% 5.25/5.45 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % Ex_less_Suc2
% 5.25/5.45 thf(fact_1910_add__is__1,axiom,
% 5.25/5.45 ! [M: nat,N: nat] :
% 5.25/5.45 ( ( ( plus_plus_nat @ M @ N )
% 5.25/5.45 = ( suc @ zero_zero_nat ) )
% 5.25/5.45 = ( ( ( M
% 5.25/5.45 = ( suc @ zero_zero_nat ) )
% 5.25/5.45 & ( N = zero_zero_nat ) )
% 5.25/5.45 | ( ( M = zero_zero_nat )
% 5.25/5.45 & ( N
% 5.25/5.45 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_is_1
% 5.25/5.45 thf(fact_1911_one__is__add,axiom,
% 5.25/5.45 ! [M: nat,N: nat] :
% 5.25/5.45 ( ( ( suc @ zero_zero_nat )
% 5.25/5.45 = ( plus_plus_nat @ M @ N ) )
% 5.25/5.45 = ( ( ( M
% 5.25/5.45 = ( suc @ zero_zero_nat ) )
% 5.25/5.45 & ( N = zero_zero_nat ) )
% 5.25/5.45 | ( ( M = zero_zero_nat )
% 5.25/5.45 & ( N
% 5.25/5.45 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % one_is_add
% 5.25/5.45 thf(fact_1912_ex__least__nat__le,axiom,
% 5.25/5.45 ! [P: nat > $o,N: nat] :
% 5.25/5.45 ( ( P @ N )
% 5.25/5.45 => ( ~ ( P @ zero_zero_nat )
% 5.25/5.45 => ? [K2: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ K2 @ N )
% 5.25/5.45 & ! [I: nat] :
% 5.25/5.45 ( ( ord_less_nat @ I @ K2 )
% 5.25/5.45 => ~ ( P @ I ) )
% 5.25/5.45 & ( P @ K2 ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % ex_least_nat_le
% 5.25/5.45 thf(fact_1913_less__imp__add__positive,axiom,
% 5.25/5.45 ! [I2: nat,J2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.45 => ? [K2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.25/5.45 & ( ( plus_plus_nat @ I2 @ K2 )
% 5.25/5.45 = J2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_imp_add_positive
% 5.25/5.45 thf(fact_1914_div__less__mono,axiom,
% 5.25/5.45 ! [A2: nat,B3: nat,N: nat] :
% 5.25/5.45 ( ( ord_less_nat @ A2 @ B3 )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ( ( ( modulo_modulo_nat @ A2 @ N )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 => ( ( ( modulo_modulo_nat @ B3 @ N )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B3 @ N ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % div_less_mono
% 5.25/5.45 thf(fact_1915_realpow__pos__nth2,axiom,
% 5.25/5.45 ! [A: real,N: nat] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.45 => ? [R3: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.25/5.45 & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 5.25/5.45 = A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % realpow_pos_nth2
% 5.25/5.45 thf(fact_1916_nat__mult__eq__cancel1,axiom,
% 5.25/5.45 ! [K: nat,M: nat,N: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.45 => ( ( ( times_times_nat @ K @ M )
% 5.25/5.45 = ( times_times_nat @ K @ N ) )
% 5.25/5.45 = ( M = N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nat_mult_eq_cancel1
% 5.25/5.45 thf(fact_1917_nat__mult__less__cancel1,axiom,
% 5.25/5.45 ! [K: nat,M: nat,N: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.45 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.25/5.45 = ( ord_less_nat @ M @ N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nat_mult_less_cancel1
% 5.25/5.45 thf(fact_1918_mult__less__mono2,axiom,
% 5.25/5.45 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.45 ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.45 => ( ord_less_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J2 ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_mono2
% 5.25/5.45 thf(fact_1919_mult__less__mono1,axiom,
% 5.25/5.45 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.45 ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.45 => ( ord_less_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J2 @ K ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_mono1
% 5.25/5.45 thf(fact_1920_One__nat__def,axiom,
% 5.25/5.45 ( one_one_nat
% 5.25/5.45 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % One_nat_def
% 5.25/5.45 thf(fact_1921_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.25/5.45 ! [M: nat,N: nat] :
% 5.25/5.45 ( ( ( divide_divide_nat @ M @ N )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 = ( ( ord_less_nat @ M @ N )
% 5.25/5.45 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % Euclidean_Division.div_eq_0_iff
% 5.25/5.45 thf(fact_1922_real__arch__pow__inv,axiom,
% 5.25/5.45 ! [Y: real,X3: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.45 => ( ( ord_less_real @ X3 @ one_one_real )
% 5.25/5.45 => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X3 @ N3 ) @ Y ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % real_arch_pow_inv
% 5.25/5.45 thf(fact_1923_nat__power__less__imp__less,axiom,
% 5.25/5.45 ! [I2: nat,M: nat,N: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 5.25/5.45 => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
% 5.25/5.45 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nat_power_less_imp_less
% 5.25/5.45 thf(fact_1924_mod__Suc,axiom,
% 5.25/5.45 ! [M: nat,N: nat] :
% 5.25/5.45 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.25/5.45 = N )
% 5.25/5.45 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.25/5.45 = zero_zero_nat ) )
% 5.25/5.45 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.25/5.45 != N )
% 5.25/5.45 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.25/5.45 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mod_Suc
% 5.25/5.45 thf(fact_1925_mult__eq__self__implies__10,axiom,
% 5.25/5.45 ! [M: nat,N: nat] :
% 5.25/5.45 ( ( M
% 5.25/5.45 = ( times_times_nat @ M @ N ) )
% 5.25/5.45 => ( ( N = one_one_nat )
% 5.25/5.45 | ( M = zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_eq_self_implies_10
% 5.25/5.45 thf(fact_1926_mod__less__divisor,axiom,
% 5.25/5.45 ! [N: nat,M: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.45 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.25/5.45
% 5.25/5.45 % mod_less_divisor
% 5.25/5.45 thf(fact_1927_pow_Osimps_I1_J,axiom,
% 5.25/5.45 ! [X3: num] :
% 5.25/5.45 ( ( pow @ X3 @ one )
% 5.25/5.45 = X3 ) ).
% 5.25/5.45
% 5.25/5.45 % pow.simps(1)
% 5.25/5.45 thf(fact_1928_mod__eq__0D,axiom,
% 5.25/5.45 ! [M: nat,D: nat] :
% 5.25/5.45 ( ( ( modulo_modulo_nat @ M @ D )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 => ? [Q3: nat] :
% 5.25/5.45 ( M
% 5.25/5.45 = ( times_times_nat @ D @ Q3 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mod_eq_0D
% 5.25/5.45 thf(fact_1929_vebt__insert_Osimps_I2_J,axiom,
% 5.25/5.45 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.25/5.45 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X3 )
% 5.25/5.45 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) ) ).
% 5.25/5.45
% 5.25/5.45 % vebt_insert.simps(2)
% 5.25/5.45 thf(fact_1930_verit__la__disequality,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( A = B )
% 5.25/5.45 | ~ ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % verit_la_disequality
% 5.25/5.45 thf(fact_1931_verit__la__disequality,axiom,
% 5.25/5.45 ! [A: num,B: num] :
% 5.25/5.45 ( ( A = B )
% 5.25/5.45 | ~ ( ord_less_eq_num @ A @ B )
% 5.25/5.45 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % verit_la_disequality
% 5.25/5.45 thf(fact_1932_verit__la__disequality,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( A = B )
% 5.25/5.45 | ~ ( ord_less_eq_nat @ A @ B )
% 5.25/5.45 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % verit_la_disequality
% 5.25/5.45 thf(fact_1933_verit__la__disequality,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( A = B )
% 5.25/5.45 | ~ ( ord_less_eq_int @ A @ B )
% 5.25/5.45 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % verit_la_disequality
% 5.25/5.45 thf(fact_1934_verit__comp__simplify1_I2_J,axiom,
% 5.25/5.45 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_comp_simplify1(2)
% 5.25/5.45 thf(fact_1935_verit__comp__simplify1_I2_J,axiom,
% 5.25/5.45 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_comp_simplify1(2)
% 5.25/5.45 thf(fact_1936_verit__comp__simplify1_I2_J,axiom,
% 5.25/5.45 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_comp_simplify1(2)
% 5.25/5.45 thf(fact_1937_verit__comp__simplify1_I2_J,axiom,
% 5.25/5.45 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_comp_simplify1(2)
% 5.25/5.45 thf(fact_1938_verit__comp__simplify1_I2_J,axiom,
% 5.25/5.45 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_comp_simplify1(2)
% 5.25/5.45 thf(fact_1939_verit__comp__simplify1_I1_J,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ~ ( ord_less_real @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_comp_simplify1(1)
% 5.25/5.45 thf(fact_1940_verit__comp__simplify1_I1_J,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ~ ( ord_less_rat @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_comp_simplify1(1)
% 5.25/5.45 thf(fact_1941_verit__comp__simplify1_I1_J,axiom,
% 5.25/5.45 ! [A: num] :
% 5.25/5.45 ~ ( ord_less_num @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_comp_simplify1(1)
% 5.25/5.45 thf(fact_1942_verit__comp__simplify1_I1_J,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ~ ( ord_less_nat @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_comp_simplify1(1)
% 5.25/5.45 thf(fact_1943_verit__comp__simplify1_I1_J,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ~ ( ord_less_int @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_comp_simplify1(1)
% 5.25/5.45 thf(fact_1944_mult__less__le__imp__less,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.45 ( ( ord_less_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_real @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_le_imp_less
% 5.25/5.45 thf(fact_1945_mult__less__le__imp__less,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.45 ( ( ord_less_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_rat @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_le_imp_less
% 5.25/5.45 thf(fact_1946_mult__less__le__imp__less,axiom,
% 5.25/5.45 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.45 ( ( ord_less_nat @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_nat @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_le_imp_less
% 5.25/5.45 thf(fact_1947_mult__less__le__imp__less,axiom,
% 5.25/5.45 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.45 ( ( ord_less_int @ A @ B )
% 5.25/5.45 => ( ( ord_less_eq_int @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_le_imp_less
% 5.25/5.45 thf(fact_1948_mult__le__less__imp__less,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_real @ C @ D )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_le_less_imp_less
% 5.25/5.45 thf(fact_1949_mult__le__less__imp__less,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_rat @ C @ D )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_le_less_imp_less
% 5.25/5.45 thf(fact_1950_mult__le__less__imp__less,axiom,
% 5.25/5.45 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.45 => ( ( ord_less_nat @ C @ D )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_le_less_imp_less
% 5.25/5.45 thf(fact_1951_mult__le__less__imp__less,axiom,
% 5.25/5.45 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.45 => ( ( ord_less_int @ C @ D )
% 5.25/5.45 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_le_less_imp_less
% 5.25/5.45 thf(fact_1952_mult__right__le__imp__le,axiom,
% 5.25/5.45 ! [A: real,C: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_le_imp_le
% 5.25/5.45 thf(fact_1953_mult__right__le__imp__le,axiom,
% 5.25/5.45 ! [A: rat,C: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_le_imp_le
% 5.25/5.45 thf(fact_1954_mult__right__le__imp__le,axiom,
% 5.25/5.45 ! [A: nat,C: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_le_imp_le
% 5.25/5.45 thf(fact_1955_mult__right__le__imp__le,axiom,
% 5.25/5.45 ! [A: int,C: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.45 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_le_imp_le
% 5.25/5.45 thf(fact_1956_mult__left__le__imp__le,axiom,
% 5.25/5.45 ! [C: real,A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_left_le_imp_le
% 5.25/5.45 thf(fact_1957_mult__left__le__imp__le,axiom,
% 5.25/5.45 ! [C: rat,A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_left_le_imp_le
% 5.25/5.45 thf(fact_1958_mult__left__le__imp__le,axiom,
% 5.25/5.45 ! [C: nat,A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_left_le_imp_le
% 5.25/5.45 thf(fact_1959_mult__left__le__imp__le,axiom,
% 5.25/5.45 ! [C: int,A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.45 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_left_le_imp_le
% 5.25/5.45 thf(fact_1960_mult__le__cancel__left__pos,axiom,
% 5.25/5.45 ! [C: real,A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.45 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_le_cancel_left_pos
% 5.25/5.45 thf(fact_1961_mult__le__cancel__left__pos,axiom,
% 5.25/5.45 ! [C: rat,A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.45 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_le_cancel_left_pos
% 5.25/5.45 thf(fact_1962_mult__le__cancel__left__pos,axiom,
% 5.25/5.45 ! [C: int,A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.45 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_le_cancel_left_pos
% 5.25/5.45 thf(fact_1963_mult__le__cancel__left__neg,axiom,
% 5.25/5.45 ! [C: real,A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.45 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_le_cancel_left_neg
% 5.25/5.45 thf(fact_1964_mult__le__cancel__left__neg,axiom,
% 5.25/5.45 ! [C: rat,A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.45 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_le_cancel_left_neg
% 5.25/5.45 thf(fact_1965_mult__le__cancel__left__neg,axiom,
% 5.25/5.45 ! [C: int,A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.45 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.45 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_le_cancel_left_neg
% 5.25/5.45 thf(fact_1966_mult__less__cancel__right,axiom,
% 5.25/5.45 ! [A: real,C: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.25/5.45 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_real @ A @ B ) )
% 5.25/5.45 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.45 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_right
% 5.25/5.45 thf(fact_1967_mult__less__cancel__right,axiom,
% 5.25/5.45 ! [A: rat,C: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.45 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_rat @ A @ B ) )
% 5.25/5.45 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_right
% 5.25/5.45 thf(fact_1968_mult__less__cancel__right,axiom,
% 5.25/5.45 ! [A: int,C: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.45 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_int @ A @ B ) )
% 5.25/5.45 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.45 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_right
% 5.25/5.45 thf(fact_1969_mult__strict__mono_H,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.45 ( ( ord_less_real @ A @ B )
% 5.25/5.45 => ( ( ord_less_real @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_mono'
% 5.25/5.45 thf(fact_1970_mult__strict__mono_H,axiom,
% 5.25/5.45 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.45 ( ( ord_less_rat @ A @ B )
% 5.25/5.45 => ( ( ord_less_rat @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_mono'
% 5.25/5.45 thf(fact_1971_mult__strict__mono_H,axiom,
% 5.25/5.45 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.45 ( ( ord_less_nat @ A @ B )
% 5.25/5.45 => ( ( ord_less_nat @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_mono'
% 5.25/5.45 thf(fact_1972_mult__strict__mono_H,axiom,
% 5.25/5.45 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.45 ( ( ord_less_int @ A @ B )
% 5.25/5.45 => ( ( ord_less_int @ C @ D )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_strict_mono'
% 5.25/5.45 thf(fact_1973_mult__right__less__imp__less,axiom,
% 5.25/5.45 ! [A: real,C: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_less_imp_less
% 5.25/5.45 thf(fact_1974_mult__right__less__imp__less,axiom,
% 5.25/5.45 ! [A: rat,C: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_less_imp_less
% 5.25/5.45 thf(fact_1975_mult__right__less__imp__less,axiom,
% 5.25/5.45 ! [A: nat,C: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.45 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_less_imp_less
% 5.25/5.45 thf(fact_1976_mult__right__less__imp__less,axiom,
% 5.25/5.45 ! [A: int,C: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_int @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_right_less_imp_less
% 5.25/5.45 thf(fact_1977_mult__less__cancel__left,axiom,
% 5.25/5.45 ! [C: real,A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.45 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.45 => ( ord_less_real @ A @ B ) )
% 5.25/5.45 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.45 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_left
% 5.25/5.45 thf(fact_1978_mult__less__cancel__left,axiom,
% 5.25/5.45 ! [C: rat,A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.45 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.45 => ( ord_less_rat @ A @ B ) )
% 5.25/5.45 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_left
% 5.25/5.45 thf(fact_1979_mult__less__cancel__left,axiom,
% 5.25/5.45 ! [C: int,A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.45 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.45 => ( ord_less_int @ A @ B ) )
% 5.25/5.45 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.45 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mult_less_cancel_left
% 5.25/5.45 thf(fact_1980_mult__strict__mono,axiom,
% 5.25/5.45 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.45 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ( ( ord_less_real @ C @ D )
% 5.25/5.46 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_strict_mono
% 5.25/5.46 thf(fact_1981_mult__strict__mono,axiom,
% 5.25/5.46 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ( ( ord_less_rat @ C @ D )
% 5.25/5.46 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_strict_mono
% 5.25/5.46 thf(fact_1982_mult__strict__mono,axiom,
% 5.25/5.46 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.46 ( ( ord_less_nat @ A @ B )
% 5.25/5.46 => ( ( ord_less_nat @ C @ D )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.46 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_strict_mono
% 5.25/5.46 thf(fact_1983_mult__strict__mono,axiom,
% 5.25/5.46 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.46 ( ( ord_less_int @ A @ B )
% 5.25/5.46 => ( ( ord_less_int @ C @ D )
% 5.25/5.46 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.46 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_strict_mono
% 5.25/5.46 thf(fact_1984_mult__left__less__imp__less,axiom,
% 5.25/5.46 ! [C: real,A: real,B: real] :
% 5.25/5.46 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_left_less_imp_less
% 5.25/5.46 thf(fact_1985_mult__left__less__imp__less,axiom,
% 5.25/5.46 ! [C: rat,A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_left_less_imp_less
% 5.25/5.46 thf(fact_1986_mult__left__less__imp__less,axiom,
% 5.25/5.46 ! [C: nat,A: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.46 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_left_less_imp_less
% 5.25/5.46 thf(fact_1987_mult__left__less__imp__less,axiom,
% 5.25/5.46 ! [C: int,A: int,B: int] :
% 5.25/5.46 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.46 => ( ord_less_int @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_left_less_imp_less
% 5.25/5.46 thf(fact_1988_mult__le__cancel__right,axiom,
% 5.25/5.46 ! [A: real,C: real,B: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_eq_real @ A @ B ) )
% 5.25/5.46 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_right
% 5.25/5.46 thf(fact_1989_mult__le__cancel__right,axiom,
% 5.25/5.46 ! [A: rat,C: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ B ) )
% 5.25/5.46 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_right
% 5.25/5.46 thf(fact_1990_mult__le__cancel__right,axiom,
% 5.25/5.46 ! [A: int,C: int,B: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.46 => ( ord_less_eq_int @ A @ B ) )
% 5.25/5.46 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.46 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_right
% 5.25/5.46 thf(fact_1991_mult__le__cancel__left,axiom,
% 5.25/5.46 ! [C: real,A: real,B: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_eq_real @ A @ B ) )
% 5.25/5.46 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_left
% 5.25/5.46 thf(fact_1992_mult__le__cancel__left,axiom,
% 5.25/5.46 ! [C: rat,A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ B ) )
% 5.25/5.46 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_left
% 5.25/5.46 thf(fact_1993_mult__le__cancel__left,axiom,
% 5.25/5.46 ! [C: int,A: int,B: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.46 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.46 => ( ord_less_eq_int @ A @ B ) )
% 5.25/5.46 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.46 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_left
% 5.25/5.46 thf(fact_1994_add__strict__increasing2,axiom,
% 5.25/5.46 ! [A: real,B: real,C: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.46 => ( ( ord_less_real @ B @ C )
% 5.25/5.46 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_strict_increasing2
% 5.25/5.46 thf(fact_1995_add__strict__increasing2,axiom,
% 5.25/5.46 ! [A: rat,B: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.46 => ( ( ord_less_rat @ B @ C )
% 5.25/5.46 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_strict_increasing2
% 5.25/5.46 thf(fact_1996_add__strict__increasing2,axiom,
% 5.25/5.46 ! [A: nat,B: nat,C: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ B @ C )
% 5.25/5.46 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_strict_increasing2
% 5.25/5.46 thf(fact_1997_add__strict__increasing2,axiom,
% 5.25/5.46 ! [A: int,B: int,C: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.46 => ( ( ord_less_int @ B @ C )
% 5.25/5.46 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_strict_increasing2
% 5.25/5.46 thf(fact_1998_add__strict__increasing,axiom,
% 5.25/5.46 ! [A: real,B: real,C: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.46 => ( ( ord_less_eq_real @ B @ C )
% 5.25/5.46 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_strict_increasing
% 5.25/5.46 thf(fact_1999_add__strict__increasing,axiom,
% 5.25/5.46 ! [A: rat,B: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.46 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.46 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_strict_increasing
% 5.25/5.46 thf(fact_2000_add__strict__increasing,axiom,
% 5.25/5.46 ! [A: nat,B: nat,C: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.46 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.46 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_strict_increasing
% 5.25/5.46 thf(fact_2001_add__strict__increasing,axiom,
% 5.25/5.46 ! [A: int,B: int,C: int] :
% 5.25/5.46 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.46 => ( ( ord_less_eq_int @ B @ C )
% 5.25/5.46 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_strict_increasing
% 5.25/5.46 thf(fact_2002_add__pos__nonneg,axiom,
% 5.25/5.46 ! [A: real,B: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.46 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_pos_nonneg
% 5.25/5.46 thf(fact_2003_add__pos__nonneg,axiom,
% 5.25/5.46 ! [A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.46 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_pos_nonneg
% 5.25/5.46 thf(fact_2004_add__pos__nonneg,axiom,
% 5.25/5.46 ! [A: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.46 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_pos_nonneg
% 5.25/5.46 thf(fact_2005_add__pos__nonneg,axiom,
% 5.25/5.46 ! [A: int,B: int] :
% 5.25/5.46 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.46 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_pos_nonneg
% 5.25/5.46 thf(fact_2006_add__nonpos__neg,axiom,
% 5.25/5.46 ! [A: real,B: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.46 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_nonpos_neg
% 5.25/5.46 thf(fact_2007_add__nonpos__neg,axiom,
% 5.25/5.46 ! [A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.46 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_nonpos_neg
% 5.25/5.46 thf(fact_2008_add__nonpos__neg,axiom,
% 5.25/5.46 ! [A: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.25/5.46 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.25/5.46 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_nonpos_neg
% 5.25/5.46 thf(fact_2009_add__nonpos__neg,axiom,
% 5.25/5.46 ! [A: int,B: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.46 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.46 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_nonpos_neg
% 5.25/5.46 thf(fact_2010_add__nonneg__pos,axiom,
% 5.25/5.46 ! [A: real,B: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.46 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.46 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_nonneg_pos
% 5.25/5.46 thf(fact_2011_add__nonneg__pos,axiom,
% 5.25/5.46 ! [A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.46 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.25/5.46 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_nonneg_pos
% 5.25/5.46 thf(fact_2012_add__nonneg__pos,axiom,
% 5.25/5.46 ! [A: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.46 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_nonneg_pos
% 5.25/5.46 thf(fact_2013_add__nonneg__pos,axiom,
% 5.25/5.46 ! [A: int,B: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.46 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.46 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_nonneg_pos
% 5.25/5.46 thf(fact_2014_add__neg__nonpos,axiom,
% 5.25/5.46 ! [A: real,B: real] :
% 5.25/5.46 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.46 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_neg_nonpos
% 5.25/5.46 thf(fact_2015_add__neg__nonpos,axiom,
% 5.25/5.46 ! [A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.46 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_neg_nonpos
% 5.25/5.46 thf(fact_2016_add__neg__nonpos,axiom,
% 5.25/5.46 ! [A: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.25/5.46 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.25/5.46 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_neg_nonpos
% 5.25/5.46 thf(fact_2017_add__neg__nonpos,axiom,
% 5.25/5.46 ! [A: int,B: int] :
% 5.25/5.46 ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.46 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.25/5.46 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_neg_nonpos
% 5.25/5.46 thf(fact_2018_field__le__epsilon,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ! [E2: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.25/5.46 => ( ord_less_eq_real @ X3 @ ( plus_plus_real @ Y @ E2 ) ) )
% 5.25/5.46 => ( ord_less_eq_real @ X3 @ Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % field_le_epsilon
% 5.25/5.46 thf(fact_2019_field__le__epsilon,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ! [E2: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.25/5.46 => ( ord_less_eq_rat @ X3 @ ( plus_plus_rat @ Y @ E2 ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % field_le_epsilon
% 5.25/5.46 thf(fact_2020_mult__left__le,axiom,
% 5.25/5.46 ! [C: real,A: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.46 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_left_le
% 5.25/5.46 thf(fact_2021_mult__left__le,axiom,
% 5.25/5.46 ! [C: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.46 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_left_le
% 5.25/5.46 thf(fact_2022_mult__left__le,axiom,
% 5.25/5.46 ! [C: nat,A: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.46 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_left_le
% 5.25/5.46 thf(fact_2023_mult__left__le,axiom,
% 5.25/5.46 ! [C: int,A: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.46 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_left_le
% 5.25/5.46 thf(fact_2024_mult__le__one,axiom,
% 5.25/5.46 ! [A: real,B: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.46 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.25/5.46 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_one
% 5.25/5.46 thf(fact_2025_mult__le__one,axiom,
% 5.25/5.46 ! [A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.46 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_one
% 5.25/5.46 thf(fact_2026_mult__le__one,axiom,
% 5.25/5.46 ! [A: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.46 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.25/5.46 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_one
% 5.25/5.46 thf(fact_2027_mult__le__one,axiom,
% 5.25/5.46 ! [A: int,B: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.46 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.25/5.46 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_one
% 5.25/5.46 thf(fact_2028_mult__right__le__one__le,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.46 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.46 => ( ord_less_eq_real @ ( times_times_real @ X3 @ Y ) @ X3 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_right_le_one_le
% 5.25/5.46 thf(fact_2029_mult__right__le__one__le,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.46 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ ( times_times_rat @ X3 @ Y ) @ X3 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_right_le_one_le
% 5.25/5.46 thf(fact_2030_mult__right__le__one__le,axiom,
% 5.25/5.46 ! [X3: int,Y: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.46 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.25/5.46 => ( ord_less_eq_int @ ( times_times_int @ X3 @ Y ) @ X3 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_right_le_one_le
% 5.25/5.46 thf(fact_2031_mult__left__le__one__le,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.46 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.46 => ( ord_less_eq_real @ ( times_times_real @ Y @ X3 ) @ X3 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_left_le_one_le
% 5.25/5.46 thf(fact_2032_mult__left__le__one__le,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.46 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X3 ) @ X3 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_left_le_one_le
% 5.25/5.46 thf(fact_2033_mult__left__le__one__le,axiom,
% 5.25/5.46 ! [X3: int,Y: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.46 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.25/5.46 => ( ord_less_eq_int @ ( times_times_int @ Y @ X3 ) @ X3 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_left_le_one_le
% 5.25/5.46 thf(fact_2034_sum__squares__ge__zero,axiom,
% 5.25/5.46 ! [X3: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_squares_ge_zero
% 5.25/5.46 thf(fact_2035_sum__squares__ge__zero,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_squares_ge_zero
% 5.25/5.46 thf(fact_2036_sum__squares__ge__zero,axiom,
% 5.25/5.46 ! [X3: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_squares_ge_zero
% 5.25/5.46 thf(fact_2037_sum__squares__le__zero__iff,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 5.25/5.46 = ( ( X3 = zero_zero_real )
% 5.25/5.46 & ( Y = zero_zero_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_squares_le_zero_iff
% 5.25/5.46 thf(fact_2038_sum__squares__le__zero__iff,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 5.25/5.46 = ( ( X3 = zero_zero_rat )
% 5.25/5.46 & ( Y = zero_zero_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_squares_le_zero_iff
% 5.25/5.46 thf(fact_2039_sum__squares__le__zero__iff,axiom,
% 5.25/5.46 ! [X3: int,Y: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 5.25/5.46 = ( ( X3 = zero_zero_int )
% 5.25/5.46 & ( Y = zero_zero_int ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_squares_le_zero_iff
% 5.25/5.46 thf(fact_2040_divide__nonpos__pos,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.46 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.46 => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonpos_pos
% 5.25/5.46 thf(fact_2041_divide__nonpos__pos,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 5.25/5.46 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.46 => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonpos_pos
% 5.25/5.46 thf(fact_2042_divide__nonpos__neg,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.46 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonpos_neg
% 5.25/5.46 thf(fact_2043_divide__nonpos__neg,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 5.25/5.46 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonpos_neg
% 5.25/5.46 thf(fact_2044_divide__nonneg__pos,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.46 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.46 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonneg_pos
% 5.25/5.46 thf(fact_2045_divide__nonneg__pos,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.25/5.46 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonneg_pos
% 5.25/5.46 thf(fact_2046_divide__nonneg__neg,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.46 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ zero_zero_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonneg_neg
% 5.25/5.46 thf(fact_2047_divide__nonneg__neg,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.25/5.46 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonneg_neg
% 5.25/5.46 thf(fact_2048_divide__le__cancel,axiom,
% 5.25/5.46 ! [A: real,C: real,B: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_eq_real @ A @ B ) )
% 5.25/5.46 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_le_cancel
% 5.25/5.46 thf(fact_2049_divide__le__cancel,axiom,
% 5.25/5.46 ! [A: rat,C: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ B ) )
% 5.25/5.46 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_le_cancel
% 5.25/5.46 thf(fact_2050_frac__less2,axiom,
% 5.25/5.46 ! [X3: real,Y: real,W: real,Z: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.46 => ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.46 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.25/5.46 => ( ( ord_less_real @ W @ Z )
% 5.25/5.46 => ( ord_less_real @ ( divide_divide_real @ X3 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % frac_less2
% 5.25/5.46 thf(fact_2051_frac__less2,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat,W: rat,Z: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 5.25/5.46 => ( ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.46 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.25/5.46 => ( ( ord_less_rat @ W @ Z )
% 5.25/5.46 => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % frac_less2
% 5.25/5.46 thf(fact_2052_frac__less,axiom,
% 5.25/5.46 ! [X3: real,Y: real,W: real,Z: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.46 => ( ( ord_less_real @ X3 @ Y )
% 5.25/5.46 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.25/5.46 => ( ( ord_less_eq_real @ W @ Z )
% 5.25/5.46 => ( ord_less_real @ ( divide_divide_real @ X3 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % frac_less
% 5.25/5.46 thf(fact_2053_frac__less,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat,W: rat,Z: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.25/5.46 => ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.46 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.25/5.46 => ( ( ord_less_eq_rat @ W @ Z )
% 5.25/5.46 => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % frac_less
% 5.25/5.46 thf(fact_2054_frac__le,axiom,
% 5.25/5.46 ! [Y: real,X3: real,W: real,Z: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.46 => ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.46 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.25/5.46 => ( ( ord_less_eq_real @ W @ Z )
% 5.25/5.46 => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % frac_le
% 5.25/5.46 thf(fact_2055_frac__le,axiom,
% 5.25/5.46 ! [Y: rat,X3: rat,W: rat,Z: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.46 => ( ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.46 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.25/5.46 => ( ( ord_less_eq_rat @ W @ Z )
% 5.25/5.46 => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % frac_le
% 5.25/5.46 thf(fact_2056_div__positive,axiom,
% 5.25/5.46 ! [B: nat,A: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.46 => ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.46 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_positive
% 5.25/5.46 thf(fact_2057_div__positive,axiom,
% 5.25/5.46 ! [B: int,A: int] :
% 5.25/5.46 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.46 => ( ( ord_less_eq_int @ B @ A )
% 5.25/5.46 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_positive
% 5.25/5.46 thf(fact_2058_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.25/5.46 ! [A: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ A @ B )
% 5.25/5.46 => ( ( divide_divide_nat @ A @ B )
% 5.25/5.46 = zero_zero_nat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % unique_euclidean_semiring_numeral_class.div_less
% 5.25/5.46 thf(fact_2059_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.25/5.46 ! [A: int,B: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.46 => ( ( ord_less_int @ A @ B )
% 5.25/5.46 => ( ( divide_divide_int @ A @ B )
% 5.25/5.46 = zero_zero_int ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % unique_euclidean_semiring_numeral_class.div_less
% 5.25/5.46 thf(fact_2060_not__sum__squares__lt__zero,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 5.25/5.46
% 5.25/5.46 % not_sum_squares_lt_zero
% 5.25/5.46 thf(fact_2061_not__sum__squares__lt__zero,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 5.25/5.46
% 5.25/5.46 % not_sum_squares_lt_zero
% 5.25/5.46 thf(fact_2062_not__sum__squares__lt__zero,axiom,
% 5.25/5.46 ! [X3: int,Y: int] :
% 5.25/5.46 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 5.25/5.46
% 5.25/5.46 % not_sum_squares_lt_zero
% 5.25/5.46 thf(fact_2063_sum__squares__gt__zero__iff,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) ) )
% 5.25/5.46 = ( ( X3 != zero_zero_real )
% 5.25/5.46 | ( Y != zero_zero_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_squares_gt_zero_iff
% 5.25/5.46 thf(fact_2064_sum__squares__gt__zero__iff,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) ) )
% 5.25/5.46 = ( ( X3 != zero_zero_rat )
% 5.25/5.46 | ( Y != zero_zero_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_squares_gt_zero_iff
% 5.25/5.46 thf(fact_2065_sum__squares__gt__zero__iff,axiom,
% 5.25/5.46 ! [X3: int,Y: int] :
% 5.25/5.46 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) ) )
% 5.25/5.46 = ( ( X3 != zero_zero_int )
% 5.25/5.46 | ( Y != zero_zero_int ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_squares_gt_zero_iff
% 5.25/5.46 thf(fact_2066_power__less__imp__less__base,axiom,
% 5.25/5.46 ! [A: real,N: nat,B: real] :
% 5.25/5.46 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.46 => ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_less_imp_less_base
% 5.25/5.46 thf(fact_2067_power__less__imp__less__base,axiom,
% 5.25/5.46 ! [A: rat,N: nat,B: rat] :
% 5.25/5.46 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.46 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_less_imp_less_base
% 5.25/5.46 thf(fact_2068_power__less__imp__less__base,axiom,
% 5.25/5.46 ! [A: nat,N: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.46 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_less_imp_less_base
% 5.25/5.46 thf(fact_2069_power__less__imp__less__base,axiom,
% 5.25/5.46 ! [A: int,N: nat,B: int] :
% 5.25/5.46 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.46 => ( ord_less_int @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_less_imp_less_base
% 5.25/5.46 thf(fact_2070_zero__less__two,axiom,
% 5.25/5.46 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.25/5.46
% 5.25/5.46 % zero_less_two
% 5.25/5.46 thf(fact_2071_zero__less__two,axiom,
% 5.25/5.46 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.25/5.46
% 5.25/5.46 % zero_less_two
% 5.25/5.46 thf(fact_2072_zero__less__two,axiom,
% 5.25/5.46 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.25/5.46
% 5.25/5.46 % zero_less_two
% 5.25/5.46 thf(fact_2073_zero__less__two,axiom,
% 5.25/5.46 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.25/5.46
% 5.25/5.46 % zero_less_two
% 5.25/5.46 thf(fact_2074_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.25/5.46 ! [C: nat,A: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.46 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.25/5.46 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.25/5.46 thf(fact_2075_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.25/5.46 ! [C: int,A: int,B: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.46 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.25/5.46 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.25/5.46 thf(fact_2076_divide__less__eq,axiom,
% 5.25/5.46 ! [B: real,C: real,A: real] :
% 5.25/5.46 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_less_eq
% 5.25/5.46 thf(fact_2077_divide__less__eq,axiom,
% 5.25/5.46 ! [B: rat,C: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_less_eq
% 5.25/5.46 thf(fact_2078_less__divide__eq,axiom,
% 5.25/5.46 ! [A: real,B: real,C: real] :
% 5.25/5.46 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_divide_eq
% 5.25/5.46 thf(fact_2079_less__divide__eq,axiom,
% 5.25/5.46 ! [A: rat,B: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_divide_eq
% 5.25/5.46 thf(fact_2080_neg__divide__less__eq,axiom,
% 5.25/5.46 ! [C: real,B: real,A: real] :
% 5.25/5.46 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.25/5.46 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % neg_divide_less_eq
% 5.25/5.46 thf(fact_2081_neg__divide__less__eq,axiom,
% 5.25/5.46 ! [C: rat,B: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.25/5.46 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % neg_divide_less_eq
% 5.25/5.46 thf(fact_2082_neg__less__divide__eq,axiom,
% 5.25/5.46 ! [C: real,A: real,B: real] :
% 5.25/5.46 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.46 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % neg_less_divide_eq
% 5.25/5.46 thf(fact_2083_neg__less__divide__eq,axiom,
% 5.25/5.46 ! [C: rat,A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.46 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % neg_less_divide_eq
% 5.25/5.46 thf(fact_2084_pos__divide__less__eq,axiom,
% 5.25/5.46 ! [C: real,B: real,A: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.25/5.46 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % pos_divide_less_eq
% 5.25/5.46 thf(fact_2085_pos__divide__less__eq,axiom,
% 5.25/5.46 ! [C: rat,B: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.25/5.46 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % pos_divide_less_eq
% 5.25/5.46 thf(fact_2086_pos__less__divide__eq,axiom,
% 5.25/5.46 ! [C: real,A: real,B: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.46 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % pos_less_divide_eq
% 5.25/5.46 thf(fact_2087_pos__less__divide__eq,axiom,
% 5.25/5.46 ! [C: rat,A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.46 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % pos_less_divide_eq
% 5.25/5.46 thf(fact_2088_mult__imp__div__pos__less,axiom,
% 5.25/5.46 ! [Y: real,X3: real,Z: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.46 => ( ( ord_less_real @ X3 @ ( times_times_real @ Z @ Y ) )
% 5.25/5.46 => ( ord_less_real @ ( divide_divide_real @ X3 @ Y ) @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_imp_div_pos_less
% 5.25/5.46 thf(fact_2089_mult__imp__div__pos__less,axiom,
% 5.25/5.46 ! [Y: rat,X3: rat,Z: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.46 => ( ( ord_less_rat @ X3 @ ( times_times_rat @ Z @ Y ) )
% 5.25/5.46 => ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y ) @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_imp_div_pos_less
% 5.25/5.46 thf(fact_2090_mult__imp__less__div__pos,axiom,
% 5.25/5.46 ! [Y: real,Z: real,X3: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.46 => ( ( ord_less_real @ ( times_times_real @ Z @ Y ) @ X3 )
% 5.25/5.46 => ( ord_less_real @ Z @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_imp_less_div_pos
% 5.25/5.46 thf(fact_2091_mult__imp__less__div__pos,axiom,
% 5.25/5.46 ! [Y: rat,Z: rat,X3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.46 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X3 )
% 5.25/5.46 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_imp_less_div_pos
% 5.25/5.46 thf(fact_2092_divide__strict__left__mono,axiom,
% 5.25/5.46 ! [B: real,A: real,C: real] :
% 5.25/5.46 ( ( ord_less_real @ B @ A )
% 5.25/5.46 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.25/5.46 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_strict_left_mono
% 5.25/5.46 thf(fact_2093_divide__strict__left__mono,axiom,
% 5.25/5.46 ! [B: rat,A: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_rat @ B @ A )
% 5.25/5.46 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.46 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_strict_left_mono
% 5.25/5.46 thf(fact_2094_divide__strict__left__mono__neg,axiom,
% 5.25/5.46 ! [A: real,B: real,C: real] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.25/5.46 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_strict_left_mono_neg
% 5.25/5.46 thf(fact_2095_divide__strict__left__mono__neg,axiom,
% 5.25/5.46 ! [A: rat,B: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.46 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_strict_left_mono_neg
% 5.25/5.46 thf(fact_2096_divide__less__eq__1,axiom,
% 5.25/5.46 ! [B: real,A: real] :
% 5.25/5.46 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.46 & ( ord_less_real @ B @ A ) )
% 5.25/5.46 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.46 & ( ord_less_real @ A @ B ) )
% 5.25/5.46 | ( A = zero_zero_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_less_eq_1
% 5.25/5.46 thf(fact_2097_divide__less__eq__1,axiom,
% 5.25/5.46 ! [B: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.46 & ( ord_less_rat @ B @ A ) )
% 5.25/5.46 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.46 & ( ord_less_rat @ A @ B ) )
% 5.25/5.46 | ( A = zero_zero_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_less_eq_1
% 5.25/5.46 thf(fact_2098_less__divide__eq__1,axiom,
% 5.25/5.46 ! [B: real,A: real] :
% 5.25/5.46 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.46 & ( ord_less_real @ A @ B ) )
% 5.25/5.46 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.46 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_divide_eq_1
% 5.25/5.46 thf(fact_2099_less__divide__eq__1,axiom,
% 5.25/5.46 ! [B: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.46 & ( ord_less_rat @ A @ B ) )
% 5.25/5.46 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.46 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_divide_eq_1
% 5.25/5.46 thf(fact_2100_power__le__one,axiom,
% 5.25/5.46 ! [A: real,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.46 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.25/5.46 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_le_one
% 5.25/5.46 thf(fact_2101_power__le__one,axiom,
% 5.25/5.46 ! [A: rat,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.46 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_le_one
% 5.25/5.46 thf(fact_2102_power__le__one,axiom,
% 5.25/5.46 ! [A: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.46 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.25/5.46 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_le_one
% 5.25/5.46 thf(fact_2103_power__le__one,axiom,
% 5.25/5.46 ! [A: int,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.46 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.25/5.46 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_le_one
% 5.25/5.46 thf(fact_2104_divide__eq__eq__numeral_I1_J,axiom,
% 5.25/5.46 ! [B: complex,C: complex,W: num] :
% 5.25/5.46 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.25/5.46 = ( numera6690914467698888265omplex @ W ) )
% 5.25/5.46 = ( ( ( C != zero_zero_complex )
% 5.25/5.46 => ( B
% 5.25/5.46 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 5.25/5.46 & ( ( C = zero_zero_complex )
% 5.25/5.46 => ( ( numera6690914467698888265omplex @ W )
% 5.25/5.46 = zero_zero_complex ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_eq_eq_numeral(1)
% 5.25/5.46 thf(fact_2105_divide__eq__eq__numeral_I1_J,axiom,
% 5.25/5.46 ! [B: real,C: real,W: num] :
% 5.25/5.46 ( ( ( divide_divide_real @ B @ C )
% 5.25/5.46 = ( numeral_numeral_real @ W ) )
% 5.25/5.46 = ( ( ( C != zero_zero_real )
% 5.25/5.46 => ( B
% 5.25/5.46 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.25/5.46 & ( ( C = zero_zero_real )
% 5.25/5.46 => ( ( numeral_numeral_real @ W )
% 5.25/5.46 = zero_zero_real ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_eq_eq_numeral(1)
% 5.25/5.46 thf(fact_2106_divide__eq__eq__numeral_I1_J,axiom,
% 5.25/5.46 ! [B: rat,C: rat,W: num] :
% 5.25/5.46 ( ( ( divide_divide_rat @ B @ C )
% 5.25/5.46 = ( numeral_numeral_rat @ W ) )
% 5.25/5.46 = ( ( ( C != zero_zero_rat )
% 5.25/5.46 => ( B
% 5.25/5.46 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.25/5.46 & ( ( C = zero_zero_rat )
% 5.25/5.46 => ( ( numeral_numeral_rat @ W )
% 5.25/5.46 = zero_zero_rat ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_eq_eq_numeral(1)
% 5.25/5.46 thf(fact_2107_eq__divide__eq__numeral_I1_J,axiom,
% 5.25/5.46 ! [W: num,B: complex,C: complex] :
% 5.25/5.46 ( ( ( numera6690914467698888265omplex @ W )
% 5.25/5.46 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.46 = ( ( ( C != zero_zero_complex )
% 5.25/5.46 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 5.25/5.46 = B ) )
% 5.25/5.46 & ( ( C = zero_zero_complex )
% 5.25/5.46 => ( ( numera6690914467698888265omplex @ W )
% 5.25/5.46 = zero_zero_complex ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % eq_divide_eq_numeral(1)
% 5.25/5.46 thf(fact_2108_eq__divide__eq__numeral_I1_J,axiom,
% 5.25/5.46 ! [W: num,B: real,C: real] :
% 5.25/5.46 ( ( ( numeral_numeral_real @ W )
% 5.25/5.46 = ( divide_divide_real @ B @ C ) )
% 5.25/5.46 = ( ( ( C != zero_zero_real )
% 5.25/5.46 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 5.25/5.46 = B ) )
% 5.25/5.46 & ( ( C = zero_zero_real )
% 5.25/5.46 => ( ( numeral_numeral_real @ W )
% 5.25/5.46 = zero_zero_real ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % eq_divide_eq_numeral(1)
% 5.25/5.46 thf(fact_2109_eq__divide__eq__numeral_I1_J,axiom,
% 5.25/5.46 ! [W: num,B: rat,C: rat] :
% 5.25/5.46 ( ( ( numeral_numeral_rat @ W )
% 5.25/5.46 = ( divide_divide_rat @ B @ C ) )
% 5.25/5.46 = ( ( ( C != zero_zero_rat )
% 5.25/5.46 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 5.25/5.46 = B ) )
% 5.25/5.46 & ( ( C = zero_zero_rat )
% 5.25/5.46 => ( ( numeral_numeral_rat @ W )
% 5.25/5.46 = zero_zero_rat ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % eq_divide_eq_numeral(1)
% 5.25/5.46 thf(fact_2110_divide__add__eq__iff,axiom,
% 5.25/5.46 ! [Z: complex,X3: complex,Y: complex] :
% 5.25/5.46 ( ( Z != zero_zero_complex )
% 5.25/5.46 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Z ) @ Y )
% 5.25/5.46 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_add_eq_iff
% 5.25/5.46 thf(fact_2111_divide__add__eq__iff,axiom,
% 5.25/5.46 ! [Z: real,X3: real,Y: real] :
% 5.25/5.46 ( ( Z != zero_zero_real )
% 5.25/5.46 => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Z ) @ Y )
% 5.25/5.46 = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_add_eq_iff
% 5.25/5.46 thf(fact_2112_divide__add__eq__iff,axiom,
% 5.25/5.46 ! [Z: rat,X3: rat,Y: rat] :
% 5.25/5.46 ( ( Z != zero_zero_rat )
% 5.25/5.46 => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Z ) @ Y )
% 5.25/5.46 = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_add_eq_iff
% 5.25/5.46 thf(fact_2113_add__divide__eq__iff,axiom,
% 5.25/5.46 ! [Z: complex,X3: complex,Y: complex] :
% 5.25/5.46 ( ( Z != zero_zero_complex )
% 5.25/5.46 => ( ( plus_plus_complex @ X3 @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.25/5.46 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X3 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_divide_eq_iff
% 5.25/5.46 thf(fact_2114_add__divide__eq__iff,axiom,
% 5.25/5.46 ! [Z: real,X3: real,Y: real] :
% 5.25/5.46 ( ( Z != zero_zero_real )
% 5.25/5.46 => ( ( plus_plus_real @ X3 @ ( divide_divide_real @ Y @ Z ) )
% 5.25/5.46 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X3 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_divide_eq_iff
% 5.25/5.46 thf(fact_2115_add__divide__eq__iff,axiom,
% 5.25/5.46 ! [Z: rat,X3: rat,Y: rat] :
% 5.25/5.46 ( ( Z != zero_zero_rat )
% 5.25/5.46 => ( ( plus_plus_rat @ X3 @ ( divide_divide_rat @ Y @ Z ) )
% 5.25/5.46 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_divide_eq_iff
% 5.25/5.46 thf(fact_2116_add__num__frac,axiom,
% 5.25/5.46 ! [Y: complex,Z: complex,X3: complex] :
% 5.25/5.46 ( ( Y != zero_zero_complex )
% 5.25/5.46 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X3 @ Y ) )
% 5.25/5.46 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_num_frac
% 5.25/5.46 thf(fact_2117_add__num__frac,axiom,
% 5.25/5.46 ! [Y: real,Z: real,X3: real] :
% 5.25/5.46 ( ( Y != zero_zero_real )
% 5.25/5.46 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X3 @ Y ) )
% 5.25/5.46 = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_num_frac
% 5.25/5.46 thf(fact_2118_add__num__frac,axiom,
% 5.25/5.46 ! [Y: rat,Z: rat,X3: rat] :
% 5.25/5.46 ( ( Y != zero_zero_rat )
% 5.25/5.46 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X3 @ Y ) )
% 5.25/5.46 = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_num_frac
% 5.25/5.46 thf(fact_2119_add__frac__num,axiom,
% 5.25/5.46 ! [Y: complex,X3: complex,Z: complex] :
% 5.25/5.46 ( ( Y != zero_zero_complex )
% 5.25/5.46 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Y ) @ Z )
% 5.25/5.46 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X3 @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_frac_num
% 5.25/5.46 thf(fact_2120_add__frac__num,axiom,
% 5.25/5.46 ! [Y: real,X3: real,Z: real] :
% 5.25/5.46 ( ( Y != zero_zero_real )
% 5.25/5.46 => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Y ) @ Z )
% 5.25/5.46 = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_frac_num
% 5.25/5.46 thf(fact_2121_add__frac__num,axiom,
% 5.25/5.46 ! [Y: rat,X3: rat,Z: rat] :
% 5.25/5.46 ( ( Y != zero_zero_rat )
% 5.25/5.46 => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Y ) @ Z )
% 5.25/5.46 = ( divide_divide_rat @ ( plus_plus_rat @ X3 @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_frac_num
% 5.25/5.46 thf(fact_2122_add__frac__eq,axiom,
% 5.25/5.46 ! [Y: complex,Z: complex,X3: complex,W: complex] :
% 5.25/5.46 ( ( Y != zero_zero_complex )
% 5.25/5.46 => ( ( Z != zero_zero_complex )
% 5.25/5.46 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X3 @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.25/5.46 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X3 @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_frac_eq
% 5.25/5.46 thf(fact_2123_add__frac__eq,axiom,
% 5.25/5.46 ! [Y: real,Z: real,X3: real,W: real] :
% 5.25/5.46 ( ( Y != zero_zero_real )
% 5.25/5.46 => ( ( Z != zero_zero_real )
% 5.25/5.46 => ( ( plus_plus_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.25/5.46 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_frac_eq
% 5.25/5.46 thf(fact_2124_add__frac__eq,axiom,
% 5.25/5.46 ! [Y: rat,Z: rat,X3: rat,W: rat] :
% 5.25/5.46 ( ( Y != zero_zero_rat )
% 5.25/5.46 => ( ( Z != zero_zero_rat )
% 5.25/5.46 => ( ( plus_plus_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.25/5.46 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_frac_eq
% 5.25/5.46 thf(fact_2125_add__divide__eq__if__simps_I1_J,axiom,
% 5.25/5.46 ! [Z: complex,A: complex,B: complex] :
% 5.25/5.46 ( ( ( Z = zero_zero_complex )
% 5.25/5.46 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.25/5.46 = A ) )
% 5.25/5.46 & ( ( Z != zero_zero_complex )
% 5.25/5.46 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.25/5.46 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_divide_eq_if_simps(1)
% 5.25/5.46 thf(fact_2126_add__divide__eq__if__simps_I1_J,axiom,
% 5.25/5.46 ! [Z: real,A: real,B: real] :
% 5.25/5.46 ( ( ( Z = zero_zero_real )
% 5.25/5.46 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.25/5.46 = A ) )
% 5.25/5.46 & ( ( Z != zero_zero_real )
% 5.25/5.46 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.25/5.46 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_divide_eq_if_simps(1)
% 5.25/5.46 thf(fact_2127_add__divide__eq__if__simps_I1_J,axiom,
% 5.25/5.46 ! [Z: rat,A: rat,B: rat] :
% 5.25/5.46 ( ( ( Z = zero_zero_rat )
% 5.25/5.46 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.25/5.46 = A ) )
% 5.25/5.46 & ( ( Z != zero_zero_rat )
% 5.25/5.46 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.25/5.46 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_divide_eq_if_simps(1)
% 5.25/5.46 thf(fact_2128_add__divide__eq__if__simps_I2_J,axiom,
% 5.25/5.46 ! [Z: complex,A: complex,B: complex] :
% 5.25/5.46 ( ( ( Z = zero_zero_complex )
% 5.25/5.46 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.25/5.46 = B ) )
% 5.25/5.46 & ( ( Z != zero_zero_complex )
% 5.25/5.46 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.25/5.46 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_divide_eq_if_simps(2)
% 5.25/5.46 thf(fact_2129_add__divide__eq__if__simps_I2_J,axiom,
% 5.25/5.46 ! [Z: real,A: real,B: real] :
% 5.25/5.46 ( ( ( Z = zero_zero_real )
% 5.25/5.46 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.25/5.46 = B ) )
% 5.25/5.46 & ( ( Z != zero_zero_real )
% 5.25/5.46 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.25/5.46 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_divide_eq_if_simps(2)
% 5.25/5.46 thf(fact_2130_add__divide__eq__if__simps_I2_J,axiom,
% 5.25/5.46 ! [Z: rat,A: rat,B: rat] :
% 5.25/5.46 ( ( ( Z = zero_zero_rat )
% 5.25/5.46 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.25/5.46 = B ) )
% 5.25/5.46 & ( ( Z != zero_zero_rat )
% 5.25/5.46 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.25/5.46 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % add_divide_eq_if_simps(2)
% 5.25/5.46 thf(fact_2131_power__le__imp__le__base,axiom,
% 5.25/5.46 ! [A: real,N: nat,B: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.46 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_le_imp_le_base
% 5.25/5.46 thf(fact_2132_power__le__imp__le__base,axiom,
% 5.25/5.46 ! [A: rat,N: nat,B: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_le_imp_le_base
% 5.25/5.46 thf(fact_2133_power__le__imp__le__base,axiom,
% 5.25/5.46 ! [A: nat,N: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.46 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_le_imp_le_base
% 5.25/5.46 thf(fact_2134_power__le__imp__le__base,axiom,
% 5.25/5.46 ! [A: int,N: nat,B: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.46 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_le_imp_le_base
% 5.25/5.46 thf(fact_2135_power__inject__base,axiom,
% 5.25/5.46 ! [A: real,N: nat,B: real] :
% 5.25/5.46 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 5.25/5.46 = ( power_power_real @ B @ ( suc @ N ) ) )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.46 => ( A = B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_inject_base
% 5.25/5.46 thf(fact_2136_power__inject__base,axiom,
% 5.25/5.46 ! [A: rat,N: nat,B: rat] :
% 5.25/5.46 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.25/5.46 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.46 => ( A = B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_inject_base
% 5.25/5.46 thf(fact_2137_power__inject__base,axiom,
% 5.25/5.46 ! [A: nat,N: nat,B: nat] :
% 5.25/5.46 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.25/5.46 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.46 => ( A = B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_inject_base
% 5.25/5.46 thf(fact_2138_power__inject__base,axiom,
% 5.25/5.46 ! [A: int,N: nat,B: int] :
% 5.25/5.46 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 5.25/5.46 = ( power_power_int @ B @ ( suc @ N ) ) )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.46 => ( A = B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_inject_base
% 5.25/5.46 thf(fact_2139_div__add__self2,axiom,
% 5.25/5.46 ! [B: nat,A: nat] :
% 5.25/5.46 ( ( B != zero_zero_nat )
% 5.25/5.46 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.25/5.46 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_add_self2
% 5.25/5.46 thf(fact_2140_div__add__self2,axiom,
% 5.25/5.46 ! [B: int,A: int] :
% 5.25/5.46 ( ( B != zero_zero_int )
% 5.25/5.46 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.25/5.46 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_add_self2
% 5.25/5.46 thf(fact_2141_div__add__self1,axiom,
% 5.25/5.46 ! [B: nat,A: nat] :
% 5.25/5.46 ( ( B != zero_zero_nat )
% 5.25/5.46 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.25/5.46 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_add_self1
% 5.25/5.46 thf(fact_2142_div__add__self1,axiom,
% 5.25/5.46 ! [B: int,A: int] :
% 5.25/5.46 ( ( B != zero_zero_int )
% 5.25/5.46 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.25/5.46 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_add_self1
% 5.25/5.46 thf(fact_2143_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.25/5.46 ! [B: code_integer,A: code_integer] :
% 5.25/5.46 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.25/5.46 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.25/5.46 thf(fact_2144_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.25/5.46 ! [B: nat,A: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.46 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.25/5.46 thf(fact_2145_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.25/5.46 ! [B: int,A: int] :
% 5.25/5.46 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.46 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.25/5.46 thf(fact_2146_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.25/5.46 ! [A: code_integer,B: code_integer] :
% 5.25/5.46 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.46 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.25/5.46 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.25/5.46 = A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % unique_euclidean_semiring_numeral_class.mod_less
% 5.25/5.46 thf(fact_2147_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.25/5.46 ! [A: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ A @ B )
% 5.25/5.46 => ( ( modulo_modulo_nat @ A @ B )
% 5.25/5.46 = A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % unique_euclidean_semiring_numeral_class.mod_less
% 5.25/5.46 thf(fact_2148_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.25/5.46 ! [A: int,B: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.46 => ( ( ord_less_int @ A @ B )
% 5.25/5.46 => ( ( modulo_modulo_int @ A @ B )
% 5.25/5.46 = A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % unique_euclidean_semiring_numeral_class.mod_less
% 5.25/5.46 thf(fact_2149_cong__exp__iff__simps_I2_J,axiom,
% 5.25/5.46 ! [N: num,Q2: num] :
% 5.25/5.46 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.25/5.46 = zero_zero_nat )
% 5.25/5.46 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.25/5.46 = zero_zero_nat ) ) ).
% 5.25/5.46
% 5.25/5.46 % cong_exp_iff_simps(2)
% 5.25/5.46 thf(fact_2150_cong__exp__iff__simps_I2_J,axiom,
% 5.25/5.46 ! [N: num,Q2: num] :
% 5.25/5.46 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.25/5.46 = zero_zero_int )
% 5.25/5.46 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.25/5.46 = zero_zero_int ) ) ).
% 5.25/5.46
% 5.25/5.46 % cong_exp_iff_simps(2)
% 5.25/5.46 thf(fact_2151_cong__exp__iff__simps_I2_J,axiom,
% 5.25/5.46 ! [N: num,Q2: num] :
% 5.25/5.46 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.25/5.46 = zero_z3403309356797280102nteger )
% 5.25/5.46 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.25/5.46 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.46
% 5.25/5.46 % cong_exp_iff_simps(2)
% 5.25/5.46 thf(fact_2152_cong__exp__iff__simps_I1_J,axiom,
% 5.25/5.46 ! [N: num] :
% 5.25/5.46 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 5.25/5.46 = zero_zero_nat ) ).
% 5.25/5.46
% 5.25/5.46 % cong_exp_iff_simps(1)
% 5.25/5.46 thf(fact_2153_cong__exp__iff__simps_I1_J,axiom,
% 5.25/5.46 ! [N: num] :
% 5.25/5.46 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 5.25/5.46 = zero_zero_int ) ).
% 5.25/5.46
% 5.25/5.46 % cong_exp_iff_simps(1)
% 5.25/5.46 thf(fact_2154_cong__exp__iff__simps_I1_J,axiom,
% 5.25/5.46 ! [N: num] :
% 5.25/5.46 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 5.25/5.46 = zero_z3403309356797280102nteger ) ).
% 5.25/5.46
% 5.25/5.46 % cong_exp_iff_simps(1)
% 5.25/5.46 thf(fact_2155_numeral__1__eq__Suc__0,axiom,
% 5.25/5.46 ( ( numeral_numeral_nat @ one )
% 5.25/5.46 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.46
% 5.25/5.46 % numeral_1_eq_Suc_0
% 5.25/5.46 thf(fact_2156_num_Osize_I5_J,axiom,
% 5.25/5.46 ! [X22: num] :
% 5.25/5.46 ( ( size_size_num @ ( bit0 @ X22 ) )
% 5.25/5.46 = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % num.size(5)
% 5.25/5.46 thf(fact_2157_ex__least__nat__less,axiom,
% 5.25/5.46 ! [P: nat > $o,N: nat] :
% 5.25/5.46 ( ( P @ N )
% 5.25/5.46 => ( ~ ( P @ zero_zero_nat )
% 5.25/5.46 => ? [K2: nat] :
% 5.25/5.46 ( ( ord_less_nat @ K2 @ N )
% 5.25/5.46 & ! [I: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ I @ K2 )
% 5.25/5.46 => ~ ( P @ I ) )
% 5.25/5.46 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ex_least_nat_less
% 5.25/5.46 thf(fact_2158_n__less__n__mult__m,axiom,
% 5.25/5.46 ! [N: nat,M: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.25/5.46 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % n_less_n_mult_m
% 5.25/5.46 thf(fact_2159_n__less__m__mult__n,axiom,
% 5.25/5.46 ! [N: nat,M: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.25/5.46 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % n_less_m_mult_n
% 5.25/5.46 thf(fact_2160_one__less__mult,axiom,
% 5.25/5.46 ! [N: nat,M: nat] :
% 5.25/5.46 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.25/5.46 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.25/5.46 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % one_less_mult
% 5.25/5.46 thf(fact_2161_length__pos__if__in__set,axiom,
% 5.25/5.46 ! [X3: real,Xs: list_real] :
% 5.25/5.46 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 5.25/5.46 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % length_pos_if_in_set
% 5.25/5.46 thf(fact_2162_length__pos__if__in__set,axiom,
% 5.25/5.46 ! [X3: complex,Xs: list_complex] :
% 5.25/5.46 ( ( member_complex @ X3 @ ( set_complex2 @ Xs ) )
% 5.25/5.46 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % length_pos_if_in_set
% 5.25/5.46 thf(fact_2163_length__pos__if__in__set,axiom,
% 5.25/5.46 ! [X3: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 5.25/5.46 ( ( member8440522571783428010at_nat @ X3 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 5.25/5.46 => ( ord_less_nat @ zero_zero_nat @ ( size_s5460976970255530739at_nat @ Xs ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % length_pos_if_in_set
% 5.25/5.46 thf(fact_2164_length__pos__if__in__set,axiom,
% 5.25/5.46 ! [X3: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.25/5.46 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.25/5.46 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % length_pos_if_in_set
% 5.25/5.46 thf(fact_2165_length__pos__if__in__set,axiom,
% 5.25/5.46 ! [X3: $o,Xs: list_o] :
% 5.25/5.46 ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 5.25/5.46 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % length_pos_if_in_set
% 5.25/5.46 thf(fact_2166_length__pos__if__in__set,axiom,
% 5.25/5.46 ! [X3: nat,Xs: list_nat] :
% 5.25/5.46 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 5.25/5.46 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % length_pos_if_in_set
% 5.25/5.46 thf(fact_2167_length__pos__if__in__set,axiom,
% 5.25/5.46 ! [X3: int,Xs: list_int] :
% 5.25/5.46 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 5.25/5.46 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % length_pos_if_in_set
% 5.25/5.46 thf(fact_2168_nat__induct__non__zero,axiom,
% 5.25/5.46 ! [N: nat,P: nat > $o] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ( P @ one_one_nat )
% 5.25/5.46 => ( ! [N3: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.25/5.46 => ( ( P @ N3 )
% 5.25/5.46 => ( P @ ( suc @ N3 ) ) ) )
% 5.25/5.46 => ( P @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % nat_induct_non_zero
% 5.25/5.46 thf(fact_2169_nat__mult__le__cancel1,axiom,
% 5.25/5.46 ! [K: nat,M: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.46 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.25/5.46 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % nat_mult_le_cancel1
% 5.25/5.46 thf(fact_2170_power__gt__expt,axiom,
% 5.25/5.46 ! [N: nat,K: nat] :
% 5.25/5.46 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.25/5.46 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_gt_expt
% 5.25/5.46 thf(fact_2171_div__greater__zero__iff,axiom,
% 5.25/5.46 ! [M: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 5.25/5.46 = ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.46 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_greater_zero_iff
% 5.25/5.46 thf(fact_2172_div__le__mono2,axiom,
% 5.25/5.46 ! [M: nat,N: nat,K: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.46 => ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.46 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_le_mono2
% 5.25/5.46 thf(fact_2173_nat__one__le__power,axiom,
% 5.25/5.46 ! [I2: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 5.25/5.46 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % nat_one_le_power
% 5.25/5.46 thf(fact_2174_nat__mult__div__cancel1,axiom,
% 5.25/5.46 ! [K: nat,M: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.46 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.25/5.46 = ( divide_divide_nat @ M @ N ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % nat_mult_div_cancel1
% 5.25/5.46 thf(fact_2175_div__less__iff__less__mult,axiom,
% 5.25/5.46 ! [Q2: nat,M: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.25/5.46 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 5.25/5.46 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_less_iff_less_mult
% 5.25/5.46 thf(fact_2176_div__less__dividend,axiom,
% 5.25/5.46 ! [N: nat,M: nat] :
% 5.25/5.46 ( ( ord_less_nat @ one_one_nat @ N )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.46 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_less_dividend
% 5.25/5.46 thf(fact_2177_div__eq__dividend__iff,axiom,
% 5.25/5.46 ! [M: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.46 => ( ( ( divide_divide_nat @ M @ N )
% 5.25/5.46 = M )
% 5.25/5.46 = ( N = one_one_nat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_eq_dividend_iff
% 5.25/5.46 thf(fact_2178_mod__le__divisor,axiom,
% 5.25/5.46 ! [N: nat,M: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.25/5.46
% 5.25/5.46 % mod_le_divisor
% 5.25/5.46 thf(fact_2179_vebt__insert_Osimps_I3_J,axiom,
% 5.25/5.46 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.25/5.46 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X3 )
% 5.25/5.46 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) ).
% 5.25/5.46
% 5.25/5.46 % vebt_insert.simps(3)
% 5.25/5.46 thf(fact_2180_field__le__mult__one__interval,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ! [Z2: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.25/5.46 => ( ( ord_less_real @ Z2 @ one_one_real )
% 5.25/5.46 => ( ord_less_eq_real @ ( times_times_real @ Z2 @ X3 ) @ Y ) ) )
% 5.25/5.46 => ( ord_less_eq_real @ X3 @ Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % field_le_mult_one_interval
% 5.25/5.46 thf(fact_2181_field__le__mult__one__interval,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ! [Z2: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 5.25/5.46 => ( ( ord_less_rat @ Z2 @ one_one_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X3 ) @ Y ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % field_le_mult_one_interval
% 5.25/5.46 thf(fact_2182_mult__less__cancel__right2,axiom,
% 5.25/5.46 ! [A: real,C: real] :
% 5.25/5.46 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.25/5.46 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_real @ A @ one_one_real ) )
% 5.25/5.46 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_less_cancel_right2
% 5.25/5.46 thf(fact_2183_mult__less__cancel__right2,axiom,
% 5.25/5.46 ! [A: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.25/5.46 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.25/5.46 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_less_cancel_right2
% 5.25/5.46 thf(fact_2184_mult__less__cancel__right2,axiom,
% 5.25/5.46 ! [A: int,C: int] :
% 5.25/5.46 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.25/5.46 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.46 => ( ord_less_int @ A @ one_one_int ) )
% 5.25/5.46 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.46 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_less_cancel_right2
% 5.25/5.46 thf(fact_2185_mult__less__cancel__right1,axiom,
% 5.25/5.46 ! [C: real,B: real] :
% 5.25/5.46 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_real @ one_one_real @ B ) )
% 5.25/5.46 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_less_cancel_right1
% 5.25/5.46 thf(fact_2186_mult__less__cancel__right1,axiom,
% 5.25/5.46 ! [C: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.25/5.46 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_less_cancel_right1
% 5.25/5.46 thf(fact_2187_mult__less__cancel__right1,axiom,
% 5.25/5.46 ! [C: int,B: int] :
% 5.25/5.46 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.46 => ( ord_less_int @ one_one_int @ B ) )
% 5.25/5.46 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.46 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_less_cancel_right1
% 5.25/5.46 thf(fact_2188_mult__less__cancel__left2,axiom,
% 5.25/5.46 ! [C: real,A: real] :
% 5.25/5.46 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.25/5.46 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_real @ A @ one_one_real ) )
% 5.25/5.46 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_less_cancel_left2
% 5.25/5.46 thf(fact_2189_mult__less__cancel__left2,axiom,
% 5.25/5.46 ! [C: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.25/5.46 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.25/5.46 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_less_cancel_left2
% 5.25/5.46 thf(fact_2190_mult__less__cancel__left2,axiom,
% 5.25/5.46 ! [C: int,A: int] :
% 5.25/5.46 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.25/5.46 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.46 => ( ord_less_int @ A @ one_one_int ) )
% 5.25/5.46 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.46 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_less_cancel_left2
% 5.25/5.46 thf(fact_2191_mult__less__cancel__left1,axiom,
% 5.25/5.46 ! [C: real,B: real] :
% 5.25/5.46 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 5.25/5.46 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_real @ one_one_real @ B ) )
% 5.25/5.46 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_less_cancel_left1
% 5.25/5.46 thf(fact_2192_mult__less__cancel__left1,axiom,
% 5.25/5.46 ! [C: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.25/5.46 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.25/5.46 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_less_cancel_left1
% 5.25/5.46 thf(fact_2193_mult__less__cancel__left1,axiom,
% 5.25/5.46 ! [C: int,B: int] :
% 5.25/5.46 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.25/5.46 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.46 => ( ord_less_int @ one_one_int @ B ) )
% 5.25/5.46 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.46 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_less_cancel_left1
% 5.25/5.46 thf(fact_2194_mult__le__cancel__right2,axiom,
% 5.25/5.46 ! [A: real,C: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.25/5.46 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_right2
% 5.25/5.46 thf(fact_2195_mult__le__cancel__right2,axiom,
% 5.25/5.46 ! [A: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.25/5.46 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_right2
% 5.25/5.46 thf(fact_2196_mult__le__cancel__right2,axiom,
% 5.25/5.46 ! [A: int,C: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.25/5.46 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.46 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.25/5.46 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.46 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_right2
% 5.25/5.46 thf(fact_2197_mult__le__cancel__right1,axiom,
% 5.25/5.46 ! [C: real,B: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.25/5.46 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_right1
% 5.25/5.46 thf(fact_2198_mult__le__cancel__right1,axiom,
% 5.25/5.46 ! [C: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.25/5.46 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_right1
% 5.25/5.46 thf(fact_2199_mult__le__cancel__right1,axiom,
% 5.25/5.46 ! [C: int,B: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.46 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.25/5.46 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.46 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_right1
% 5.25/5.46 thf(fact_2200_mult__le__cancel__left2,axiom,
% 5.25/5.46 ! [C: real,A: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.25/5.46 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_left2
% 5.25/5.46 thf(fact_2201_mult__le__cancel__left2,axiom,
% 5.25/5.46 ! [C: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.25/5.46 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_left2
% 5.25/5.46 thf(fact_2202_mult__le__cancel__left2,axiom,
% 5.25/5.46 ! [C: int,A: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.25/5.46 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.46 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.25/5.46 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.46 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_left2
% 5.25/5.46 thf(fact_2203_mult__le__cancel__left1,axiom,
% 5.25/5.46 ! [C: real,B: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.25/5.46 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_left1
% 5.25/5.46 thf(fact_2204_mult__le__cancel__left1,axiom,
% 5.25/5.46 ! [C: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.25/5.46 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_left1
% 5.25/5.46 thf(fact_2205_mult__le__cancel__left1,axiom,
% 5.25/5.46 ! [C: int,B: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.25/5.46 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.46 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.25/5.46 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.46 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_left1
% 5.25/5.46 thf(fact_2206_divide__left__mono__neg,axiom,
% 5.25/5.46 ! [A: real,B: real,C: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.25/5.46 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_left_mono_neg
% 5.25/5.46 thf(fact_2207_divide__left__mono__neg,axiom,
% 5.25/5.46 ! [A: rat,B: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.46 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_left_mono_neg
% 5.25/5.46 thf(fact_2208_mult__imp__le__div__pos,axiom,
% 5.25/5.46 ! [Y: real,Z: real,X3: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.46 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y ) @ X3 )
% 5.25/5.46 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_imp_le_div_pos
% 5.25/5.46 thf(fact_2209_mult__imp__le__div__pos,axiom,
% 5.25/5.46 ! [Y: rat,Z: rat,X3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.46 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X3 )
% 5.25/5.46 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_imp_le_div_pos
% 5.25/5.46 thf(fact_2210_mult__imp__div__pos__le,axiom,
% 5.25/5.46 ! [Y: real,X3: real,Z: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.46 => ( ( ord_less_eq_real @ X3 @ ( times_times_real @ Z @ Y ) )
% 5.25/5.46 => ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_imp_div_pos_le
% 5.25/5.46 thf(fact_2211_mult__imp__div__pos__le,axiom,
% 5.25/5.46 ! [Y: rat,X3: rat,Z: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.46 => ( ( ord_less_eq_rat @ X3 @ ( times_times_rat @ Z @ Y ) )
% 5.25/5.46 => ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_imp_div_pos_le
% 5.25/5.46 thf(fact_2212_pos__le__divide__eq,axiom,
% 5.25/5.46 ! [C: real,A: real,B: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.46 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % pos_le_divide_eq
% 5.25/5.46 thf(fact_2213_pos__le__divide__eq,axiom,
% 5.25/5.46 ! [C: rat,A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.46 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % pos_le_divide_eq
% 5.25/5.46 thf(fact_2214_pos__divide__le__eq,axiom,
% 5.25/5.46 ! [C: real,B: real,A: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.25/5.46 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % pos_divide_le_eq
% 5.25/5.46 thf(fact_2215_pos__divide__le__eq,axiom,
% 5.25/5.46 ! [C: rat,B: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.25/5.46 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % pos_divide_le_eq
% 5.25/5.46 thf(fact_2216_neg__le__divide__eq,axiom,
% 5.25/5.46 ! [C: real,A: real,B: real] :
% 5.25/5.46 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.46 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % neg_le_divide_eq
% 5.25/5.46 thf(fact_2217_neg__le__divide__eq,axiom,
% 5.25/5.46 ! [C: rat,A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.46 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % neg_le_divide_eq
% 5.25/5.46 thf(fact_2218_neg__divide__le__eq,axiom,
% 5.25/5.46 ! [C: real,B: real,A: real] :
% 5.25/5.46 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.25/5.46 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % neg_divide_le_eq
% 5.25/5.46 thf(fact_2219_neg__divide__le__eq,axiom,
% 5.25/5.46 ! [C: rat,B: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.25/5.46 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % neg_divide_le_eq
% 5.25/5.46 thf(fact_2220_divide__left__mono,axiom,
% 5.25/5.46 ! [B: real,A: real,C: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ B @ A )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.25/5.46 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_left_mono
% 5.25/5.46 thf(fact_2221_divide__left__mono,axiom,
% 5.25/5.46 ! [B: rat,A: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.46 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_left_mono
% 5.25/5.46 thf(fact_2222_le__divide__eq,axiom,
% 5.25/5.46 ! [A: real,B: real,C: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % le_divide_eq
% 5.25/5.46 thf(fact_2223_le__divide__eq,axiom,
% 5.25/5.46 ! [A: rat,B: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % le_divide_eq
% 5.25/5.46 thf(fact_2224_divide__le__eq,axiom,
% 5.25/5.46 ! [B: real,C: real,A: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_le_eq
% 5.25/5.46 thf(fact_2225_divide__le__eq,axiom,
% 5.25/5.46 ! [B: rat,C: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_le_eq
% 5.25/5.46 thf(fact_2226_convex__bound__le,axiom,
% 5.25/5.46 ! [X3: real,A: real,Y: real,U: real,V: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ X3 @ A )
% 5.25/5.46 => ( ( ord_less_eq_real @ Y @ A )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.25/5.46 => ( ( ( plus_plus_real @ U @ V )
% 5.25/5.46 = one_one_real )
% 5.25/5.46 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X3 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % convex_bound_le
% 5.25/5.46 thf(fact_2227_convex__bound__le,axiom,
% 5.25/5.46 ! [X3: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X3 @ A )
% 5.25/5.46 => ( ( ord_less_eq_rat @ Y @ A )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.25/5.46 => ( ( ( plus_plus_rat @ U @ V )
% 5.25/5.46 = one_one_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X3 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % convex_bound_le
% 5.25/5.46 thf(fact_2228_convex__bound__le,axiom,
% 5.25/5.46 ! [X3: int,A: int,Y: int,U: int,V: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ X3 @ A )
% 5.25/5.46 => ( ( ord_less_eq_int @ Y @ A )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.25/5.46 => ( ( ( plus_plus_int @ U @ V )
% 5.25/5.46 = one_one_int )
% 5.25/5.46 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X3 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % convex_bound_le
% 5.25/5.46 thf(fact_2229_le__divide__eq__1,axiom,
% 5.25/5.46 ! [B: real,A: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.46 & ( ord_less_eq_real @ A @ B ) )
% 5.25/5.46 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.46 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % le_divide_eq_1
% 5.25/5.46 thf(fact_2230_le__divide__eq__1,axiom,
% 5.25/5.46 ! [B: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.46 & ( ord_less_eq_rat @ A @ B ) )
% 5.25/5.46 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.46 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % le_divide_eq_1
% 5.25/5.46 thf(fact_2231_divide__le__eq__1,axiom,
% 5.25/5.46 ! [B: real,A: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.46 & ( ord_less_eq_real @ B @ A ) )
% 5.25/5.46 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.46 & ( ord_less_eq_real @ A @ B ) )
% 5.25/5.46 | ( A = zero_zero_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_le_eq_1
% 5.25/5.46 thf(fact_2232_divide__le__eq__1,axiom,
% 5.25/5.46 ! [B: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.46 & ( ord_less_eq_rat @ B @ A ) )
% 5.25/5.46 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.46 & ( ord_less_eq_rat @ A @ B ) )
% 5.25/5.46 | ( A = zero_zero_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_le_eq_1
% 5.25/5.46 thf(fact_2233_less__divide__eq__numeral_I1_J,axiom,
% 5.25/5.46 ! [W: num,B: real,C: real] :
% 5.25/5.46 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_divide_eq_numeral(1)
% 5.25/5.46 thf(fact_2234_less__divide__eq__numeral_I1_J,axiom,
% 5.25/5.46 ! [W: num,B: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_divide_eq_numeral(1)
% 5.25/5.46 thf(fact_2235_divide__less__eq__numeral_I1_J,axiom,
% 5.25/5.46 ! [B: real,C: real,W: num] :
% 5.25/5.46 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_less_eq_numeral(1)
% 5.25/5.46 thf(fact_2236_divide__less__eq__numeral_I1_J,axiom,
% 5.25/5.46 ! [B: rat,C: rat,W: num] :
% 5.25/5.46 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_less_eq_numeral(1)
% 5.25/5.46 thf(fact_2237_power__Suc__less,axiom,
% 5.25/5.46 ! [A: real,N: nat] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.46 => ( ( ord_less_real @ A @ one_one_real )
% 5.25/5.46 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_less
% 5.25/5.46 thf(fact_2238_power__Suc__less,axiom,
% 5.25/5.46 ! [A: rat,N: nat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.46 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.25/5.46 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_less
% 5.25/5.46 thf(fact_2239_power__Suc__less,axiom,
% 5.25/5.46 ! [A: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.25/5.46 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_less
% 5.25/5.46 thf(fact_2240_power__Suc__less,axiom,
% 5.25/5.46 ! [A: int,N: nat] :
% 5.25/5.46 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.46 => ( ( ord_less_int @ A @ one_one_int )
% 5.25/5.46 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_less
% 5.25/5.46 thf(fact_2241_power__Suc__le__self,axiom,
% 5.25/5.46 ! [A: real,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.46 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.25/5.46 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_le_self
% 5.25/5.46 thf(fact_2242_power__Suc__le__self,axiom,
% 5.25/5.46 ! [A: rat,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.46 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_le_self
% 5.25/5.46 thf(fact_2243_power__Suc__le__self,axiom,
% 5.25/5.46 ! [A: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.46 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.25/5.46 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_le_self
% 5.25/5.46 thf(fact_2244_power__Suc__le__self,axiom,
% 5.25/5.46 ! [A: int,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.46 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.25/5.46 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_le_self
% 5.25/5.46 thf(fact_2245_power__Suc__less__one,axiom,
% 5.25/5.46 ! [A: real,N: nat] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.46 => ( ( ord_less_real @ A @ one_one_real )
% 5.25/5.46 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_less_one
% 5.25/5.46 thf(fact_2246_power__Suc__less__one,axiom,
% 5.25/5.46 ! [A: rat,N: nat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.46 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.25/5.46 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_less_one
% 5.25/5.46 thf(fact_2247_power__Suc__less__one,axiom,
% 5.25/5.46 ! [A: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.25/5.46 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_less_one
% 5.25/5.46 thf(fact_2248_power__Suc__less__one,axiom,
% 5.25/5.46 ! [A: int,N: nat] :
% 5.25/5.46 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.46 => ( ( ord_less_int @ A @ one_one_int )
% 5.25/5.46 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_less_one
% 5.25/5.46 thf(fact_2249_power__strict__decreasing,axiom,
% 5.25/5.46 ! [N: nat,N5: nat,A: real] :
% 5.25/5.46 ( ( ord_less_nat @ N @ N5 )
% 5.25/5.46 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.46 => ( ( ord_less_real @ A @ one_one_real )
% 5.25/5.46 => ( ord_less_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_strict_decreasing
% 5.25/5.46 thf(fact_2250_power__strict__decreasing,axiom,
% 5.25/5.46 ! [N: nat,N5: nat,A: rat] :
% 5.25/5.46 ( ( ord_less_nat @ N @ N5 )
% 5.25/5.46 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.46 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.25/5.46 => ( ord_less_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_strict_decreasing
% 5.25/5.46 thf(fact_2251_power__strict__decreasing,axiom,
% 5.25/5.46 ! [N: nat,N5: nat,A: nat] :
% 5.25/5.46 ( ( ord_less_nat @ N @ N5 )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.25/5.46 => ( ord_less_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_strict_decreasing
% 5.25/5.46 thf(fact_2252_power__strict__decreasing,axiom,
% 5.25/5.46 ! [N: nat,N5: nat,A: int] :
% 5.25/5.46 ( ( ord_less_nat @ N @ N5 )
% 5.25/5.46 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.46 => ( ( ord_less_int @ A @ one_one_int )
% 5.25/5.46 => ( ord_less_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_strict_decreasing
% 5.25/5.46 thf(fact_2253_power__decreasing,axiom,
% 5.25/5.46 ! [N: nat,N5: nat,A: real] :
% 5.25/5.46 ( ( ord_less_eq_nat @ N @ N5 )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.46 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.25/5.46 => ( ord_less_eq_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_decreasing
% 5.25/5.46 thf(fact_2254_power__decreasing,axiom,
% 5.25/5.46 ! [N: nat,N5: nat,A: rat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ N @ N5 )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.46 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_decreasing
% 5.25/5.46 thf(fact_2255_power__decreasing,axiom,
% 5.25/5.46 ! [N: nat,N5: nat,A: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ N @ N5 )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.46 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.25/5.46 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_decreasing
% 5.25/5.46 thf(fact_2256_power__decreasing,axiom,
% 5.25/5.46 ! [N: nat,N5: nat,A: int] :
% 5.25/5.46 ( ( ord_less_eq_nat @ N @ N5 )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.46 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.25/5.46 => ( ord_less_eq_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_decreasing
% 5.25/5.46 thf(fact_2257_zero__power2,axiom,
% 5.25/5.46 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.46 = zero_zero_rat ) ).
% 5.25/5.46
% 5.25/5.46 % zero_power2
% 5.25/5.46 thf(fact_2258_zero__power2,axiom,
% 5.25/5.46 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.46 = zero_zero_nat ) ).
% 5.25/5.46
% 5.25/5.46 % zero_power2
% 5.25/5.46 thf(fact_2259_zero__power2,axiom,
% 5.25/5.46 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.46 = zero_zero_real ) ).
% 5.25/5.46
% 5.25/5.46 % zero_power2
% 5.25/5.46 thf(fact_2260_zero__power2,axiom,
% 5.25/5.46 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.46 = zero_zero_int ) ).
% 5.25/5.46
% 5.25/5.46 % zero_power2
% 5.25/5.46 thf(fact_2261_zero__power2,axiom,
% 5.25/5.46 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.46 = zero_zero_complex ) ).
% 5.25/5.46
% 5.25/5.46 % zero_power2
% 5.25/5.46 thf(fact_2262_self__le__power,axiom,
% 5.25/5.46 ! [A: real,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % self_le_power
% 5.25/5.46 thf(fact_2263_self__le__power,axiom,
% 5.25/5.46 ! [A: rat,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % self_le_power
% 5.25/5.46 thf(fact_2264_self__le__power,axiom,
% 5.25/5.46 ! [A: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % self_le_power
% 5.25/5.46 thf(fact_2265_self__le__power,axiom,
% 5.25/5.46 ! [A: int,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % self_le_power
% 5.25/5.46 thf(fact_2266_one__less__power,axiom,
% 5.25/5.46 ! [A: real,N: nat] :
% 5.25/5.46 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % one_less_power
% 5.25/5.46 thf(fact_2267_one__less__power,axiom,
% 5.25/5.46 ! [A: rat,N: nat] :
% 5.25/5.46 ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % one_less_power
% 5.25/5.46 thf(fact_2268_one__less__power,axiom,
% 5.25/5.46 ! [A: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % one_less_power
% 5.25/5.46 thf(fact_2269_one__less__power,axiom,
% 5.25/5.46 ! [A: int,N: nat] :
% 5.25/5.46 ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % one_less_power
% 5.25/5.46 thf(fact_2270_numeral__2__eq__2,axiom,
% 5.25/5.46 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.25/5.46 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % numeral_2_eq_2
% 5.25/5.46 thf(fact_2271_pos2,axiom,
% 5.25/5.46 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.25/5.46
% 5.25/5.46 % pos2
% 5.25/5.46 thf(fact_2272_less__eq__div__iff__mult__less__eq,axiom,
% 5.25/5.46 ! [Q2: nat,M: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.25/5.46 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 5.25/5.46 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_eq_div_iff_mult_less_eq
% 5.25/5.46 thf(fact_2273_split__div,axiom,
% 5.25/5.46 ! [P: nat > $o,M: nat,N: nat] :
% 5.25/5.46 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.25/5.46 = ( ( ( N = zero_zero_nat )
% 5.25/5.46 => ( P @ zero_zero_nat ) )
% 5.25/5.46 & ( ( N != zero_zero_nat )
% 5.25/5.46 => ! [I3: nat,J3: nat] :
% 5.25/5.46 ( ( ord_less_nat @ J3 @ N )
% 5.25/5.46 => ( ( M
% 5.25/5.46 = ( plus_plus_nat @ ( times_times_nat @ N @ I3 ) @ J3 ) )
% 5.25/5.46 => ( P @ I3 ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % split_div
% 5.25/5.46 thf(fact_2274_dividend__less__div__times,axiom,
% 5.25/5.46 ! [N: nat,M: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dividend_less_div_times
% 5.25/5.46 thf(fact_2275_dividend__less__times__div,axiom,
% 5.25/5.46 ! [N: nat,M: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dividend_less_times_div
% 5.25/5.46 thf(fact_2276_split__mod,axiom,
% 5.25/5.46 ! [P: nat > $o,M: nat,N: nat] :
% 5.25/5.46 ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 5.25/5.46 = ( ( ( N = zero_zero_nat )
% 5.25/5.46 => ( P @ M ) )
% 5.25/5.46 & ( ( N != zero_zero_nat )
% 5.25/5.46 => ! [I3: nat,J3: nat] :
% 5.25/5.46 ( ( ord_less_nat @ J3 @ N )
% 5.25/5.46 => ( ( M
% 5.25/5.46 = ( plus_plus_nat @ ( times_times_nat @ N @ I3 ) @ J3 ) )
% 5.25/5.46 => ( P @ J3 ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % split_mod
% 5.25/5.46 thf(fact_2277_verit__le__mono__div,axiom,
% 5.25/5.46 ! [A2: nat,B3: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ A2 @ B3 )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ord_less_eq_nat
% 5.25/5.46 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 5.25/5.46 @ ( if_nat
% 5.25/5.46 @ ( ( modulo_modulo_nat @ B3 @ N )
% 5.25/5.46 = zero_zero_nat )
% 5.25/5.46 @ one_one_nat
% 5.25/5.46 @ zero_zero_nat ) )
% 5.25/5.46 @ ( divide_divide_nat @ B3 @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % verit_le_mono_div
% 5.25/5.46 thf(fact_2278_convex__bound__lt,axiom,
% 5.25/5.46 ! [X3: real,A: real,Y: real,U: real,V: real] :
% 5.25/5.46 ( ( ord_less_real @ X3 @ A )
% 5.25/5.46 => ( ( ord_less_real @ Y @ A )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.25/5.46 => ( ( ( plus_plus_real @ U @ V )
% 5.25/5.46 = one_one_real )
% 5.25/5.46 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X3 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % convex_bound_lt
% 5.25/5.46 thf(fact_2279_convex__bound__lt,axiom,
% 5.25/5.46 ! [X3: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X3 @ A )
% 5.25/5.46 => ( ( ord_less_rat @ Y @ A )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.25/5.46 => ( ( ( plus_plus_rat @ U @ V )
% 5.25/5.46 = one_one_rat )
% 5.25/5.46 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X3 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % convex_bound_lt
% 5.25/5.46 thf(fact_2280_convex__bound__lt,axiom,
% 5.25/5.46 ! [X3: int,A: int,Y: int,U: int,V: int] :
% 5.25/5.46 ( ( ord_less_int @ X3 @ A )
% 5.25/5.46 => ( ( ord_less_int @ Y @ A )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.25/5.46 => ( ( ( plus_plus_int @ U @ V )
% 5.25/5.46 = one_one_int )
% 5.25/5.46 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X3 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % convex_bound_lt
% 5.25/5.46 thf(fact_2281_le__divide__eq__numeral_I1_J,axiom,
% 5.25/5.46 ! [W: num,B: real,C: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % le_divide_eq_numeral(1)
% 5.25/5.46 thf(fact_2282_le__divide__eq__numeral_I1_J,axiom,
% 5.25/5.46 ! [W: num,B: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % le_divide_eq_numeral(1)
% 5.25/5.46 thf(fact_2283_divide__le__eq__numeral_I1_J,axiom,
% 5.25/5.46 ! [B: real,C: real,W: num] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.25/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.46 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_le_eq_numeral(1)
% 5.25/5.46 thf(fact_2284_divide__le__eq__numeral_I1_J,axiom,
% 5.25/5.46 ! [B: rat,C: rat,W: num] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.25/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.46 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.25/5.46 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_le_eq_numeral(1)
% 5.25/5.46 thf(fact_2285_half__gt__zero__iff,axiom,
% 5.25/5.46 ! [A: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.46 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % half_gt_zero_iff
% 5.25/5.46 thf(fact_2286_half__gt__zero__iff,axiom,
% 5.25/5.46 ! [A: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.25/5.46 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % half_gt_zero_iff
% 5.25/5.46 thf(fact_2287_half__gt__zero,axiom,
% 5.25/5.46 ! [A: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.46 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % half_gt_zero
% 5.25/5.46 thf(fact_2288_half__gt__zero,axiom,
% 5.25/5.46 ! [A: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.46 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % half_gt_zero
% 5.25/5.46 thf(fact_2289_power2__le__imp__le,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.46 => ( ord_less_eq_real @ X3 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_le_imp_le
% 5.25/5.46 thf(fact_2290_power2__le__imp__le,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.46 => ( ord_less_eq_rat @ X3 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_le_imp_le
% 5.25/5.46 thf(fact_2291_power2__le__imp__le,axiom,
% 5.25/5.46 ! [X3: nat,Y: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.25/5.46 => ( ord_less_eq_nat @ X3 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_le_imp_le
% 5.25/5.46 thf(fact_2292_power2__le__imp__le,axiom,
% 5.25/5.46 ! [X3: int,Y: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.46 => ( ord_less_eq_int @ X3 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_le_imp_le
% 5.25/5.46 thf(fact_2293_power2__eq__imp__eq,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.46 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.46 => ( X3 = Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_eq_imp_eq
% 5.25/5.46 thf(fact_2294_power2__eq__imp__eq,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.46 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.46 => ( X3 = Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_eq_imp_eq
% 5.25/5.46 thf(fact_2295_power2__eq__imp__eq,axiom,
% 5.25/5.46 ! [X3: nat,Y: nat] :
% 5.25/5.46 ( ( ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.46 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.25/5.46 => ( X3 = Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_eq_imp_eq
% 5.25/5.46 thf(fact_2296_power2__eq__imp__eq,axiom,
% 5.25/5.46 ! [X3: int,Y: int] :
% 5.25/5.46 ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.46 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.46 => ( X3 = Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_eq_imp_eq
% 5.25/5.46 thf(fact_2297_zero__le__power2,axiom,
% 5.25/5.46 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % zero_le_power2
% 5.25/5.46 thf(fact_2298_zero__le__power2,axiom,
% 5.25/5.46 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % zero_le_power2
% 5.25/5.46 thf(fact_2299_zero__le__power2,axiom,
% 5.25/5.46 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % zero_le_power2
% 5.25/5.46 thf(fact_2300_power2__less__0,axiom,
% 5.25/5.46 ! [A: real] :
% 5.25/5.46 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.25/5.46
% 5.25/5.46 % power2_less_0
% 5.25/5.46 thf(fact_2301_power2__less__0,axiom,
% 5.25/5.46 ! [A: rat] :
% 5.25/5.46 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.25/5.46
% 5.25/5.46 % power2_less_0
% 5.25/5.46 thf(fact_2302_power2__less__0,axiom,
% 5.25/5.46 ! [A: int] :
% 5.25/5.46 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.25/5.46
% 5.25/5.46 % power2_less_0
% 5.25/5.46 thf(fact_2303_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.25/5.46 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.46 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.25/5.46 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.25/5.46 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.25/5.46 thf(fact_2304_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.25/5.46 ! [C: nat,A: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.46 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.25/5.46 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.25/5.46 thf(fact_2305_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.25/5.46 ! [C: int,A: int,B: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.46 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.25/5.46 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.25/5.46 thf(fact_2306_exp__add__not__zero__imp__right,axiom,
% 5.25/5.46 ! [M: nat,N: nat] :
% 5.25/5.46 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.46 != zero_zero_nat )
% 5.25/5.46 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.46 != zero_zero_nat ) ) ).
% 5.25/5.46
% 5.25/5.46 % exp_add_not_zero_imp_right
% 5.25/5.46 thf(fact_2307_exp__add__not__zero__imp__right,axiom,
% 5.25/5.46 ! [M: nat,N: nat] :
% 5.25/5.46 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.46 != zero_zero_int )
% 5.25/5.46 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.25/5.46 != zero_zero_int ) ) ).
% 5.25/5.46
% 5.25/5.46 % exp_add_not_zero_imp_right
% 5.25/5.46 thf(fact_2308_exp__add__not__zero__imp__left,axiom,
% 5.25/5.46 ! [M: nat,N: nat] :
% 5.25/5.46 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.46 != zero_zero_nat )
% 5.25/5.46 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.25/5.46 != zero_zero_nat ) ) ).
% 5.25/5.46
% 5.25/5.46 % exp_add_not_zero_imp_left
% 5.25/5.46 thf(fact_2309_exp__add__not__zero__imp__left,axiom,
% 5.25/5.46 ! [M: nat,N: nat] :
% 5.25/5.46 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.46 != zero_zero_int )
% 5.25/5.46 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.25/5.46 != zero_zero_int ) ) ).
% 5.25/5.46
% 5.25/5.46 % exp_add_not_zero_imp_left
% 5.25/5.46 thf(fact_2310_less__2__cases__iff,axiom,
% 5.25/5.46 ! [N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.46 = ( ( N = zero_zero_nat )
% 5.25/5.46 | ( N
% 5.25/5.46 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_2_cases_iff
% 5.25/5.46 thf(fact_2311_less__2__cases,axiom,
% 5.25/5.46 ! [N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.46 => ( ( N = zero_zero_nat )
% 5.25/5.46 | ( N
% 5.25/5.46 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_2_cases
% 5.25/5.46 thf(fact_2312_nat__induct2,axiom,
% 5.25/5.46 ! [P: nat > $o,N: nat] :
% 5.25/5.46 ( ( P @ zero_zero_nat )
% 5.25/5.46 => ( ( P @ one_one_nat )
% 5.25/5.46 => ( ! [N3: nat] :
% 5.25/5.46 ( ( P @ N3 )
% 5.25/5.46 => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.46 => ( P @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % nat_induct2
% 5.25/5.46 thf(fact_2313_split__div_H,axiom,
% 5.25/5.46 ! [P: nat > $o,M: nat,N: nat] :
% 5.25/5.46 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.25/5.46 = ( ( ( N = zero_zero_nat )
% 5.25/5.46 & ( P @ zero_zero_nat ) )
% 5.25/5.46 | ? [Q4: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q4 ) @ M )
% 5.25/5.46 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q4 ) ) )
% 5.25/5.46 & ( P @ Q4 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % split_div'
% 5.25/5.46 thf(fact_2314_Suc__times__mod__eq,axiom,
% 5.25/5.46 ! [M: nat,N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.25/5.46 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 5.25/5.46 = one_one_nat ) ) ).
% 5.25/5.46
% 5.25/5.46 % Suc_times_mod_eq
% 5.25/5.46 thf(fact_2315_power2__less__imp__less,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.46 => ( ord_less_real @ X3 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_less_imp_less
% 5.25/5.46 thf(fact_2316_power2__less__imp__less,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.46 => ( ord_less_rat @ X3 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_less_imp_less
% 5.25/5.46 thf(fact_2317_power2__less__imp__less,axiom,
% 5.25/5.46 ! [X3: nat,Y: nat] :
% 5.25/5.46 ( ( ord_less_nat @ ( power_power_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.25/5.46 => ( ord_less_nat @ X3 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_less_imp_less
% 5.25/5.46 thf(fact_2318_power2__less__imp__less,axiom,
% 5.25/5.46 ! [X3: int,Y: int] :
% 5.25/5.46 ( ( ord_less_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.46 => ( ord_less_int @ X3 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_less_imp_less
% 5.25/5.46 thf(fact_2319_sum__power2__le__zero__iff,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.25/5.46 = ( ( X3 = zero_zero_real )
% 5.25/5.46 & ( Y = zero_zero_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_power2_le_zero_iff
% 5.25/5.46 thf(fact_2320_sum__power2__le__zero__iff,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.25/5.46 = ( ( X3 = zero_zero_rat )
% 5.25/5.46 & ( Y = zero_zero_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_power2_le_zero_iff
% 5.25/5.46 thf(fact_2321_sum__power2__le__zero__iff,axiom,
% 5.25/5.46 ! [X3: int,Y: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.25/5.46 = ( ( X3 = zero_zero_int )
% 5.25/5.46 & ( Y = zero_zero_int ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_power2_le_zero_iff
% 5.25/5.46 thf(fact_2322_sum__power2__ge__zero,axiom,
% 5.25/5.46 ! [X3: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_power2_ge_zero
% 5.25/5.46 thf(fact_2323_sum__power2__ge__zero,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_power2_ge_zero
% 5.25/5.46 thf(fact_2324_sum__power2__ge__zero,axiom,
% 5.25/5.46 ! [X3: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_power2_ge_zero
% 5.25/5.46 thf(fact_2325_sum__power2__gt__zero__iff,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.46 = ( ( X3 != zero_zero_real )
% 5.25/5.46 | ( Y != zero_zero_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_power2_gt_zero_iff
% 5.25/5.46 thf(fact_2326_sum__power2__gt__zero__iff,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.46 = ( ( X3 != zero_zero_rat )
% 5.25/5.46 | ( Y != zero_zero_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_power2_gt_zero_iff
% 5.25/5.46 thf(fact_2327_sum__power2__gt__zero__iff,axiom,
% 5.25/5.46 ! [X3: int,Y: int] :
% 5.25/5.46 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.46 = ( ( X3 != zero_zero_int )
% 5.25/5.46 | ( Y != zero_zero_int ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % sum_power2_gt_zero_iff
% 5.25/5.46 thf(fact_2328_not__sum__power2__lt__zero,axiom,
% 5.25/5.46 ! [X3: real,Y: real] :
% 5.25/5.46 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.25/5.46
% 5.25/5.46 % not_sum_power2_lt_zero
% 5.25/5.46 thf(fact_2329_not__sum__power2__lt__zero,axiom,
% 5.25/5.46 ! [X3: rat,Y: rat] :
% 5.25/5.46 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.25/5.46
% 5.25/5.46 % not_sum_power2_lt_zero
% 5.25/5.46 thf(fact_2330_not__sum__power2__lt__zero,axiom,
% 5.25/5.46 ! [X3: int,Y: int] :
% 5.25/5.46 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.25/5.46
% 5.25/5.46 % not_sum_power2_lt_zero
% 5.25/5.46 thf(fact_2331_divmod__digit__0_I2_J,axiom,
% 5.25/5.46 ! [B: nat,A: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.46 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.25/5.46 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.25/5.46 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divmod_digit_0(2)
% 5.25/5.46 thf(fact_2332_divmod__digit__0_I2_J,axiom,
% 5.25/5.46 ! [B: int,A: int] :
% 5.25/5.46 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.46 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.25/5.46 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.25/5.46 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divmod_digit_0(2)
% 5.25/5.46 thf(fact_2333_divmod__digit__0_I2_J,axiom,
% 5.25/5.46 ! [B: code_integer,A: code_integer] :
% 5.25/5.46 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.25/5.46 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.25/5.46 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 5.25/5.46 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divmod_digit_0(2)
% 5.25/5.46 thf(fact_2334_bits__stable__imp__add__self,axiom,
% 5.25/5.46 ! [A: nat] :
% 5.25/5.46 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.46 = A )
% 5.25/5.46 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.46 = zero_zero_nat ) ) ).
% 5.25/5.46
% 5.25/5.46 % bits_stable_imp_add_self
% 5.25/5.46 thf(fact_2335_bits__stable__imp__add__self,axiom,
% 5.25/5.46 ! [A: int] :
% 5.25/5.46 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.46 = A )
% 5.25/5.46 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.25/5.46 = zero_zero_int ) ) ).
% 5.25/5.46
% 5.25/5.46 % bits_stable_imp_add_self
% 5.25/5.46 thf(fact_2336_bits__stable__imp__add__self,axiom,
% 5.25/5.46 ! [A: code_integer] :
% 5.25/5.46 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.46 = A )
% 5.25/5.46 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.25/5.46 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.46
% 5.25/5.46 % bits_stable_imp_add_self
% 5.25/5.46 thf(fact_2337_zero__le__even__power_H,axiom,
% 5.25/5.46 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % zero_le_even_power'
% 5.25/5.46 thf(fact_2338_zero__le__even__power_H,axiom,
% 5.25/5.46 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % zero_le_even_power'
% 5.25/5.46 thf(fact_2339_zero__le__even__power_H,axiom,
% 5.25/5.46 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % zero_le_even_power'
% 5.25/5.46 thf(fact_2340_verit__comp__simplify1_I3_J,axiom,
% 5.25/5.46 ! [B4: real,A4: real] :
% 5.25/5.46 ( ( ~ ( ord_less_eq_real @ B4 @ A4 ) )
% 5.25/5.46 = ( ord_less_real @ A4 @ B4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(3)
% 5.25/5.46 thf(fact_2341_verit__comp__simplify1_I3_J,axiom,
% 5.25/5.46 ! [B4: rat,A4: rat] :
% 5.25/5.46 ( ( ~ ( ord_less_eq_rat @ B4 @ A4 ) )
% 5.25/5.46 = ( ord_less_rat @ A4 @ B4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(3)
% 5.25/5.46 thf(fact_2342_verit__comp__simplify1_I3_J,axiom,
% 5.25/5.46 ! [B4: num,A4: num] :
% 5.25/5.46 ( ( ~ ( ord_less_eq_num @ B4 @ A4 ) )
% 5.25/5.46 = ( ord_less_num @ A4 @ B4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(3)
% 5.25/5.46 thf(fact_2343_verit__comp__simplify1_I3_J,axiom,
% 5.25/5.46 ! [B4: nat,A4: nat] :
% 5.25/5.46 ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 5.25/5.46 = ( ord_less_nat @ A4 @ B4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(3)
% 5.25/5.46 thf(fact_2344_verit__comp__simplify1_I3_J,axiom,
% 5.25/5.46 ! [B4: int,A4: int] :
% 5.25/5.46 ( ( ~ ( ord_less_eq_int @ B4 @ A4 ) )
% 5.25/5.46 = ( ord_less_int @ A4 @ B4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(3)
% 5.25/5.46 thf(fact_2345_nat__bit__induct,axiom,
% 5.25/5.46 ! [P: nat > $o,N: nat] :
% 5.25/5.46 ( ( P @ zero_zero_nat )
% 5.25/5.46 => ( ! [N3: nat] :
% 5.25/5.46 ( ( P @ N3 )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.25/5.46 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.25/5.46 => ( ! [N3: nat] :
% 5.25/5.46 ( ( P @ N3 )
% 5.25/5.46 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.25/5.46 => ( P @ N ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % nat_bit_induct
% 5.25/5.46 thf(fact_2346_Suc__n__div__2__gt__zero,axiom,
% 5.25/5.46 ! [N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Suc_n_div_2_gt_zero
% 5.25/5.46 thf(fact_2347_div__2__gt__zero,axiom,
% 5.25/5.46 ! [N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.25/5.46 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_2_gt_zero
% 5.25/5.46 thf(fact_2348_verit__eq__simplify_I10_J,axiom,
% 5.25/5.46 ! [X22: num] :
% 5.25/5.46 ( one
% 5.25/5.46 != ( bit0 @ X22 ) ) ).
% 5.25/5.46
% 5.25/5.46 % verit_eq_simplify(10)
% 5.25/5.46 thf(fact_2349_divmod__digit__0_I1_J,axiom,
% 5.25/5.46 ! [B: nat,A: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.46 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.25/5.46 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.25/5.46 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divmod_digit_0(1)
% 5.25/5.46 thf(fact_2350_divmod__digit__0_I1_J,axiom,
% 5.25/5.46 ! [B: int,A: int] :
% 5.25/5.46 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.46 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.25/5.46 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.25/5.46 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divmod_digit_0(1)
% 5.25/5.46 thf(fact_2351_divmod__digit__0_I1_J,axiom,
% 5.25/5.46 ! [B: code_integer,A: code_integer] :
% 5.25/5.46 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.25/5.46 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.25/5.46 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.25/5.46 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divmod_digit_0(1)
% 5.25/5.46 thf(fact_2352_odd__0__le__power__imp__0__le,axiom,
% 5.25/5.46 ! [A: real,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.46 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % odd_0_le_power_imp_0_le
% 5.25/5.46 thf(fact_2353_odd__0__le__power__imp__0__le,axiom,
% 5.25/5.46 ! [A: rat,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % odd_0_le_power_imp_0_le
% 5.25/5.46 thf(fact_2354_odd__0__le__power__imp__0__le,axiom,
% 5.25/5.46 ! [A: int,N: nat] :
% 5.25/5.46 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.46 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % odd_0_le_power_imp_0_le
% 5.25/5.46 thf(fact_2355_odd__power__less__zero,axiom,
% 5.25/5.46 ! [A: real,N: nat] :
% 5.25/5.46 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.46 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 5.25/5.46
% 5.25/5.46 % odd_power_less_zero
% 5.25/5.46 thf(fact_2356_odd__power__less__zero,axiom,
% 5.25/5.46 ! [A: rat,N: nat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 5.25/5.46
% 5.25/5.46 % odd_power_less_zero
% 5.25/5.46 thf(fact_2357_odd__power__less__zero,axiom,
% 5.25/5.46 ! [A: int,N: nat] :
% 5.25/5.46 ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.46 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 5.25/5.46
% 5.25/5.46 % odd_power_less_zero
% 5.25/5.46 thf(fact_2358_mod__double__modulus,axiom,
% 5.25/5.46 ! [M: code_integer,X3: code_integer] :
% 5.25/5.46 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.25/5.46 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 5.25/5.46 => ( ( ( modulo364778990260209775nteger @ X3 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.46 = ( modulo364778990260209775nteger @ X3 @ M ) )
% 5.25/5.46 | ( ( modulo364778990260209775nteger @ X3 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.46 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X3 @ M ) @ M ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mod_double_modulus
% 5.25/5.46 thf(fact_2359_mod__double__modulus,axiom,
% 5.25/5.46 ! [M: nat,X3: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ X3 )
% 5.25/5.46 => ( ( ( modulo_modulo_nat @ X3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.46 = ( modulo_modulo_nat @ X3 @ M ) )
% 5.25/5.46 | ( ( modulo_modulo_nat @ X3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.46 = ( plus_plus_nat @ ( modulo_modulo_nat @ X3 @ M ) @ M ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mod_double_modulus
% 5.25/5.46 thf(fact_2360_mod__double__modulus,axiom,
% 5.25/5.46 ! [M: int,X3: int] :
% 5.25/5.46 ( ( ord_less_int @ zero_zero_int @ M )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.46 => ( ( ( modulo_modulo_int @ X3 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.46 = ( modulo_modulo_int @ X3 @ M ) )
% 5.25/5.46 | ( ( modulo_modulo_int @ X3 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.46 = ( plus_plus_int @ ( modulo_modulo_int @ X3 @ M ) @ M ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mod_double_modulus
% 5.25/5.46 thf(fact_2361_invar__vebt_Ointros_I5_J,axiom,
% 5.25/5.46 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.25/5.46 ( ! [X5: vEBT_VEBT] :
% 5.25/5.46 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.46 => ( vEBT_invar_vebt @ X5 @ N ) )
% 5.25/5.46 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.25/5.46 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.25/5.46 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.46 => ( ( M
% 5.25/5.46 = ( suc @ N ) )
% 5.25/5.46 => ( ( Deg
% 5.25/5.46 = ( plus_plus_nat @ N @ M ) )
% 5.25/5.46 => ( ! [I4: nat] :
% 5.25/5.46 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.46 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X4 ) )
% 5.25/5.46 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.25/5.46 => ( ( ( Mi = Ma )
% 5.25/5.46 => ! [X5: vEBT_VEBT] :
% 5.25/5.46 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.46 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.25/5.46 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.25/5.46 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.25/5.46 => ( ( ( Mi != Ma )
% 5.25/5.46 => ! [I4: nat] :
% 5.25/5.46 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.46 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.25/5.46 = I4 )
% 5.25/5.46 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.25/5.46 & ! [X5: nat] :
% 5.25/5.46 ( ( ( ( vEBT_VEBT_high @ X5 @ N )
% 5.25/5.46 = I4 )
% 5.25/5.46 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N ) ) )
% 5.25/5.46 => ( ( ord_less_nat @ Mi @ X5 )
% 5.25/5.46 & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 5.25/5.46 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % invar_vebt.intros(5)
% 5.25/5.46 thf(fact_2362_invar__vebt_Ointros_I4_J,axiom,
% 5.25/5.46 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.25/5.46 ( ! [X5: vEBT_VEBT] :
% 5.25/5.46 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.46 => ( vEBT_invar_vebt @ X5 @ N ) )
% 5.25/5.46 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.25/5.46 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.25/5.46 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.46 => ( ( M = N )
% 5.25/5.46 => ( ( Deg
% 5.25/5.46 = ( plus_plus_nat @ N @ M ) )
% 5.25/5.46 => ( ! [I4: nat] :
% 5.25/5.46 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.46 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X4 ) )
% 5.25/5.46 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.25/5.46 => ( ( ( Mi = Ma )
% 5.25/5.46 => ! [X5: vEBT_VEBT] :
% 5.25/5.46 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.46 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.25/5.46 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.25/5.46 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.25/5.46 => ( ( ( Mi != Ma )
% 5.25/5.46 => ! [I4: nat] :
% 5.25/5.46 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.46 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.25/5.46 = I4 )
% 5.25/5.46 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.25/5.46 & ! [X5: nat] :
% 5.25/5.46 ( ( ( ( vEBT_VEBT_high @ X5 @ N )
% 5.25/5.46 = I4 )
% 5.25/5.46 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N ) ) )
% 5.25/5.46 => ( ( ord_less_nat @ Mi @ X5 )
% 5.25/5.46 & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 5.25/5.46 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % invar_vebt.intros(4)
% 5.25/5.46 thf(fact_2363_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.25/5.46 ! [X3: nat,N: nat,M: nat] :
% 5.25/5.46 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.46 => ( ord_less_nat @ ( vEBT_VEBT_low @ X3 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % VEBT_internal.exp_split_high_low(2)
% 5.25/5.46 thf(fact_2364_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.25/5.46 ! [X3: nat,N: nat,M: nat] :
% 5.25/5.46 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.46 => ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % VEBT_internal.exp_split_high_low(1)
% 5.25/5.46 thf(fact_2365_buildup__gives__valid,axiom,
% 5.25/5.46 ! [N: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.46 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 5.25/5.46
% 5.25/5.46 % buildup_gives_valid
% 5.25/5.46 thf(fact_2366_double__eq__0__iff,axiom,
% 5.25/5.46 ! [A: real] :
% 5.25/5.46 ( ( ( plus_plus_real @ A @ A )
% 5.25/5.46 = zero_zero_real )
% 5.25/5.46 = ( A = zero_zero_real ) ) ).
% 5.25/5.46
% 5.25/5.46 % double_eq_0_iff
% 5.25/5.46 thf(fact_2367_double__eq__0__iff,axiom,
% 5.25/5.46 ! [A: rat] :
% 5.25/5.46 ( ( ( plus_plus_rat @ A @ A )
% 5.25/5.46 = zero_zero_rat )
% 5.25/5.46 = ( A = zero_zero_rat ) ) ).
% 5.25/5.46
% 5.25/5.46 % double_eq_0_iff
% 5.25/5.46 thf(fact_2368_double__eq__0__iff,axiom,
% 5.25/5.46 ! [A: int] :
% 5.25/5.46 ( ( ( plus_plus_int @ A @ A )
% 5.25/5.46 = zero_zero_int )
% 5.25/5.46 = ( A = zero_zero_int ) ) ).
% 5.25/5.46
% 5.25/5.46 % double_eq_0_iff
% 5.25/5.46 thf(fact_2369_vebt__member_Osimps_I4_J,axiom,
% 5.25/5.46 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 5.25/5.46 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X3 ) ).
% 5.25/5.46
% 5.25/5.46 % vebt_member.simps(4)
% 5.25/5.46 thf(fact_2370_mult__le__cancel__iff2,axiom,
% 5.25/5.46 ! [Z: real,X3: real,Y: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.25/5.46 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X3 ) @ ( times_times_real @ Z @ Y ) )
% 5.25/5.46 = ( ord_less_eq_real @ X3 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_iff2
% 5.25/5.46 thf(fact_2371_mult__le__cancel__iff2,axiom,
% 5.25/5.46 ! [Z: rat,X3: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.25/5.46 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X3 ) @ ( times_times_rat @ Z @ Y ) )
% 5.25/5.46 = ( ord_less_eq_rat @ X3 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % mult_le_cancel_iff2
% 5.25/5.46 thf(fact_2372_mult__le__cancel__iff2,axiom,
% 5.25/5.46 ! [Z: int,X3: int,Y: int] :
% 5.25/5.46 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.25/5.46 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X3 ) @ ( times_times_int @ Z @ Y ) )
% 5.25/5.46 = ( ord_less_eq_int @ X3 @ Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_le_cancel_iff2
% 5.25/5.47 thf(fact_2373_mult__le__cancel__iff1,axiom,
% 5.25/5.47 ! [Z: real,X3: real,Y: real] :
% 5.25/5.47 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.25/5.47 => ( ( ord_less_eq_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ Y @ Z ) )
% 5.25/5.47 = ( ord_less_eq_real @ X3 @ Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_le_cancel_iff1
% 5.25/5.47 thf(fact_2374_mult__le__cancel__iff1,axiom,
% 5.25/5.47 ! [Z: rat,X3: rat,Y: rat] :
% 5.25/5.47 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.25/5.47 => ( ( ord_less_eq_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 5.25/5.47 = ( ord_less_eq_rat @ X3 @ Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_le_cancel_iff1
% 5.25/5.47 thf(fact_2375_mult__le__cancel__iff1,axiom,
% 5.25/5.47 ! [Z: int,X3: int,Y: int] :
% 5.25/5.47 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.25/5.47 => ( ( ord_less_eq_int @ ( times_times_int @ X3 @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.25/5.47 = ( ord_less_eq_int @ X3 @ Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_le_cancel_iff1
% 5.25/5.47 thf(fact_2376_divides__aux__eq,axiom,
% 5.25/5.47 ! [Q2: nat,R2: nat] :
% 5.25/5.47 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.25/5.47 = ( R2 = zero_zero_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % divides_aux_eq
% 5.25/5.47 thf(fact_2377_divides__aux__eq,axiom,
% 5.25/5.47 ! [Q2: int,R2: int] :
% 5.25/5.47 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.25/5.47 = ( R2 = zero_zero_int ) ) ).
% 5.25/5.47
% 5.25/5.47 % divides_aux_eq
% 5.25/5.47 thf(fact_2378_product__nth,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_num,Ys2: list_num] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_num @ Xs ) @ ( size_size_list_num @ Ys2 ) ) )
% 5.25/5.47 => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs @ Ys2 ) @ N )
% 5.25/5.47 = ( product_Pair_num_num @ ( nth_num @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys2 ) ) ) @ ( nth_num @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % product_nth
% 5.25/5.47 thf(fact_2379_product__nth,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_Code_integer,Ys2: list_o] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs ) @ ( size_size_list_o @ Ys2 ) ) )
% 5.25/5.47 => ( ( nth_Pr8522763379788166057eger_o @ ( produc3607205314601156340eger_o @ Xs @ Ys2 ) @ N )
% 5.25/5.47 = ( produc6677183202524767010eger_o @ ( nth_Code_integer @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) @ ( nth_o @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % product_nth
% 5.25/5.47 thf(fact_2380_product__nth,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) )
% 5.25/5.47 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys2 ) @ N )
% 5.25/5.47 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) @ ( nth_VEBT_VEBT @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % product_nth
% 5.25/5.47 thf(fact_2381_product__nth,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_o] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys2 ) ) )
% 5.25/5.47 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys2 ) @ N )
% 5.25/5.47 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) @ ( nth_o @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % product_nth
% 5.25/5.47 thf(fact_2382_product__nth,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_nat] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys2 ) ) )
% 5.25/5.47 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys2 ) @ N )
% 5.25/5.47 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) @ ( nth_nat @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % product_nth
% 5.25/5.47 thf(fact_2383_product__nth,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_int] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys2 ) ) )
% 5.25/5.47 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys2 ) @ N )
% 5.25/5.47 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) @ ( nth_int @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % product_nth
% 5.25/5.47 thf(fact_2384_product__nth,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_o,Ys2: list_VEBT_VEBT] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) )
% 5.25/5.47 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys2 ) @ N )
% 5.25/5.47 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) @ ( nth_VEBT_VEBT @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % product_nth
% 5.25/5.47 thf(fact_2385_product__nth,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_o,Ys2: list_o] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys2 ) ) )
% 5.25/5.47 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs @ Ys2 ) @ N )
% 5.25/5.47 = ( product_Pair_o_o @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) @ ( nth_o @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % product_nth
% 5.25/5.47 thf(fact_2386_product__nth,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_o,Ys2: list_nat] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys2 ) ) )
% 5.25/5.47 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs @ Ys2 ) @ N )
% 5.25/5.47 = ( product_Pair_o_nat @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) @ ( nth_nat @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % product_nth
% 5.25/5.47 thf(fact_2387_product__nth,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_o,Ys2: list_int] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys2 ) ) )
% 5.25/5.47 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys2 ) @ N )
% 5.25/5.47 = ( product_Pair_o_int @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) @ ( nth_int @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % product_nth
% 5.25/5.47 thf(fact_2388_VEBT_Oinject_I1_J,axiom,
% 5.25/5.47 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.25/5.47 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.25/5.47 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.25/5.47 = ( ( X11 = Y11 )
% 5.25/5.47 & ( X12 = Y12 )
% 5.25/5.47 & ( X13 = Y13 )
% 5.25/5.47 & ( X14 = Y14 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT.inject(1)
% 5.25/5.47 thf(fact_2389_unset__bit__nonnegative__int__iff,axiom,
% 5.25/5.47 ! [N: nat,K: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 5.25/5.47 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.25/5.47
% 5.25/5.47 % unset_bit_nonnegative_int_iff
% 5.25/5.47 thf(fact_2390_flip__bit__nonnegative__int__iff,axiom,
% 5.25/5.47 ! [N: nat,K: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 5.25/5.47 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.25/5.47
% 5.25/5.47 % flip_bit_nonnegative_int_iff
% 5.25/5.47 thf(fact_2391_set__bit__nonnegative__int__iff,axiom,
% 5.25/5.47 ! [N: nat,K: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 5.25/5.47 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_bit_nonnegative_int_iff
% 5.25/5.47 thf(fact_2392_set__bit__negative__int__iff,axiom,
% 5.25/5.47 ! [N: nat,K: int] :
% 5.25/5.47 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 5.25/5.47 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_bit_negative_int_iff
% 5.25/5.47 thf(fact_2393_flip__bit__negative__int__iff,axiom,
% 5.25/5.47 ! [N: nat,K: int] :
% 5.25/5.47 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 5.25/5.47 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.25/5.47
% 5.25/5.47 % flip_bit_negative_int_iff
% 5.25/5.47 thf(fact_2394_unset__bit__negative__int__iff,axiom,
% 5.25/5.47 ! [N: nat,K: int] :
% 5.25/5.47 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 5.25/5.47 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.25/5.47
% 5.25/5.47 % unset_bit_negative_int_iff
% 5.25/5.47 thf(fact_2395_length__product,axiom,
% 5.25/5.47 ! [Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 5.25/5.47 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys2 ) )
% 5.25/5.47 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % length_product
% 5.25/5.47 thf(fact_2396_length__product,axiom,
% 5.25/5.47 ! [Xs: list_VEBT_VEBT,Ys2: list_o] :
% 5.25/5.47 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys2 ) )
% 5.25/5.47 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % length_product
% 5.25/5.47 thf(fact_2397_length__product,axiom,
% 5.25/5.47 ! [Xs: list_VEBT_VEBT,Ys2: list_nat] :
% 5.25/5.47 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys2 ) )
% 5.25/5.47 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % length_product
% 5.25/5.47 thf(fact_2398_length__product,axiom,
% 5.25/5.47 ! [Xs: list_VEBT_VEBT,Ys2: list_int] :
% 5.25/5.47 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys2 ) )
% 5.25/5.47 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % length_product
% 5.25/5.47 thf(fact_2399_length__product,axiom,
% 5.25/5.47 ! [Xs: list_o,Ys2: list_VEBT_VEBT] :
% 5.25/5.47 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys2 ) )
% 5.25/5.47 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % length_product
% 5.25/5.47 thf(fact_2400_length__product,axiom,
% 5.25/5.47 ! [Xs: list_o,Ys2: list_o] :
% 5.25/5.47 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs @ Ys2 ) )
% 5.25/5.47 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % length_product
% 5.25/5.47 thf(fact_2401_length__product,axiom,
% 5.25/5.47 ! [Xs: list_o,Ys2: list_nat] :
% 5.25/5.47 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs @ Ys2 ) )
% 5.25/5.47 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % length_product
% 5.25/5.47 thf(fact_2402_length__product,axiom,
% 5.25/5.47 ! [Xs: list_o,Ys2: list_int] :
% 5.25/5.47 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs @ Ys2 ) )
% 5.25/5.47 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % length_product
% 5.25/5.47 thf(fact_2403_length__product,axiom,
% 5.25/5.47 ! [Xs: list_nat,Ys2: list_VEBT_VEBT] :
% 5.25/5.47 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys2 ) )
% 5.25/5.47 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % length_product
% 5.25/5.47 thf(fact_2404_length__product,axiom,
% 5.25/5.47 ! [Xs: list_nat,Ys2: list_o] :
% 5.25/5.47 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs @ Ys2 ) )
% 5.25/5.47 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % length_product
% 5.25/5.47 thf(fact_2405_zle__add1__eq__le,axiom,
% 5.25/5.47 ! [W: int,Z: int] :
% 5.25/5.47 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.25/5.47 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.25/5.47
% 5.25/5.47 % zle_add1_eq_le
% 5.25/5.47 thf(fact_2406_mod__pos__pos__trivial,axiom,
% 5.25/5.47 ! [K: int,L2: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.47 => ( ( ord_less_int @ K @ L2 )
% 5.25/5.47 => ( ( modulo_modulo_int @ K @ L2 )
% 5.25/5.47 = K ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mod_pos_pos_trivial
% 5.25/5.47 thf(fact_2407_mod__neg__neg__trivial,axiom,
% 5.25/5.47 ! [K: int,L2: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.25/5.47 => ( ( ord_less_int @ L2 @ K )
% 5.25/5.47 => ( ( modulo_modulo_int @ K @ L2 )
% 5.25/5.47 = K ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mod_neg_neg_trivial
% 5.25/5.47 thf(fact_2408_add1__zle__eq,axiom,
% 5.25/5.47 ! [W: int,Z: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 5.25/5.47 = ( ord_less_int @ W @ Z ) ) ).
% 5.25/5.47
% 5.25/5.47 % add1_zle_eq
% 5.25/5.47 thf(fact_2409_int__ge__induct,axiom,
% 5.25/5.47 ! [K: int,I2: int,P: int > $o] :
% 5.25/5.47 ( ( ord_less_eq_int @ K @ I2 )
% 5.25/5.47 => ( ( P @ K )
% 5.25/5.47 => ( ! [I4: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ K @ I4 )
% 5.25/5.47 => ( ( P @ I4 )
% 5.25/5.47 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 5.25/5.47 => ( P @ I2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % int_ge_induct
% 5.25/5.47 thf(fact_2410_int__gr__induct,axiom,
% 5.25/5.47 ! [K: int,I2: int,P: int > $o] :
% 5.25/5.47 ( ( ord_less_int @ K @ I2 )
% 5.25/5.47 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.25/5.47 => ( ! [I4: int] :
% 5.25/5.47 ( ( ord_less_int @ K @ I4 )
% 5.25/5.47 => ( ( P @ I4 )
% 5.25/5.47 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 5.25/5.47 => ( P @ I2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % int_gr_induct
% 5.25/5.47 thf(fact_2411_le__imp__0__less,axiom,
% 5.25/5.47 ! [Z: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.47 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % le_imp_0_less
% 5.25/5.47 thf(fact_2412_zless__add1__eq,axiom,
% 5.25/5.47 ! [W: int,Z: int] :
% 5.25/5.47 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.25/5.47 = ( ( ord_less_int @ W @ Z )
% 5.25/5.47 | ( W = Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % zless_add1_eq
% 5.25/5.47 thf(fact_2413_split__zmod,axiom,
% 5.25/5.47 ! [P: int > $o,N: int,K: int] :
% 5.25/5.47 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 5.25/5.47 = ( ( ( K = zero_zero_int )
% 5.25/5.47 => ( P @ N ) )
% 5.25/5.47 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.47 => ! [I3: int,J3: int] :
% 5.25/5.47 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.25/5.47 & ( ord_less_int @ J3 @ K )
% 5.25/5.47 & ( N
% 5.25/5.47 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.25/5.47 => ( P @ J3 ) ) )
% 5.25/5.47 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.25/5.47 => ! [I3: int,J3: int] :
% 5.25/5.47 ( ( ( ord_less_int @ K @ J3 )
% 5.25/5.47 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.25/5.47 & ( N
% 5.25/5.47 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.25/5.47 => ( P @ J3 ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % split_zmod
% 5.25/5.47 thf(fact_2414_odd__less__0__iff,axiom,
% 5.25/5.47 ! [Z: int] :
% 5.25/5.47 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 5.25/5.47 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.25/5.47
% 5.25/5.47 % odd_less_0_iff
% 5.25/5.47 thf(fact_2415_q__pos__lemma,axiom,
% 5.25/5.47 ! [B4: int,Q5: int,R4: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.25/5.47 => ( ( ord_less_int @ R4 @ B4 )
% 5.25/5.47 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.25/5.47 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % q_pos_lemma
% 5.25/5.47 thf(fact_2416_zmult__zless__mono2,axiom,
% 5.25/5.47 ! [I2: int,J2: int,K: int] :
% 5.25/5.47 ( ( ord_less_int @ I2 @ J2 )
% 5.25/5.47 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.47 => ( ord_less_int @ ( times_times_int @ K @ I2 ) @ ( times_times_int @ K @ J2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % zmult_zless_mono2
% 5.25/5.47 thf(fact_2417_int__mod__neg__eq,axiom,
% 5.25/5.47 ! [A: int,B: int,Q2: int,R2: int] :
% 5.25/5.47 ( ( A
% 5.25/5.47 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.25/5.47 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.25/5.47 => ( ( ord_less_int @ B @ R2 )
% 5.25/5.47 => ( ( modulo_modulo_int @ A @ B )
% 5.25/5.47 = R2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % int_mod_neg_eq
% 5.25/5.47 thf(fact_2418_int__mod__pos__eq,axiom,
% 5.25/5.47 ! [A: int,B: int,Q2: int,R2: int] :
% 5.25/5.47 ( ( A
% 5.25/5.47 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.25/5.47 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.25/5.47 => ( ( ord_less_int @ R2 @ B )
% 5.25/5.47 => ( ( modulo_modulo_int @ A @ B )
% 5.25/5.47 = R2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % int_mod_pos_eq
% 5.25/5.47 thf(fact_2419_pos__zmult__eq__1__iff,axiom,
% 5.25/5.47 ! [M: int,N: int] :
% 5.25/5.47 ( ( ord_less_int @ zero_zero_int @ M )
% 5.25/5.47 => ( ( ( times_times_int @ M @ N )
% 5.25/5.47 = one_one_int )
% 5.25/5.47 = ( ( M = one_one_int )
% 5.25/5.47 & ( N = one_one_int ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pos_zmult_eq_1_iff
% 5.25/5.47 thf(fact_2420_zless__imp__add1__zle,axiom,
% 5.25/5.47 ! [W: int,Z: int] :
% 5.25/5.47 ( ( ord_less_int @ W @ Z )
% 5.25/5.47 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 5.25/5.47
% 5.25/5.47 % zless_imp_add1_zle
% 5.25/5.47 thf(fact_2421_zdiv__mono2__lemma,axiom,
% 5.25/5.47 ! [B: int,Q2: int,R2: int,B4: int,Q5: int,R4: int] :
% 5.25/5.47 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 5.25/5.47 = ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.25/5.47 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.25/5.47 => ( ( ord_less_int @ R4 @ B4 )
% 5.25/5.47 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.25/5.47 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.25/5.47 => ( ( ord_less_eq_int @ B4 @ B )
% 5.25/5.47 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % zdiv_mono2_lemma
% 5.25/5.47 thf(fact_2422_zdiv__mono2__neg__lemma,axiom,
% 5.25/5.47 ! [B: int,Q2: int,R2: int,B4: int,Q5: int,R4: int] :
% 5.25/5.47 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 5.25/5.47 = ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.25/5.47 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) @ zero_zero_int )
% 5.25/5.47 => ( ( ord_less_int @ R2 @ B )
% 5.25/5.47 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.25/5.47 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.25/5.47 => ( ( ord_less_eq_int @ B4 @ B )
% 5.25/5.47 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % zdiv_mono2_neg_lemma
% 5.25/5.47 thf(fact_2423_int__one__le__iff__zero__less,axiom,
% 5.25/5.47 ! [Z: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ one_one_int @ Z )
% 5.25/5.47 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.25/5.47
% 5.25/5.47 % int_one_le_iff_zero_less
% 5.25/5.47 thf(fact_2424_unique__quotient__lemma,axiom,
% 5.25/5.47 ! [B: int,Q5: int,R4: int,Q2: int,R2: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.25/5.47 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.25/5.47 => ( ( ord_less_int @ R4 @ B )
% 5.25/5.47 => ( ( ord_less_int @ R2 @ B )
% 5.25/5.47 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % unique_quotient_lemma
% 5.25/5.47 thf(fact_2425_unique__quotient__lemma__neg,axiom,
% 5.25/5.47 ! [B: int,Q5: int,R4: int,Q2: int,R2: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.25/5.47 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.25/5.47 => ( ( ord_less_int @ B @ R2 )
% 5.25/5.47 => ( ( ord_less_int @ B @ R4 )
% 5.25/5.47 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % unique_quotient_lemma_neg
% 5.25/5.47 thf(fact_2426_odd__nonzero,axiom,
% 5.25/5.47 ! [Z: int] :
% 5.25/5.47 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 5.25/5.47 != zero_zero_int ) ).
% 5.25/5.47
% 5.25/5.47 % odd_nonzero
% 5.25/5.47 thf(fact_2427_times__int__code_I2_J,axiom,
% 5.25/5.47 ! [L2: int] :
% 5.25/5.47 ( ( times_times_int @ zero_zero_int @ L2 )
% 5.25/5.47 = zero_zero_int ) ).
% 5.25/5.47
% 5.25/5.47 % times_int_code(2)
% 5.25/5.47 thf(fact_2428_times__int__code_I1_J,axiom,
% 5.25/5.47 ! [K: int] :
% 5.25/5.47 ( ( times_times_int @ K @ zero_zero_int )
% 5.25/5.47 = zero_zero_int ) ).
% 5.25/5.47
% 5.25/5.47 % times_int_code(1)
% 5.25/5.47 thf(fact_2429_zero__one__enat__neq_I1_J,axiom,
% 5.25/5.47 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.25/5.47
% 5.25/5.47 % zero_one_enat_neq(1)
% 5.25/5.47 thf(fact_2430_zmod__eq__0D,axiom,
% 5.25/5.47 ! [M: int,D: int] :
% 5.25/5.47 ( ( ( modulo_modulo_int @ M @ D )
% 5.25/5.47 = zero_zero_int )
% 5.25/5.47 => ? [Q3: int] :
% 5.25/5.47 ( M
% 5.25/5.47 = ( times_times_int @ D @ Q3 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % zmod_eq_0D
% 5.25/5.47 thf(fact_2431_zmod__eq__0__iff,axiom,
% 5.25/5.47 ! [M: int,D: int] :
% 5.25/5.47 ( ( ( modulo_modulo_int @ M @ D )
% 5.25/5.47 = zero_zero_int )
% 5.25/5.47 = ( ? [Q4: int] :
% 5.25/5.47 ( M
% 5.25/5.47 = ( times_times_int @ D @ Q4 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % zmod_eq_0_iff
% 5.25/5.47 thf(fact_2432_imult__is__0,axiom,
% 5.25/5.47 ! [M: extended_enat,N: extended_enat] :
% 5.25/5.47 ( ( ( times_7803423173614009249d_enat @ M @ N )
% 5.25/5.47 = zero_z5237406670263579293d_enat )
% 5.25/5.47 = ( ( M = zero_z5237406670263579293d_enat )
% 5.25/5.47 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % imult_is_0
% 5.25/5.47 thf(fact_2433_signed__take__bit__mult,axiom,
% 5.25/5.47 ! [N: nat,K: int,L2: int] :
% 5.25/5.47 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.25/5.47 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % signed_take_bit_mult
% 5.25/5.47 thf(fact_2434_plus__int__code_I2_J,axiom,
% 5.25/5.47 ! [L2: int] :
% 5.25/5.47 ( ( plus_plus_int @ zero_zero_int @ L2 )
% 5.25/5.47 = L2 ) ).
% 5.25/5.47
% 5.25/5.47 % plus_int_code(2)
% 5.25/5.47 thf(fact_2435_plus__int__code_I1_J,axiom,
% 5.25/5.47 ! [K: int] :
% 5.25/5.47 ( ( plus_plus_int @ K @ zero_zero_int )
% 5.25/5.47 = K ) ).
% 5.25/5.47
% 5.25/5.47 % plus_int_code(1)
% 5.25/5.47 thf(fact_2436_iadd__is__0,axiom,
% 5.25/5.47 ! [M: extended_enat,N: extended_enat] :
% 5.25/5.47 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 5.25/5.47 = zero_z5237406670263579293d_enat )
% 5.25/5.47 = ( ( M = zero_z5237406670263579293d_enat )
% 5.25/5.47 & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % iadd_is_0
% 5.25/5.47 thf(fact_2437_signed__take__bit__add,axiom,
% 5.25/5.47 ! [N: nat,K: int,L2: int] :
% 5.25/5.47 ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.25/5.47 = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % signed_take_bit_add
% 5.25/5.47 thf(fact_2438_mod__pos__neg__trivial,axiom,
% 5.25/5.47 ! [K: int,L2: int] :
% 5.25/5.47 ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.47 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.25/5.47 => ( ( modulo_modulo_int @ K @ L2 )
% 5.25/5.47 = ( plus_plus_int @ K @ L2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mod_pos_neg_trivial
% 5.25/5.47 thf(fact_2439_set__bit__greater__eq,axiom,
% 5.25/5.47 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_bit_greater_eq
% 5.25/5.47 thf(fact_2440_Euclidean__Division_Opos__mod__bound,axiom,
% 5.25/5.47 ! [L2: int,K: int] :
% 5.25/5.47 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.25/5.47 => ( ord_less_int @ ( modulo_modulo_int @ K @ L2 ) @ L2 ) ) ).
% 5.25/5.47
% 5.25/5.47 % Euclidean_Division.pos_mod_bound
% 5.25/5.47 thf(fact_2441_neg__mod__bound,axiom,
% 5.25/5.47 ! [L2: int,K: int] :
% 5.25/5.47 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.25/5.47 => ( ord_less_int @ L2 @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % neg_mod_bound
% 5.25/5.47 thf(fact_2442_unset__bit__less__eq,axiom,
% 5.25/5.47 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 5.25/5.47
% 5.25/5.47 % unset_bit_less_eq
% 5.25/5.47 thf(fact_2443_Euclidean__Division_Opos__mod__sign,axiom,
% 5.25/5.47 ! [L2: int,K: int] :
% 5.25/5.47 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.25/5.47 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % Euclidean_Division.pos_mod_sign
% 5.25/5.47 thf(fact_2444_neg__mod__sign,axiom,
% 5.25/5.47 ! [L2: int,K: int] :
% 5.25/5.47 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.25/5.47 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L2 ) @ zero_zero_int ) ) ).
% 5.25/5.47
% 5.25/5.47 % neg_mod_sign
% 5.25/5.47 thf(fact_2445_zmod__le__nonneg__dividend,axiom,
% 5.25/5.47 ! [M: int,K: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.25/5.47 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 5.25/5.47
% 5.25/5.47 % zmod_le_nonneg_dividend
% 5.25/5.47 thf(fact_2446_zmod__trivial__iff,axiom,
% 5.25/5.47 ! [I2: int,K: int] :
% 5.25/5.47 ( ( ( modulo_modulo_int @ I2 @ K )
% 5.25/5.47 = I2 )
% 5.25/5.47 = ( ( K = zero_zero_int )
% 5.25/5.47 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.25/5.47 & ( ord_less_int @ I2 @ K ) )
% 5.25/5.47 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 5.25/5.47 & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % zmod_trivial_iff
% 5.25/5.47 thf(fact_2447_verit__la__generic,axiom,
% 5.25/5.47 ! [A: int,X3: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ A @ X3 )
% 5.25/5.47 | ( A = X3 )
% 5.25/5.47 | ( ord_less_eq_int @ X3 @ A ) ) ).
% 5.25/5.47
% 5.25/5.47 % verit_la_generic
% 5.25/5.47 thf(fact_2448_pos__mod__conj,axiom,
% 5.25/5.47 ! [B: int,A: int] :
% 5.25/5.47 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.47 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 5.25/5.47 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pos_mod_conj
% 5.25/5.47 thf(fact_2449_neg__mod__conj,axiom,
% 5.25/5.47 ! [B: int,A: int] :
% 5.25/5.47 ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.47 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 5.25/5.47 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % neg_mod_conj
% 5.25/5.47 thf(fact_2450_less__eq__int__code_I1_J,axiom,
% 5.25/5.47 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.25/5.47
% 5.25/5.47 % less_eq_int_code(1)
% 5.25/5.47 thf(fact_2451_int__distrib_I2_J,axiom,
% 5.25/5.47 ! [W: int,Z1: int,Z22: int] :
% 5.25/5.47 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 5.25/5.47 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % int_distrib(2)
% 5.25/5.47 thf(fact_2452_int__distrib_I1_J,axiom,
% 5.25/5.47 ! [Z1: int,Z22: int,W: int] :
% 5.25/5.47 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 5.25/5.47 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % int_distrib(1)
% 5.25/5.47 thf(fact_2453_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.25/5.47 ! [X3: produc3368934014287244435at_num] :
% 5.25/5.47 ~ ! [F2: nat > num > num,A5: nat,B5: nat,Acc: num] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc851828971589881931at_num @ F2 @ ( produc1195630363706982562at_num @ A5 @ ( product_Pair_nat_num @ B5 @ Acc ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % fold_atLeastAtMost_nat.cases
% 5.25/5.47 thf(fact_2454_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.25/5.47 ! [X3: produc4471711990508489141at_nat] :
% 5.25/5.47 ~ ! [F2: nat > nat > nat,A5: nat,B5: nat,Acc: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A5 @ ( product_Pair_nat_nat @ B5 @ Acc ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % fold_atLeastAtMost_nat.cases
% 5.25/5.47 thf(fact_2455_vebt__buildup_Ocases,axiom,
% 5.25/5.47 ! [X3: nat] :
% 5.25/5.47 ( ( X3 != zero_zero_nat )
% 5.25/5.47 => ( ( X3
% 5.25/5.47 != ( suc @ zero_zero_nat ) )
% 5.25/5.47 => ~ ! [Va: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % vebt_buildup.cases
% 5.25/5.47 thf(fact_2456_mult__less__iff1,axiom,
% 5.25/5.47 ! [Z: real,X3: real,Y: real] :
% 5.25/5.47 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.25/5.47 => ( ( ord_less_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ Y @ Z ) )
% 5.25/5.47 = ( ord_less_real @ X3 @ Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_less_iff1
% 5.25/5.47 thf(fact_2457_mult__less__iff1,axiom,
% 5.25/5.47 ! [Z: rat,X3: rat,Y: rat] :
% 5.25/5.47 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.25/5.47 => ( ( ord_less_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 5.25/5.47 = ( ord_less_rat @ X3 @ Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_less_iff1
% 5.25/5.47 thf(fact_2458_mult__less__iff1,axiom,
% 5.25/5.47 ! [Z: int,X3: int,Y: int] :
% 5.25/5.47 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.25/5.47 => ( ( ord_less_int @ ( times_times_int @ X3 @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.25/5.47 = ( ord_less_int @ X3 @ Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_less_iff1
% 5.25/5.47 thf(fact_2459_vebt__member_Osimps_I3_J,axiom,
% 5.25/5.47 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X3: nat] :
% 5.25/5.47 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X3 ) ).
% 5.25/5.47
% 5.25/5.47 % vebt_member.simps(3)
% 5.25/5.47 thf(fact_2460_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 5.25/5.47 ! [Uz: product_prod_nat_nat,Va2: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.25/5.47 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va2 @ Vb @ Vc ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.minNull.simps(5)
% 5.25/5.47 thf(fact_2461_incr__mult__lemma,axiom,
% 5.25/5.47 ! [D: int,P: int > $o,K: int] :
% 5.25/5.47 ( ( ord_less_int @ zero_zero_int @ D )
% 5.25/5.47 => ( ! [X5: int] :
% 5.25/5.47 ( ( P @ X5 )
% 5.25/5.47 => ( P @ ( plus_plus_int @ X5 @ D ) ) )
% 5.25/5.47 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.47 => ! [X: int] :
% 5.25/5.47 ( ( P @ X )
% 5.25/5.47 => ( P @ ( plus_plus_int @ X @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % incr_mult_lemma
% 5.25/5.47 thf(fact_2462_buildup__nothing__in__leaf,axiom,
% 5.25/5.47 ! [N: nat,X3: nat] :
% 5.25/5.47 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X3 ) ).
% 5.25/5.47
% 5.25/5.47 % buildup_nothing_in_leaf
% 5.25/5.47 thf(fact_2463_invar__vebt_Ointros_I3_J,axiom,
% 5.25/5.47 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.25/5.47 ( ! [X5: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X5 @ N ) )
% 5.25/5.47 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.25/5.47 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.47 => ( ( M
% 5.25/5.47 = ( suc @ N ) )
% 5.25/5.47 => ( ( Deg
% 5.25/5.47 = ( plus_plus_nat @ N @ M ) )
% 5.25/5.47 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 5.25/5.47 => ( ! [X5: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.47 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % invar_vebt.intros(3)
% 5.25/5.47 thf(fact_2464_pos__eucl__rel__int__mult__2,axiom,
% 5.25/5.47 ! [B: int,A: int,Q2: int,R2: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.47 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.25/5.47 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pos_eucl_rel_int_mult_2
% 5.25/5.47 thf(fact_2465_insert__simp__excp,axiom,
% 5.25/5.47 ! [Mi: nat,Deg: nat,TreeList: list_VEBT_VEBT,X3: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.25/5.47 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.25/5.47 => ( ( ord_less_nat @ X3 @ Mi )
% 5.25/5.47 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.25/5.47 => ( ( X3 != Ma )
% 5.25/5.47 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X3 )
% 5.25/5.47 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X3 @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % insert_simp_excp
% 5.25/5.47 thf(fact_2466_insert__simp__norm,axiom,
% 5.25/5.47 ! [X3: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.25/5.47 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.25/5.47 => ( ( ord_less_nat @ Mi @ X3 )
% 5.25/5.47 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.25/5.47 => ( ( X3 != Ma )
% 5.25/5.47 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X3 )
% 5.25/5.47 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X3 @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % insert_simp_norm
% 5.25/5.47 thf(fact_2467_Leaf__0__not,axiom,
% 5.25/5.47 ! [A: $o,B: $o] :
% 5.25/5.47 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 5.25/5.47
% 5.25/5.47 % Leaf_0_not
% 5.25/5.47 thf(fact_2468_deg__1__Leafy,axiom,
% 5.25/5.47 ! [T: vEBT_VEBT,N: nat] :
% 5.25/5.47 ( ( vEBT_invar_vebt @ T @ N )
% 5.25/5.47 => ( ( N = one_one_nat )
% 5.25/5.47 => ? [A5: $o,B5: $o] :
% 5.25/5.47 ( T
% 5.25/5.47 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % deg_1_Leafy
% 5.25/5.47 thf(fact_2469_deg__1__Leaf,axiom,
% 5.25/5.47 ! [T: vEBT_VEBT] :
% 5.25/5.47 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.25/5.47 => ? [A5: $o,B5: $o] :
% 5.25/5.47 ( T
% 5.25/5.47 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % deg_1_Leaf
% 5.25/5.47 thf(fact_2470_deg1Leaf,axiom,
% 5.25/5.47 ! [T: vEBT_VEBT] :
% 5.25/5.47 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.25/5.47 = ( ? [A3: $o,B2: $o] :
% 5.25/5.47 ( T
% 5.25/5.47 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % deg1Leaf
% 5.25/5.47 thf(fact_2471_list__update__overwrite,axiom,
% 5.25/5.47 ! [Xs: list_VEBT_VEBT,I2: nat,X3: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.25/5.47 ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X3 ) @ I2 @ Y )
% 5.25/5.47 = ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % list_update_overwrite
% 5.25/5.47 thf(fact_2472_length__list__update,axiom,
% 5.25/5.47 ! [Xs: list_VEBT_VEBT,I2: nat,X3: vEBT_VEBT] :
% 5.25/5.47 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X3 ) )
% 5.25/5.47 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 5.25/5.47
% 5.25/5.47 % length_list_update
% 5.25/5.47 thf(fact_2473_length__list__update,axiom,
% 5.25/5.47 ! [Xs: list_o,I2: nat,X3: $o] :
% 5.25/5.47 ( ( size_size_list_o @ ( list_update_o @ Xs @ I2 @ X3 ) )
% 5.25/5.47 = ( size_size_list_o @ Xs ) ) ).
% 5.25/5.47
% 5.25/5.47 % length_list_update
% 5.25/5.47 thf(fact_2474_length__list__update,axiom,
% 5.25/5.47 ! [Xs: list_nat,I2: nat,X3: nat] :
% 5.25/5.47 ( ( size_size_list_nat @ ( list_update_nat @ Xs @ I2 @ X3 ) )
% 5.25/5.47 = ( size_size_list_nat @ Xs ) ) ).
% 5.25/5.47
% 5.25/5.47 % length_list_update
% 5.25/5.47 thf(fact_2475_length__list__update,axiom,
% 5.25/5.47 ! [Xs: list_int,I2: nat,X3: int] :
% 5.25/5.47 ( ( size_size_list_int @ ( list_update_int @ Xs @ I2 @ X3 ) )
% 5.25/5.47 = ( size_size_list_int @ Xs ) ) ).
% 5.25/5.47
% 5.25/5.47 % length_list_update
% 5.25/5.47 thf(fact_2476_max__Suc__Suc,axiom,
% 5.25/5.47 ! [M: nat,N: nat] :
% 5.25/5.47 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.25/5.47 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_Suc_Suc
% 5.25/5.47 thf(fact_2477_max__0R,axiom,
% 5.25/5.47 ! [N: nat] :
% 5.25/5.47 ( ( ord_max_nat @ N @ zero_zero_nat )
% 5.25/5.47 = N ) ).
% 5.25/5.47
% 5.25/5.47 % max_0R
% 5.25/5.47 thf(fact_2478_max__0L,axiom,
% 5.25/5.47 ! [N: nat] :
% 5.25/5.47 ( ( ord_max_nat @ zero_zero_nat @ N )
% 5.25/5.47 = N ) ).
% 5.25/5.47
% 5.25/5.47 % max_0L
% 5.25/5.47 thf(fact_2479_max__nat_Oright__neutral,axiom,
% 5.25/5.47 ! [A: nat] :
% 5.25/5.47 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.25/5.47 = A ) ).
% 5.25/5.47
% 5.25/5.47 % max_nat.right_neutral
% 5.25/5.47 thf(fact_2480_max__nat_Oneutr__eq__iff,axiom,
% 5.25/5.47 ! [A: nat,B: nat] :
% 5.25/5.47 ( ( zero_zero_nat
% 5.25/5.47 = ( ord_max_nat @ A @ B ) )
% 5.25/5.47 = ( ( A = zero_zero_nat )
% 5.25/5.47 & ( B = zero_zero_nat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_nat.neutr_eq_iff
% 5.25/5.47 thf(fact_2481_max__nat_Oleft__neutral,axiom,
% 5.25/5.47 ! [A: nat] :
% 5.25/5.47 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.25/5.47 = A ) ).
% 5.25/5.47
% 5.25/5.47 % max_nat.left_neutral
% 5.25/5.47 thf(fact_2482_max__nat_Oeq__neutr__iff,axiom,
% 5.25/5.47 ! [A: nat,B: nat] :
% 5.25/5.47 ( ( ( ord_max_nat @ A @ B )
% 5.25/5.47 = zero_zero_nat )
% 5.25/5.47 = ( ( A = zero_zero_nat )
% 5.25/5.47 & ( B = zero_zero_nat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_nat.eq_neutr_iff
% 5.25/5.47 thf(fact_2483_nth__list__update__neq,axiom,
% 5.25/5.47 ! [I2: nat,J2: nat,Xs: list_nat,X3: nat] :
% 5.25/5.47 ( ( I2 != J2 )
% 5.25/5.47 => ( ( nth_nat @ ( list_update_nat @ Xs @ I2 @ X3 ) @ J2 )
% 5.25/5.47 = ( nth_nat @ Xs @ J2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nth_list_update_neq
% 5.25/5.47 thf(fact_2484_nth__list__update__neq,axiom,
% 5.25/5.47 ! [I2: nat,J2: nat,Xs: list_int,X3: int] :
% 5.25/5.47 ( ( I2 != J2 )
% 5.25/5.47 => ( ( nth_int @ ( list_update_int @ Xs @ I2 @ X3 ) @ J2 )
% 5.25/5.47 = ( nth_int @ Xs @ J2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nth_list_update_neq
% 5.25/5.47 thf(fact_2485_nth__list__update__neq,axiom,
% 5.25/5.47 ! [I2: nat,J2: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 5.25/5.47 ( ( I2 != J2 )
% 5.25/5.47 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X3 ) @ J2 )
% 5.25/5.47 = ( nth_VEBT_VEBT @ Xs @ J2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nth_list_update_neq
% 5.25/5.47 thf(fact_2486_list__update__id,axiom,
% 5.25/5.47 ! [Xs: list_nat,I2: nat] :
% 5.25/5.47 ( ( list_update_nat @ Xs @ I2 @ ( nth_nat @ Xs @ I2 ) )
% 5.25/5.47 = Xs ) ).
% 5.25/5.47
% 5.25/5.47 % list_update_id
% 5.25/5.47 thf(fact_2487_list__update__id,axiom,
% 5.25/5.47 ! [Xs: list_int,I2: nat] :
% 5.25/5.47 ( ( list_update_int @ Xs @ I2 @ ( nth_int @ Xs @ I2 ) )
% 5.25/5.47 = Xs ) ).
% 5.25/5.47
% 5.25/5.47 % list_update_id
% 5.25/5.47 thf(fact_2488_list__update__id,axiom,
% 5.25/5.47 ! [Xs: list_VEBT_VEBT,I2: nat] :
% 5.25/5.47 ( ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ ( nth_VEBT_VEBT @ Xs @ I2 ) )
% 5.25/5.47 = Xs ) ).
% 5.25/5.47
% 5.25/5.47 % list_update_id
% 5.25/5.47 thf(fact_2489_max__number__of_I1_J,axiom,
% 5.25/5.47 ! [U: num,V: num] :
% 5.25/5.47 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.25/5.47 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.25/5.47 = ( numera1916890842035813515d_enat @ V ) ) )
% 5.25/5.47 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.25/5.47 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.25/5.47 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_number_of(1)
% 5.25/5.47 thf(fact_2490_max__number__of_I1_J,axiom,
% 5.25/5.47 ! [U: num,V: num] :
% 5.25/5.47 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.25/5.47 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.25/5.47 = ( numeral_numeral_real @ V ) ) )
% 5.25/5.47 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.25/5.47 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.25/5.47 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_number_of(1)
% 5.25/5.47 thf(fact_2491_max__number__of_I1_J,axiom,
% 5.25/5.47 ! [U: num,V: num] :
% 5.25/5.47 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.25/5.47 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.25/5.47 = ( numeral_numeral_rat @ V ) ) )
% 5.25/5.47 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.25/5.47 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.25/5.47 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_number_of(1)
% 5.25/5.47 thf(fact_2492_max__number__of_I1_J,axiom,
% 5.25/5.47 ! [U: num,V: num] :
% 5.25/5.47 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.25/5.47 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.25/5.47 = ( numeral_numeral_nat @ V ) ) )
% 5.25/5.47 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.25/5.47 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.25/5.47 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_number_of(1)
% 5.25/5.47 thf(fact_2493_max__number__of_I1_J,axiom,
% 5.25/5.47 ! [U: num,V: num] :
% 5.25/5.47 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.25/5.47 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.25/5.47 = ( numeral_numeral_int @ V ) ) )
% 5.25/5.47 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.25/5.47 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.25/5.47 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_number_of(1)
% 5.25/5.47 thf(fact_2494_max__0__1_I4_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X3 ) @ zero_z5237406670263579293d_enat )
% 5.25/5.47 = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(4)
% 5.25/5.47 thf(fact_2495_max__0__1_I4_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_real @ ( numeral_numeral_real @ X3 ) @ zero_zero_real )
% 5.25/5.47 = ( numeral_numeral_real @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(4)
% 5.25/5.47 thf(fact_2496_max__0__1_I4_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_rat @ ( numeral_numeral_rat @ X3 ) @ zero_zero_rat )
% 5.25/5.47 = ( numeral_numeral_rat @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(4)
% 5.25/5.47 thf(fact_2497_max__0__1_I4_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_nat @ ( numeral_numeral_nat @ X3 ) @ zero_zero_nat )
% 5.25/5.47 = ( numeral_numeral_nat @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(4)
% 5.25/5.47 thf(fact_2498_max__0__1_I4_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_int @ ( numeral_numeral_int @ X3 ) @ zero_zero_int )
% 5.25/5.47 = ( numeral_numeral_int @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(4)
% 5.25/5.47 thf(fact_2499_max__0__1_I3_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X3 ) )
% 5.25/5.47 = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(3)
% 5.25/5.47 thf(fact_2500_max__0__1_I3_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X3 ) )
% 5.25/5.47 = ( numeral_numeral_real @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(3)
% 5.25/5.47 thf(fact_2501_max__0__1_I3_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X3 ) )
% 5.25/5.47 = ( numeral_numeral_rat @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(3)
% 5.25/5.47 thf(fact_2502_max__0__1_I3_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X3 ) )
% 5.25/5.47 = ( numeral_numeral_nat @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(3)
% 5.25/5.47 thf(fact_2503_max__0__1_I3_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X3 ) )
% 5.25/5.47 = ( numeral_numeral_int @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(3)
% 5.25/5.47 thf(fact_2504_max__0__1_I2_J,axiom,
% 5.25/5.47 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 5.25/5.47 = one_one_real ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(2)
% 5.25/5.47 thf(fact_2505_max__0__1_I2_J,axiom,
% 5.25/5.47 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 5.25/5.47 = one_one_rat ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(2)
% 5.25/5.47 thf(fact_2506_max__0__1_I2_J,axiom,
% 5.25/5.47 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 5.25/5.47 = one_one_nat ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(2)
% 5.25/5.47 thf(fact_2507_max__0__1_I2_J,axiom,
% 5.25/5.47 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 5.25/5.47 = one_on7984719198319812577d_enat ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(2)
% 5.25/5.47 thf(fact_2508_max__0__1_I2_J,axiom,
% 5.25/5.47 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 5.25/5.47 = one_one_int ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(2)
% 5.25/5.47 thf(fact_2509_max__0__1_I1_J,axiom,
% 5.25/5.47 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 5.25/5.47 = one_one_real ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(1)
% 5.25/5.47 thf(fact_2510_max__0__1_I1_J,axiom,
% 5.25/5.47 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 5.25/5.47 = one_one_rat ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(1)
% 5.25/5.47 thf(fact_2511_max__0__1_I1_J,axiom,
% 5.25/5.47 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 5.25/5.47 = one_one_nat ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(1)
% 5.25/5.47 thf(fact_2512_max__0__1_I1_J,axiom,
% 5.25/5.47 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 5.25/5.47 = one_on7984719198319812577d_enat ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(1)
% 5.25/5.47 thf(fact_2513_max__0__1_I1_J,axiom,
% 5.25/5.47 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 5.25/5.47 = one_one_int ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(1)
% 5.25/5.47 thf(fact_2514_max__0__1_I6_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X3 ) @ one_on7984719198319812577d_enat )
% 5.25/5.47 = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(6)
% 5.25/5.47 thf(fact_2515_max__0__1_I6_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_real @ ( numeral_numeral_real @ X3 ) @ one_one_real )
% 5.25/5.47 = ( numeral_numeral_real @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(6)
% 5.25/5.47 thf(fact_2516_max__0__1_I6_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_rat @ ( numeral_numeral_rat @ X3 ) @ one_one_rat )
% 5.25/5.47 = ( numeral_numeral_rat @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(6)
% 5.25/5.47 thf(fact_2517_max__0__1_I6_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_nat @ ( numeral_numeral_nat @ X3 ) @ one_one_nat )
% 5.25/5.47 = ( numeral_numeral_nat @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(6)
% 5.25/5.47 thf(fact_2518_max__0__1_I6_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_int @ ( numeral_numeral_int @ X3 ) @ one_one_int )
% 5.25/5.47 = ( numeral_numeral_int @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(6)
% 5.25/5.47 thf(fact_2519_max__0__1_I5_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X3 ) )
% 5.25/5.47 = ( numera1916890842035813515d_enat @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(5)
% 5.25/5.47 thf(fact_2520_max__0__1_I5_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X3 ) )
% 5.25/5.47 = ( numeral_numeral_real @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(5)
% 5.25/5.47 thf(fact_2521_max__0__1_I5_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X3 ) )
% 5.25/5.47 = ( numeral_numeral_rat @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(5)
% 5.25/5.47 thf(fact_2522_max__0__1_I5_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X3 ) )
% 5.25/5.47 = ( numeral_numeral_nat @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(5)
% 5.25/5.47 thf(fact_2523_max__0__1_I5_J,axiom,
% 5.25/5.47 ! [X3: num] :
% 5.25/5.47 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X3 ) )
% 5.25/5.47 = ( numeral_numeral_int @ X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_0_1(5)
% 5.25/5.47 thf(fact_2524_list__update__beyond,axiom,
% 5.25/5.47 ! [Xs: list_VEBT_VEBT,I2: nat,X3: vEBT_VEBT] :
% 5.25/5.47 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ I2 )
% 5.25/5.47 => ( ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X3 )
% 5.25/5.47 = Xs ) ) ).
% 5.25/5.47
% 5.25/5.47 % list_update_beyond
% 5.25/5.47 thf(fact_2525_list__update__beyond,axiom,
% 5.25/5.47 ! [Xs: list_o,I2: nat,X3: $o] :
% 5.25/5.47 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ I2 )
% 5.25/5.47 => ( ( list_update_o @ Xs @ I2 @ X3 )
% 5.25/5.47 = Xs ) ) ).
% 5.25/5.47
% 5.25/5.47 % list_update_beyond
% 5.25/5.47 thf(fact_2526_list__update__beyond,axiom,
% 5.25/5.47 ! [Xs: list_nat,I2: nat,X3: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I2 )
% 5.25/5.47 => ( ( list_update_nat @ Xs @ I2 @ X3 )
% 5.25/5.47 = Xs ) ) ).
% 5.25/5.47
% 5.25/5.47 % list_update_beyond
% 5.25/5.47 thf(fact_2527_list__update__beyond,axiom,
% 5.25/5.47 ! [Xs: list_int,I2: nat,X3: int] :
% 5.25/5.47 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ I2 )
% 5.25/5.47 => ( ( list_update_int @ Xs @ I2 @ X3 )
% 5.25/5.47 = Xs ) ) ).
% 5.25/5.47
% 5.25/5.47 % list_update_beyond
% 5.25/5.47 thf(fact_2528_nth__list__update__eq,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.47 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X3 ) @ I2 )
% 5.25/5.47 = X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % nth_list_update_eq
% 5.25/5.47 thf(fact_2529_nth__list__update__eq,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_o,X3: $o] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 5.25/5.47 => ( ( nth_o @ ( list_update_o @ Xs @ I2 @ X3 ) @ I2 )
% 5.25/5.47 = X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % nth_list_update_eq
% 5.25/5.47 thf(fact_2530_nth__list__update__eq,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_nat,X3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.47 => ( ( nth_nat @ ( list_update_nat @ Xs @ I2 @ X3 ) @ I2 )
% 5.25/5.47 = X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % nth_list_update_eq
% 5.25/5.47 thf(fact_2531_nth__list__update__eq,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_int,X3: int] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 5.25/5.47 => ( ( nth_int @ ( list_update_int @ Xs @ I2 @ X3 ) @ I2 )
% 5.25/5.47 = X3 ) ) ).
% 5.25/5.47
% 5.25/5.47 % nth_list_update_eq
% 5.25/5.47 thf(fact_2532_set__swap,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_VEBT_VEBT,J2: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.47 => ( ( ord_less_nat @ J2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.47 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ ( nth_VEBT_VEBT @ Xs @ J2 ) ) @ J2 @ ( nth_VEBT_VEBT @ Xs @ I2 ) ) )
% 5.25/5.47 = ( set_VEBT_VEBT2 @ Xs ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_swap
% 5.25/5.47 thf(fact_2533_set__swap,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_o,J2: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 5.25/5.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_o @ Xs ) )
% 5.25/5.47 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs @ I2 @ ( nth_o @ Xs @ J2 ) ) @ J2 @ ( nth_o @ Xs @ I2 ) ) )
% 5.25/5.47 = ( set_o2 @ Xs ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_swap
% 5.25/5.47 thf(fact_2534_set__swap,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_nat,J2: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.47 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I2 @ ( nth_nat @ Xs @ J2 ) ) @ J2 @ ( nth_nat @ Xs @ I2 ) ) )
% 5.25/5.47 = ( set_nat2 @ Xs ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_swap
% 5.25/5.47 thf(fact_2535_set__swap,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_int,J2: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 5.25/5.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs ) )
% 5.25/5.47 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs @ I2 @ ( nth_int @ Xs @ J2 ) ) @ J2 @ ( nth_int @ Xs @ I2 ) ) )
% 5.25/5.47 = ( set_int2 @ Xs ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_swap
% 5.25/5.47 thf(fact_2536_unique__quotient,axiom,
% 5.25/5.47 ! [A: int,B: int,Q2: int,R2: int,Q5: int,R4: int] :
% 5.25/5.47 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.25/5.47 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.25/5.47 => ( Q2 = Q5 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % unique_quotient
% 5.25/5.47 thf(fact_2537_unique__remainder,axiom,
% 5.25/5.47 ! [A: int,B: int,Q2: int,R2: int,Q5: int,R4: int] :
% 5.25/5.47 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.25/5.47 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.25/5.47 => ( R2 = R4 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % unique_remainder
% 5.25/5.47 thf(fact_2538_list__update__swap,axiom,
% 5.25/5.47 ! [I2: nat,I5: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT,X6: vEBT_VEBT] :
% 5.25/5.47 ( ( I2 != I5 )
% 5.25/5.47 => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X3 ) @ I5 @ X6 )
% 5.25/5.47 = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I5 @ X6 ) @ I2 @ X3 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % list_update_swap
% 5.25/5.47 thf(fact_2539_VEBT__internal_OminNull_Ocases,axiom,
% 5.25/5.47 ! [X3: vEBT_VEBT] :
% 5.25/5.47 ( ( X3
% 5.25/5.47 != ( vEBT_Leaf @ $false @ $false ) )
% 5.25/5.47 => ( ! [Uv: $o] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( vEBT_Leaf @ $true @ Uv ) )
% 5.25/5.47 => ( ! [Uu: $o] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( vEBT_Leaf @ Uu @ $true ) )
% 5.25/5.47 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) )
% 5.25/5.47 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.minNull.cases
% 5.25/5.47 thf(fact_2540_max__add__distrib__right,axiom,
% 5.25/5.47 ! [X3: real,Y: real,Z: real] :
% 5.25/5.47 ( ( plus_plus_real @ X3 @ ( ord_max_real @ Y @ Z ) )
% 5.25/5.47 = ( ord_max_real @ ( plus_plus_real @ X3 @ Y ) @ ( plus_plus_real @ X3 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_add_distrib_right
% 5.25/5.47 thf(fact_2541_max__add__distrib__right,axiom,
% 5.25/5.47 ! [X3: rat,Y: rat,Z: rat] :
% 5.25/5.47 ( ( plus_plus_rat @ X3 @ ( ord_max_rat @ Y @ Z ) )
% 5.25/5.47 = ( ord_max_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( plus_plus_rat @ X3 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_add_distrib_right
% 5.25/5.47 thf(fact_2542_max__add__distrib__right,axiom,
% 5.25/5.47 ! [X3: nat,Y: nat,Z: nat] :
% 5.25/5.47 ( ( plus_plus_nat @ X3 @ ( ord_max_nat @ Y @ Z ) )
% 5.25/5.47 = ( ord_max_nat @ ( plus_plus_nat @ X3 @ Y ) @ ( plus_plus_nat @ X3 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_add_distrib_right
% 5.25/5.47 thf(fact_2543_max__add__distrib__right,axiom,
% 5.25/5.47 ! [X3: int,Y: int,Z: int] :
% 5.25/5.47 ( ( plus_plus_int @ X3 @ ( ord_max_int @ Y @ Z ) )
% 5.25/5.47 = ( ord_max_int @ ( plus_plus_int @ X3 @ Y ) @ ( plus_plus_int @ X3 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_add_distrib_right
% 5.25/5.47 thf(fact_2544_max__add__distrib__left,axiom,
% 5.25/5.47 ! [X3: real,Y: real,Z: real] :
% 5.25/5.47 ( ( plus_plus_real @ ( ord_max_real @ X3 @ Y ) @ Z )
% 5.25/5.47 = ( ord_max_real @ ( plus_plus_real @ X3 @ Z ) @ ( plus_plus_real @ Y @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_add_distrib_left
% 5.25/5.47 thf(fact_2545_max__add__distrib__left,axiom,
% 5.25/5.47 ! [X3: rat,Y: rat,Z: rat] :
% 5.25/5.47 ( ( plus_plus_rat @ ( ord_max_rat @ X3 @ Y ) @ Z )
% 5.25/5.47 = ( ord_max_rat @ ( plus_plus_rat @ X3 @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_add_distrib_left
% 5.25/5.47 thf(fact_2546_max__add__distrib__left,axiom,
% 5.25/5.47 ! [X3: nat,Y: nat,Z: nat] :
% 5.25/5.47 ( ( plus_plus_nat @ ( ord_max_nat @ X3 @ Y ) @ Z )
% 5.25/5.47 = ( ord_max_nat @ ( plus_plus_nat @ X3 @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_add_distrib_left
% 5.25/5.47 thf(fact_2547_max__add__distrib__left,axiom,
% 5.25/5.47 ! [X3: int,Y: int,Z: int] :
% 5.25/5.47 ( ( plus_plus_int @ ( ord_max_int @ X3 @ Y ) @ Z )
% 5.25/5.47 = ( ord_max_int @ ( plus_plus_int @ X3 @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_add_distrib_left
% 5.25/5.47 thf(fact_2548_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 5.25/5.47 ! [X3: vEBT_VEBT] :
% 5.25/5.47 ( ( vEBT_VEBT_minNull @ X3 )
% 5.25/5.47 => ( ( X3
% 5.25/5.47 != ( vEBT_Leaf @ $false @ $false ) )
% 5.25/5.47 => ~ ! [Uw: nat,Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.minNull.elims(2)
% 5.25/5.47 thf(fact_2549_nat__add__max__right,axiom,
% 5.25/5.47 ! [M: nat,N: nat,Q2: nat] :
% 5.25/5.47 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.25/5.47 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nat_add_max_right
% 5.25/5.47 thf(fact_2550_nat__add__max__left,axiom,
% 5.25/5.47 ! [M: nat,N: nat,Q2: nat] :
% 5.25/5.47 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.25/5.47 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nat_add_max_left
% 5.25/5.47 thf(fact_2551_VEBT_Oexhaust,axiom,
% 5.25/5.47 ! [Y: vEBT_VEBT] :
% 5.25/5.47 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.25/5.47 ( Y
% 5.25/5.47 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.25/5.47 => ~ ! [X21: $o,X222: $o] :
% 5.25/5.47 ( Y
% 5.25/5.47 != ( vEBT_Leaf @ X21 @ X222 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT.exhaust
% 5.25/5.47 thf(fact_2552_VEBT_Odistinct_I1_J,axiom,
% 5.25/5.47 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X212: $o,X223: $o] :
% 5.25/5.47 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.25/5.47 != ( vEBT_Leaf @ X212 @ X223 ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT.distinct(1)
% 5.25/5.47 thf(fact_2553_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.25/5.47 ! [X3: produc9072475918466114483BT_nat] :
% 5.25/5.47 ( ! [Uu: $o,Uv: $o,D3: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ D3 ) )
% 5.25/5.47 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Deg3 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.valid'.cases
% 5.25/5.47 thf(fact_2554_nat__mult__max__right,axiom,
% 5.25/5.47 ! [M: nat,N: nat,Q2: nat] :
% 5.25/5.47 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.25/5.47 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nat_mult_max_right
% 5.25/5.47 thf(fact_2555_nat__mult__max__left,axiom,
% 5.25/5.47 ! [M: nat,N: nat,Q2: nat] :
% 5.25/5.47 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.25/5.47 = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nat_mult_max_left
% 5.25/5.47 thf(fact_2556_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.25/5.47 ! [A: $o,B: $o,X3: nat] :
% 5.25/5.47 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 5.25/5.47 = ( ( ( X3 = zero_zero_nat )
% 5.25/5.47 => A )
% 5.25/5.47 & ( ( X3 != zero_zero_nat )
% 5.25/5.47 => ( ( ( X3 = one_one_nat )
% 5.25/5.47 => B )
% 5.25/5.47 & ( X3 = one_one_nat ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.naive_member.simps(1)
% 5.25/5.47 thf(fact_2557_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 5.25/5.47 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.minNull.simps(1)
% 5.25/5.47 thf(fact_2558_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 5.25/5.47 ! [Uv2: $o] :
% 5.25/5.47 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv2 ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.minNull.simps(2)
% 5.25/5.47 thf(fact_2559_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 5.25/5.47 ! [Uu2: $o] :
% 5.25/5.47 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu2 @ $true ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.minNull.simps(3)
% 5.25/5.47 thf(fact_2560_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 5.25/5.47 ! [X3: vEBT_VEBT,Y: $o] :
% 5.25/5.47 ( ( ( vEBT_VEBT_minNull @ X3 )
% 5.25/5.47 = Y )
% 5.25/5.47 => ( ( ( X3
% 5.25/5.47 = ( vEBT_Leaf @ $false @ $false ) )
% 5.25/5.47 => ~ Y )
% 5.25/5.47 => ( ( ? [Uv: $o] :
% 5.25/5.47 ( X3
% 5.25/5.47 = ( vEBT_Leaf @ $true @ Uv ) )
% 5.25/5.47 => Y )
% 5.25/5.47 => ( ( ? [Uu: $o] :
% 5.25/5.47 ( X3
% 5.25/5.47 = ( vEBT_Leaf @ Uu @ $true ) )
% 5.25/5.47 => Y )
% 5.25/5.47 => ( ( ? [Uw: nat,Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.25/5.47 ( X3
% 5.25/5.47 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) )
% 5.25/5.47 => ~ Y )
% 5.25/5.47 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.25/5.47 ( X3
% 5.25/5.47 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.25/5.47 => Y ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.minNull.elims(1)
% 5.25/5.47 thf(fact_2561_eucl__rel__int__by0,axiom,
% 5.25/5.47 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 5.25/5.47
% 5.25/5.47 % eucl_rel_int_by0
% 5.25/5.47 thf(fact_2562_div__int__unique,axiom,
% 5.25/5.47 ! [K: int,L2: int,Q2: int,R2: int] :
% 5.25/5.47 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.25/5.47 => ( ( divide_divide_int @ K @ L2 )
% 5.25/5.47 = Q2 ) ) ).
% 5.25/5.47
% 5.25/5.47 % div_int_unique
% 5.25/5.47 thf(fact_2563_mod__int__unique,axiom,
% 5.25/5.47 ! [K: int,L2: int,Q2: int,R2: int] :
% 5.25/5.47 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.25/5.47 => ( ( modulo_modulo_int @ K @ L2 )
% 5.25/5.47 = R2 ) ) ).
% 5.25/5.47
% 5.25/5.47 % mod_int_unique
% 5.25/5.47 thf(fact_2564_set__update__subsetI,axiom,
% 5.25/5.47 ! [Xs: list_real,A2: set_real,X3: real,I2: nat] :
% 5.25/5.47 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 5.25/5.47 => ( ( member_real @ X3 @ A2 )
% 5.25/5.47 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I2 @ X3 ) ) @ A2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_update_subsetI
% 5.25/5.47 thf(fact_2565_set__update__subsetI,axiom,
% 5.25/5.47 ! [Xs: list_complex,A2: set_complex,X3: complex,I2: nat] :
% 5.25/5.47 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.25/5.47 => ( ( member_complex @ X3 @ A2 )
% 5.25/5.47 => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs @ I2 @ X3 ) ) @ A2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_update_subsetI
% 5.25/5.47 thf(fact_2566_set__update__subsetI,axiom,
% 5.25/5.47 ! [Xs: list_P6011104703257516679at_nat,A2: set_Pr1261947904930325089at_nat,X3: product_prod_nat_nat,I2: nat] :
% 5.25/5.47 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ A2 )
% 5.25/5.47 => ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 5.25/5.47 => ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs @ I2 @ X3 ) ) @ A2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_update_subsetI
% 5.25/5.47 thf(fact_2567_set__update__subsetI,axiom,
% 5.25/5.47 ! [Xs: list_nat,A2: set_nat,X3: nat,I2: nat] :
% 5.25/5.47 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.25/5.47 => ( ( member_nat @ X3 @ A2 )
% 5.25/5.47 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I2 @ X3 ) ) @ A2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_update_subsetI
% 5.25/5.47 thf(fact_2568_set__update__subsetI,axiom,
% 5.25/5.47 ! [Xs: list_VEBT_VEBT,A2: set_VEBT_VEBT,X3: vEBT_VEBT,I2: nat] :
% 5.25/5.47 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.25/5.47 => ( ( member_VEBT_VEBT @ X3 @ A2 )
% 5.25/5.47 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X3 ) ) @ A2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_update_subsetI
% 5.25/5.47 thf(fact_2569_set__update__subsetI,axiom,
% 5.25/5.47 ! [Xs: list_int,A2: set_int,X3: int,I2: nat] :
% 5.25/5.47 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.25/5.47 => ( ( member_int @ X3 @ A2 )
% 5.25/5.47 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I2 @ X3 ) ) @ A2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_update_subsetI
% 5.25/5.47 thf(fact_2570_vebt__member_Osimps_I2_J,axiom,
% 5.25/5.47 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X3: nat] :
% 5.25/5.47 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X3 ) ).
% 5.25/5.47
% 5.25/5.47 % vebt_member.simps(2)
% 5.25/5.47 thf(fact_2571_vebt__insert_Ocases,axiom,
% 5.25/5.47 ! [X3: produc9072475918466114483BT_nat] :
% 5.25/5.47 ( ! [A5: $o,B5: $o,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X5 ) )
% 5.25/5.47 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ X5 ) )
% 5.25/5.47 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ X5 ) )
% 5.25/5.47 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ X5 ) )
% 5.25/5.47 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X5 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % vebt_insert.cases
% 5.25/5.47 thf(fact_2572_VEBT__internal_Omembermima_Ocases,axiom,
% 5.25/5.47 ! [X3: produc9072475918466114483BT_nat] :
% 5.25/5.47 ( ! [Uu: $o,Uv: $o,Uw: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) )
% 5.25/5.47 => ( ! [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) @ Uz2 ) )
% 5.25/5.47 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X5 ) )
% 5.25/5.47 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ X5 ) )
% 5.25/5.47 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ X5 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.membermima.cases
% 5.25/5.47 thf(fact_2573_vebt__member_Ocases,axiom,
% 5.25/5.47 ! [X3: produc9072475918466114483BT_nat] :
% 5.25/5.47 ( ! [A5: $o,B5: $o,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X5 ) )
% 5.25/5.47 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X5 ) )
% 5.25/5.47 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X5 ) )
% 5.25/5.47 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X5 ) )
% 5.25/5.47 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X5 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % vebt_member.cases
% 5.25/5.47 thf(fact_2574_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 5.25/5.47 ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.minNull.simps(4)
% 5.25/5.47 thf(fact_2575_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.25/5.47 ! [X3: produc9072475918466114483BT_nat] :
% 5.25/5.47 ( ! [A5: $o,B5: $o,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X5 ) )
% 5.25/5.47 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) )
% 5.25/5.47 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT,X5: nat] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ X5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.naive_member.cases
% 5.25/5.47 thf(fact_2576_invar__vebt_Ointros_I1_J,axiom,
% 5.25/5.47 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % invar_vebt.intros(1)
% 5.25/5.47 thf(fact_2577_vebt__buildup_Osimps_I2_J,axiom,
% 5.25/5.47 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.25/5.47 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.25/5.47
% 5.25/5.47 % vebt_buildup.simps(2)
% 5.25/5.47 thf(fact_2578_eucl__rel__int__dividesI,axiom,
% 5.25/5.47 ! [L2: int,K: int,Q2: int] :
% 5.25/5.47 ( ( L2 != zero_zero_int )
% 5.25/5.47 => ( ( K
% 5.25/5.47 = ( times_times_int @ Q2 @ L2 ) )
% 5.25/5.47 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % eucl_rel_int_dividesI
% 5.25/5.47 thf(fact_2579_vebt__member_Osimps_I1_J,axiom,
% 5.25/5.47 ! [A: $o,B: $o,X3: nat] :
% 5.25/5.47 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 5.25/5.47 = ( ( ( X3 = zero_zero_nat )
% 5.25/5.47 => A )
% 5.25/5.47 & ( ( X3 != zero_zero_nat )
% 5.25/5.47 => ( ( ( X3 = one_one_nat )
% 5.25/5.47 => B )
% 5.25/5.47 & ( X3 = one_one_nat ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % vebt_member.simps(1)
% 5.25/5.47 thf(fact_2580_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.25/5.47 ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.25/5.47 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.naive_member.simps(2)
% 5.25/5.47 thf(fact_2581_vebt__insert_Osimps_I1_J,axiom,
% 5.25/5.47 ! [X3: nat,A: $o,B: $o] :
% 5.25/5.47 ( ( ( X3 = zero_zero_nat )
% 5.25/5.47 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 5.25/5.47 = ( vEBT_Leaf @ $true @ B ) ) )
% 5.25/5.47 & ( ( X3 != zero_zero_nat )
% 5.25/5.47 => ( ( ( X3 = one_one_nat )
% 5.25/5.47 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 5.25/5.47 = ( vEBT_Leaf @ A @ $true ) ) )
% 5.25/5.47 & ( ( X3 != one_one_nat )
% 5.25/5.47 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X3 )
% 5.25/5.47 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % vebt_insert.simps(1)
% 5.25/5.47 thf(fact_2582_set__update__memI,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_real,X3: real] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.25/5.47 => ( member_real @ X3 @ ( set_real2 @ ( list_update_real @ Xs @ N @ X3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_update_memI
% 5.25/5.47 thf(fact_2583_set__update__memI,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_complex,X3: complex] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.25/5.47 => ( member_complex @ X3 @ ( set_complex2 @ ( list_update_complex @ Xs @ N @ X3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_update_memI
% 5.25/5.47 thf(fact_2584_set__update__memI,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_P6011104703257516679at_nat,X3: product_prod_nat_nat] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs ) )
% 5.25/5.47 => ( member8440522571783428010at_nat @ X3 @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs @ N @ X3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_update_memI
% 5.25/5.47 thf(fact_2585_set__update__memI,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.47 => ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N @ X3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_update_memI
% 5.25/5.47 thf(fact_2586_set__update__memI,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_o,X3: $o] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.25/5.47 => ( member_o @ X3 @ ( set_o2 @ ( list_update_o @ Xs @ N @ X3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_update_memI
% 5.25/5.47 thf(fact_2587_set__update__memI,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_nat,X3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.25/5.47 => ( member_nat @ X3 @ ( set_nat2 @ ( list_update_nat @ Xs @ N @ X3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_update_memI
% 5.25/5.47 thf(fact_2588_set__update__memI,axiom,
% 5.25/5.47 ! [N: nat,Xs: list_int,X3: int] :
% 5.25/5.47 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.25/5.47 => ( member_int @ X3 @ ( set_int2 @ ( list_update_int @ Xs @ N @ X3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % set_update_memI
% 5.25/5.47 thf(fact_2589_list__update__same__conv,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.47 => ( ( ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X3 )
% 5.25/5.47 = Xs )
% 5.25/5.47 = ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 5.25/5.47 = X3 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % list_update_same_conv
% 5.25/5.47 thf(fact_2590_list__update__same__conv,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_o,X3: $o] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 5.25/5.47 => ( ( ( list_update_o @ Xs @ I2 @ X3 )
% 5.25/5.47 = Xs )
% 5.25/5.47 = ( ( nth_o @ Xs @ I2 )
% 5.25/5.47 = X3 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % list_update_same_conv
% 5.25/5.47 thf(fact_2591_list__update__same__conv,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_nat,X3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.47 => ( ( ( list_update_nat @ Xs @ I2 @ X3 )
% 5.25/5.47 = Xs )
% 5.25/5.47 = ( ( nth_nat @ Xs @ I2 )
% 5.25/5.47 = X3 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % list_update_same_conv
% 5.25/5.47 thf(fact_2592_list__update__same__conv,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_int,X3: int] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 5.25/5.47 => ( ( ( list_update_int @ Xs @ I2 @ X3 )
% 5.25/5.47 = Xs )
% 5.25/5.47 = ( ( nth_int @ Xs @ I2 )
% 5.25/5.47 = X3 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % list_update_same_conv
% 5.25/5.47 thf(fact_2593_nth__list__update,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_VEBT_VEBT,J2: nat,X3: vEBT_VEBT] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.47 => ( ( ( I2 = J2 )
% 5.25/5.47 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X3 ) @ J2 )
% 5.25/5.47 = X3 ) )
% 5.25/5.47 & ( ( I2 != J2 )
% 5.25/5.47 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X3 ) @ J2 )
% 5.25/5.47 = ( nth_VEBT_VEBT @ Xs @ J2 ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nth_list_update
% 5.25/5.47 thf(fact_2594_nth__list__update,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_o,X3: $o,J2: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 5.25/5.47 => ( ( nth_o @ ( list_update_o @ Xs @ I2 @ X3 ) @ J2 )
% 5.25/5.47 = ( ( ( I2 = J2 )
% 5.25/5.47 => X3 )
% 5.25/5.47 & ( ( I2 != J2 )
% 5.25/5.47 => ( nth_o @ Xs @ J2 ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nth_list_update
% 5.25/5.47 thf(fact_2595_nth__list__update,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_nat,J2: nat,X3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.47 => ( ( ( I2 = J2 )
% 5.25/5.47 => ( ( nth_nat @ ( list_update_nat @ Xs @ I2 @ X3 ) @ J2 )
% 5.25/5.47 = X3 ) )
% 5.25/5.47 & ( ( I2 != J2 )
% 5.25/5.47 => ( ( nth_nat @ ( list_update_nat @ Xs @ I2 @ X3 ) @ J2 )
% 5.25/5.47 = ( nth_nat @ Xs @ J2 ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nth_list_update
% 5.25/5.47 thf(fact_2596_nth__list__update,axiom,
% 5.25/5.47 ! [I2: nat,Xs: list_int,J2: nat,X3: int] :
% 5.25/5.47 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 5.25/5.47 => ( ( ( I2 = J2 )
% 5.25/5.47 => ( ( nth_int @ ( list_update_int @ Xs @ I2 @ X3 ) @ J2 )
% 5.25/5.47 = X3 ) )
% 5.25/5.47 & ( ( I2 != J2 )
% 5.25/5.47 => ( ( nth_int @ ( list_update_int @ Xs @ I2 @ X3 ) @ J2 )
% 5.25/5.47 = ( nth_int @ Xs @ J2 ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nth_list_update
% 5.25/5.47 thf(fact_2597_pinf_I1_J,axiom,
% 5.25/5.47 ! [P: real > $o,P3: real > $o,Q: real > $o,Q6: real > $o] :
% 5.25/5.47 ( ? [Z4: real] :
% 5.25/5.47 ! [X5: real] :
% 5.25/5.47 ( ( ord_less_real @ Z4 @ X5 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: real] :
% 5.25/5.47 ! [X5: real] :
% 5.25/5.47 ( ( ord_less_real @ Z4 @ X5 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ Z2 @ X )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 & ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(1)
% 5.25/5.47 thf(fact_2598_pinf_I1_J,axiom,
% 5.25/5.47 ! [P: rat > $o,P3: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.25/5.47 ( ? [Z4: rat] :
% 5.25/5.47 ! [X5: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z4 @ X5 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: rat] :
% 5.25/5.47 ! [X5: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z4 @ X5 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z2 @ X )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 & ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(1)
% 5.25/5.47 thf(fact_2599_pinf_I1_J,axiom,
% 5.25/5.47 ! [P: num > $o,P3: num > $o,Q: num > $o,Q6: num > $o] :
% 5.25/5.47 ( ? [Z4: num] :
% 5.25/5.47 ! [X5: num] :
% 5.25/5.47 ( ( ord_less_num @ Z4 @ X5 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: num] :
% 5.25/5.47 ! [X5: num] :
% 5.25/5.47 ( ( ord_less_num @ Z4 @ X5 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ Z2 @ X )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 & ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(1)
% 5.25/5.47 thf(fact_2600_pinf_I1_J,axiom,
% 5.25/5.47 ! [P: nat > $o,P3: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.25/5.47 ( ? [Z4: nat] :
% 5.25/5.47 ! [X5: nat] :
% 5.25/5.47 ( ( ord_less_nat @ Z4 @ X5 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: nat] :
% 5.25/5.47 ! [X5: nat] :
% 5.25/5.47 ( ( ord_less_nat @ Z4 @ X5 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ Z2 @ X )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 & ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(1)
% 5.25/5.47 thf(fact_2601_pinf_I1_J,axiom,
% 5.25/5.47 ! [P: int > $o,P3: int > $o,Q: int > $o,Q6: int > $o] :
% 5.25/5.47 ( ? [Z4: int] :
% 5.25/5.47 ! [X5: int] :
% 5.25/5.47 ( ( ord_less_int @ Z4 @ X5 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: int] :
% 5.25/5.47 ! [X5: int] :
% 5.25/5.47 ( ( ord_less_int @ Z4 @ X5 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ Z2 @ X )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 & ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(1)
% 5.25/5.47 thf(fact_2602_pinf_I2_J,axiom,
% 5.25/5.47 ! [P: real > $o,P3: real > $o,Q: real > $o,Q6: real > $o] :
% 5.25/5.47 ( ? [Z4: real] :
% 5.25/5.47 ! [X5: real] :
% 5.25/5.47 ( ( ord_less_real @ Z4 @ X5 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: real] :
% 5.25/5.47 ! [X5: real] :
% 5.25/5.47 ( ( ord_less_real @ Z4 @ X5 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ Z2 @ X )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 | ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(2)
% 5.25/5.47 thf(fact_2603_pinf_I2_J,axiom,
% 5.25/5.47 ! [P: rat > $o,P3: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.25/5.47 ( ? [Z4: rat] :
% 5.25/5.47 ! [X5: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z4 @ X5 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: rat] :
% 5.25/5.47 ! [X5: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z4 @ X5 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z2 @ X )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 | ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(2)
% 5.25/5.47 thf(fact_2604_pinf_I2_J,axiom,
% 5.25/5.47 ! [P: num > $o,P3: num > $o,Q: num > $o,Q6: num > $o] :
% 5.25/5.47 ( ? [Z4: num] :
% 5.25/5.47 ! [X5: num] :
% 5.25/5.47 ( ( ord_less_num @ Z4 @ X5 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: num] :
% 5.25/5.47 ! [X5: num] :
% 5.25/5.47 ( ( ord_less_num @ Z4 @ X5 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ Z2 @ X )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 | ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(2)
% 5.25/5.47 thf(fact_2605_pinf_I2_J,axiom,
% 5.25/5.47 ! [P: nat > $o,P3: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.25/5.47 ( ? [Z4: nat] :
% 5.25/5.47 ! [X5: nat] :
% 5.25/5.47 ( ( ord_less_nat @ Z4 @ X5 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: nat] :
% 5.25/5.47 ! [X5: nat] :
% 5.25/5.47 ( ( ord_less_nat @ Z4 @ X5 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ Z2 @ X )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 | ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(2)
% 5.25/5.47 thf(fact_2606_pinf_I2_J,axiom,
% 5.25/5.47 ! [P: int > $o,P3: int > $o,Q: int > $o,Q6: int > $o] :
% 5.25/5.47 ( ? [Z4: int] :
% 5.25/5.47 ! [X5: int] :
% 5.25/5.47 ( ( ord_less_int @ Z4 @ X5 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: int] :
% 5.25/5.47 ! [X5: int] :
% 5.25/5.47 ( ( ord_less_int @ Z4 @ X5 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ Z2 @ X )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 | ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(2)
% 5.25/5.47 thf(fact_2607_pinf_I3_J,axiom,
% 5.25/5.47 ! [T: real] :
% 5.25/5.47 ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ Z2 @ X )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(3)
% 5.25/5.47 thf(fact_2608_pinf_I3_J,axiom,
% 5.25/5.47 ! [T: rat] :
% 5.25/5.47 ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z2 @ X )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(3)
% 5.25/5.47 thf(fact_2609_pinf_I3_J,axiom,
% 5.25/5.47 ! [T: num] :
% 5.25/5.47 ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ Z2 @ X )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(3)
% 5.25/5.47 thf(fact_2610_pinf_I3_J,axiom,
% 5.25/5.47 ! [T: nat] :
% 5.25/5.47 ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ Z2 @ X )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(3)
% 5.25/5.47 thf(fact_2611_pinf_I3_J,axiom,
% 5.25/5.47 ! [T: int] :
% 5.25/5.47 ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ Z2 @ X )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(3)
% 5.25/5.47 thf(fact_2612_pinf_I4_J,axiom,
% 5.25/5.47 ! [T: real] :
% 5.25/5.47 ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ Z2 @ X )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(4)
% 5.25/5.47 thf(fact_2613_pinf_I4_J,axiom,
% 5.25/5.47 ! [T: rat] :
% 5.25/5.47 ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z2 @ X )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(4)
% 5.25/5.47 thf(fact_2614_pinf_I4_J,axiom,
% 5.25/5.47 ! [T: num] :
% 5.25/5.47 ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ Z2 @ X )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(4)
% 5.25/5.47 thf(fact_2615_pinf_I4_J,axiom,
% 5.25/5.47 ! [T: nat] :
% 5.25/5.47 ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ Z2 @ X )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(4)
% 5.25/5.47 thf(fact_2616_pinf_I4_J,axiom,
% 5.25/5.47 ! [T: int] :
% 5.25/5.47 ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ Z2 @ X )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(4)
% 5.25/5.47 thf(fact_2617_pinf_I5_J,axiom,
% 5.25/5.47 ! [T: real] :
% 5.25/5.47 ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ Z2 @ X )
% 5.25/5.47 => ~ ( ord_less_real @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(5)
% 5.25/5.47 thf(fact_2618_pinf_I5_J,axiom,
% 5.25/5.47 ! [T: rat] :
% 5.25/5.47 ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z2 @ X )
% 5.25/5.47 => ~ ( ord_less_rat @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(5)
% 5.25/5.47 thf(fact_2619_pinf_I5_J,axiom,
% 5.25/5.47 ! [T: num] :
% 5.25/5.47 ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ Z2 @ X )
% 5.25/5.47 => ~ ( ord_less_num @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(5)
% 5.25/5.47 thf(fact_2620_pinf_I5_J,axiom,
% 5.25/5.47 ! [T: nat] :
% 5.25/5.47 ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ Z2 @ X )
% 5.25/5.47 => ~ ( ord_less_nat @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(5)
% 5.25/5.47 thf(fact_2621_pinf_I5_J,axiom,
% 5.25/5.47 ! [T: int] :
% 5.25/5.47 ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ Z2 @ X )
% 5.25/5.47 => ~ ( ord_less_int @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(5)
% 5.25/5.47 thf(fact_2622_pinf_I7_J,axiom,
% 5.25/5.47 ! [T: real] :
% 5.25/5.47 ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ Z2 @ X )
% 5.25/5.47 => ( ord_less_real @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(7)
% 5.25/5.47 thf(fact_2623_pinf_I7_J,axiom,
% 5.25/5.47 ! [T: rat] :
% 5.25/5.47 ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z2 @ X )
% 5.25/5.47 => ( ord_less_rat @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(7)
% 5.25/5.47 thf(fact_2624_pinf_I7_J,axiom,
% 5.25/5.47 ! [T: num] :
% 5.25/5.47 ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ Z2 @ X )
% 5.25/5.47 => ( ord_less_num @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(7)
% 5.25/5.47 thf(fact_2625_pinf_I7_J,axiom,
% 5.25/5.47 ! [T: nat] :
% 5.25/5.47 ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ Z2 @ X )
% 5.25/5.47 => ( ord_less_nat @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(7)
% 5.25/5.47 thf(fact_2626_pinf_I7_J,axiom,
% 5.25/5.47 ! [T: int] :
% 5.25/5.47 ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ Z2 @ X )
% 5.25/5.47 => ( ord_less_int @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(7)
% 5.25/5.47 thf(fact_2627_minf_I1_J,axiom,
% 5.25/5.47 ! [P: real > $o,P3: real > $o,Q: real > $o,Q6: real > $o] :
% 5.25/5.47 ( ? [Z4: real] :
% 5.25/5.47 ! [X5: real] :
% 5.25/5.47 ( ( ord_less_real @ X5 @ Z4 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: real] :
% 5.25/5.47 ! [X5: real] :
% 5.25/5.47 ( ( ord_less_real @ X5 @ Z4 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ X @ Z2 )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 & ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(1)
% 5.25/5.47 thf(fact_2628_minf_I1_J,axiom,
% 5.25/5.47 ! [P: rat > $o,P3: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.25/5.47 ( ? [Z4: rat] :
% 5.25/5.47 ! [X5: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X5 @ Z4 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: rat] :
% 5.25/5.47 ! [X5: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X5 @ Z4 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X @ Z2 )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 & ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(1)
% 5.25/5.47 thf(fact_2629_minf_I1_J,axiom,
% 5.25/5.47 ! [P: num > $o,P3: num > $o,Q: num > $o,Q6: num > $o] :
% 5.25/5.47 ( ? [Z4: num] :
% 5.25/5.47 ! [X5: num] :
% 5.25/5.47 ( ( ord_less_num @ X5 @ Z4 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: num] :
% 5.25/5.47 ! [X5: num] :
% 5.25/5.47 ( ( ord_less_num @ X5 @ Z4 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ X @ Z2 )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 & ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(1)
% 5.25/5.47 thf(fact_2630_minf_I1_J,axiom,
% 5.25/5.47 ! [P: nat > $o,P3: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.25/5.47 ( ? [Z4: nat] :
% 5.25/5.47 ! [X5: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X5 @ Z4 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: nat] :
% 5.25/5.47 ! [X5: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X5 @ Z4 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X @ Z2 )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 & ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(1)
% 5.25/5.47 thf(fact_2631_minf_I1_J,axiom,
% 5.25/5.47 ! [P: int > $o,P3: int > $o,Q: int > $o,Q6: int > $o] :
% 5.25/5.47 ( ? [Z4: int] :
% 5.25/5.47 ! [X5: int] :
% 5.25/5.47 ( ( ord_less_int @ X5 @ Z4 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: int] :
% 5.25/5.47 ! [X5: int] :
% 5.25/5.47 ( ( ord_less_int @ X5 @ Z4 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ X @ Z2 )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 & ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(1)
% 5.25/5.47 thf(fact_2632_minf_I2_J,axiom,
% 5.25/5.47 ! [P: real > $o,P3: real > $o,Q: real > $o,Q6: real > $o] :
% 5.25/5.47 ( ? [Z4: real] :
% 5.25/5.47 ! [X5: real] :
% 5.25/5.47 ( ( ord_less_real @ X5 @ Z4 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: real] :
% 5.25/5.47 ! [X5: real] :
% 5.25/5.47 ( ( ord_less_real @ X5 @ Z4 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ X @ Z2 )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 | ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(2)
% 5.25/5.47 thf(fact_2633_minf_I2_J,axiom,
% 5.25/5.47 ! [P: rat > $o,P3: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.25/5.47 ( ? [Z4: rat] :
% 5.25/5.47 ! [X5: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X5 @ Z4 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: rat] :
% 5.25/5.47 ! [X5: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X5 @ Z4 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X @ Z2 )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 | ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(2)
% 5.25/5.47 thf(fact_2634_minf_I2_J,axiom,
% 5.25/5.47 ! [P: num > $o,P3: num > $o,Q: num > $o,Q6: num > $o] :
% 5.25/5.47 ( ? [Z4: num] :
% 5.25/5.47 ! [X5: num] :
% 5.25/5.47 ( ( ord_less_num @ X5 @ Z4 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: num] :
% 5.25/5.47 ! [X5: num] :
% 5.25/5.47 ( ( ord_less_num @ X5 @ Z4 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ X @ Z2 )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 | ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(2)
% 5.25/5.47 thf(fact_2635_minf_I2_J,axiom,
% 5.25/5.47 ! [P: nat > $o,P3: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.25/5.47 ( ? [Z4: nat] :
% 5.25/5.47 ! [X5: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X5 @ Z4 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: nat] :
% 5.25/5.47 ! [X5: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X5 @ Z4 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X @ Z2 )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 | ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(2)
% 5.25/5.47 thf(fact_2636_minf_I2_J,axiom,
% 5.25/5.47 ! [P: int > $o,P3: int > $o,Q: int > $o,Q6: int > $o] :
% 5.25/5.47 ( ? [Z4: int] :
% 5.25/5.47 ! [X5: int] :
% 5.25/5.47 ( ( ord_less_int @ X5 @ Z4 )
% 5.25/5.47 => ( ( P @ X5 )
% 5.25/5.47 = ( P3 @ X5 ) ) )
% 5.25/5.47 => ( ? [Z4: int] :
% 5.25/5.47 ! [X5: int] :
% 5.25/5.47 ( ( ord_less_int @ X5 @ Z4 )
% 5.25/5.47 => ( ( Q @ X5 )
% 5.25/5.47 = ( Q6 @ X5 ) ) )
% 5.25/5.47 => ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ X @ Z2 )
% 5.25/5.47 => ( ( ( P @ X )
% 5.25/5.47 | ( Q @ X ) )
% 5.25/5.47 = ( ( P3 @ X )
% 5.25/5.47 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(2)
% 5.25/5.47 thf(fact_2637_minf_I3_J,axiom,
% 5.25/5.47 ! [T: real] :
% 5.25/5.47 ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ X @ Z2 )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(3)
% 5.25/5.47 thf(fact_2638_minf_I3_J,axiom,
% 5.25/5.47 ! [T: rat] :
% 5.25/5.47 ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X @ Z2 )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(3)
% 5.25/5.47 thf(fact_2639_minf_I3_J,axiom,
% 5.25/5.47 ! [T: num] :
% 5.25/5.47 ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ X @ Z2 )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(3)
% 5.25/5.47 thf(fact_2640_minf_I3_J,axiom,
% 5.25/5.47 ! [T: nat] :
% 5.25/5.47 ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X @ Z2 )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(3)
% 5.25/5.47 thf(fact_2641_minf_I3_J,axiom,
% 5.25/5.47 ! [T: int] :
% 5.25/5.47 ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ X @ Z2 )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(3)
% 5.25/5.47 thf(fact_2642_minf_I4_J,axiom,
% 5.25/5.47 ! [T: real] :
% 5.25/5.47 ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ X @ Z2 )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(4)
% 5.25/5.47 thf(fact_2643_minf_I4_J,axiom,
% 5.25/5.47 ! [T: rat] :
% 5.25/5.47 ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X @ Z2 )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(4)
% 5.25/5.47 thf(fact_2644_minf_I4_J,axiom,
% 5.25/5.47 ! [T: num] :
% 5.25/5.47 ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ X @ Z2 )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(4)
% 5.25/5.47 thf(fact_2645_minf_I4_J,axiom,
% 5.25/5.47 ! [T: nat] :
% 5.25/5.47 ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X @ Z2 )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(4)
% 5.25/5.47 thf(fact_2646_minf_I4_J,axiom,
% 5.25/5.47 ! [T: int] :
% 5.25/5.47 ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ X @ Z2 )
% 5.25/5.47 => ( X != T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(4)
% 5.25/5.47 thf(fact_2647_minf_I5_J,axiom,
% 5.25/5.47 ! [T: real] :
% 5.25/5.47 ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ X @ Z2 )
% 5.25/5.47 => ( ord_less_real @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(5)
% 5.25/5.47 thf(fact_2648_minf_I5_J,axiom,
% 5.25/5.47 ! [T: rat] :
% 5.25/5.47 ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X @ Z2 )
% 5.25/5.47 => ( ord_less_rat @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(5)
% 5.25/5.47 thf(fact_2649_minf_I5_J,axiom,
% 5.25/5.47 ! [T: num] :
% 5.25/5.47 ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ X @ Z2 )
% 5.25/5.47 => ( ord_less_num @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(5)
% 5.25/5.47 thf(fact_2650_minf_I5_J,axiom,
% 5.25/5.47 ! [T: nat] :
% 5.25/5.47 ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X @ Z2 )
% 5.25/5.47 => ( ord_less_nat @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(5)
% 5.25/5.47 thf(fact_2651_minf_I5_J,axiom,
% 5.25/5.47 ! [T: int] :
% 5.25/5.47 ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ X @ Z2 )
% 5.25/5.47 => ( ord_less_int @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(5)
% 5.25/5.47 thf(fact_2652_minf_I7_J,axiom,
% 5.25/5.47 ! [T: real] :
% 5.25/5.47 ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ X @ Z2 )
% 5.25/5.47 => ~ ( ord_less_real @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(7)
% 5.25/5.47 thf(fact_2653_minf_I7_J,axiom,
% 5.25/5.47 ! [T: rat] :
% 5.25/5.47 ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X @ Z2 )
% 5.25/5.47 => ~ ( ord_less_rat @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(7)
% 5.25/5.47 thf(fact_2654_minf_I7_J,axiom,
% 5.25/5.47 ! [T: num] :
% 5.25/5.47 ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ X @ Z2 )
% 5.25/5.47 => ~ ( ord_less_num @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(7)
% 5.25/5.47 thf(fact_2655_minf_I7_J,axiom,
% 5.25/5.47 ! [T: nat] :
% 5.25/5.47 ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X @ Z2 )
% 5.25/5.47 => ~ ( ord_less_nat @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(7)
% 5.25/5.47 thf(fact_2656_minf_I7_J,axiom,
% 5.25/5.47 ! [T: int] :
% 5.25/5.47 ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ X @ Z2 )
% 5.25/5.47 => ~ ( ord_less_int @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(7)
% 5.25/5.47 thf(fact_2657_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 5.25/5.47 ! [X3: vEBT_VEBT] :
% 5.25/5.47 ( ~ ( vEBT_VEBT_minNull @ X3 )
% 5.25/5.47 => ( ! [Uv: $o] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( vEBT_Leaf @ $true @ Uv ) )
% 5.25/5.47 => ( ! [Uu: $o] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( vEBT_Leaf @ Uu @ $true ) )
% 5.25/5.47 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.25/5.47 ( X3
% 5.25/5.47 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.minNull.elims(3)
% 5.25/5.47 thf(fact_2658_eucl__rel__int,axiom,
% 5.25/5.47 ! [K: int,L2: int] : ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L2 ) @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % eucl_rel_int
% 5.25/5.47 thf(fact_2659_vebt__insert_Osimps_I4_J,axiom,
% 5.25/5.47 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 5.25/5.47 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X3 )
% 5.25/5.47 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) ) ).
% 5.25/5.47
% 5.25/5.47 % vebt_insert.simps(4)
% 5.25/5.47 thf(fact_2660_pinf_I6_J,axiom,
% 5.25/5.47 ! [T: real] :
% 5.25/5.47 ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ Z2 @ X )
% 5.25/5.47 => ~ ( ord_less_eq_real @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(6)
% 5.25/5.47 thf(fact_2661_pinf_I6_J,axiom,
% 5.25/5.47 ! [T: rat] :
% 5.25/5.47 ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z2 @ X )
% 5.25/5.47 => ~ ( ord_less_eq_rat @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(6)
% 5.25/5.47 thf(fact_2662_pinf_I6_J,axiom,
% 5.25/5.47 ! [T: num] :
% 5.25/5.47 ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ Z2 @ X )
% 5.25/5.47 => ~ ( ord_less_eq_num @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(6)
% 5.25/5.47 thf(fact_2663_pinf_I6_J,axiom,
% 5.25/5.47 ! [T: nat] :
% 5.25/5.47 ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ Z2 @ X )
% 5.25/5.47 => ~ ( ord_less_eq_nat @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(6)
% 5.25/5.47 thf(fact_2664_pinf_I6_J,axiom,
% 5.25/5.47 ! [T: int] :
% 5.25/5.47 ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ Z2 @ X )
% 5.25/5.47 => ~ ( ord_less_eq_int @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(6)
% 5.25/5.47 thf(fact_2665_pinf_I8_J,axiom,
% 5.25/5.47 ! [T: real] :
% 5.25/5.47 ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ Z2 @ X )
% 5.25/5.47 => ( ord_less_eq_real @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(8)
% 5.25/5.47 thf(fact_2666_pinf_I8_J,axiom,
% 5.25/5.47 ! [T: rat] :
% 5.25/5.47 ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z2 @ X )
% 5.25/5.47 => ( ord_less_eq_rat @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(8)
% 5.25/5.47 thf(fact_2667_pinf_I8_J,axiom,
% 5.25/5.47 ! [T: num] :
% 5.25/5.47 ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ Z2 @ X )
% 5.25/5.47 => ( ord_less_eq_num @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(8)
% 5.25/5.47 thf(fact_2668_pinf_I8_J,axiom,
% 5.25/5.47 ! [T: nat] :
% 5.25/5.47 ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ Z2 @ X )
% 5.25/5.47 => ( ord_less_eq_nat @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(8)
% 5.25/5.47 thf(fact_2669_pinf_I8_J,axiom,
% 5.25/5.47 ! [T: int] :
% 5.25/5.47 ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ Z2 @ X )
% 5.25/5.47 => ( ord_less_eq_int @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % pinf(8)
% 5.25/5.47 thf(fact_2670_minf_I6_J,axiom,
% 5.25/5.47 ! [T: real] :
% 5.25/5.47 ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ X @ Z2 )
% 5.25/5.47 => ( ord_less_eq_real @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(6)
% 5.25/5.47 thf(fact_2671_minf_I6_J,axiom,
% 5.25/5.47 ! [T: rat] :
% 5.25/5.47 ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X @ Z2 )
% 5.25/5.47 => ( ord_less_eq_rat @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(6)
% 5.25/5.47 thf(fact_2672_minf_I6_J,axiom,
% 5.25/5.47 ! [T: num] :
% 5.25/5.47 ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ X @ Z2 )
% 5.25/5.47 => ( ord_less_eq_num @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(6)
% 5.25/5.47 thf(fact_2673_minf_I6_J,axiom,
% 5.25/5.47 ! [T: nat] :
% 5.25/5.47 ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X @ Z2 )
% 5.25/5.47 => ( ord_less_eq_nat @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(6)
% 5.25/5.47 thf(fact_2674_minf_I6_J,axiom,
% 5.25/5.47 ! [T: int] :
% 5.25/5.47 ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ X @ Z2 )
% 5.25/5.47 => ( ord_less_eq_int @ X @ T ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(6)
% 5.25/5.47 thf(fact_2675_minf_I8_J,axiom,
% 5.25/5.47 ! [T: real] :
% 5.25/5.47 ? [Z2: real] :
% 5.25/5.47 ! [X: real] :
% 5.25/5.47 ( ( ord_less_real @ X @ Z2 )
% 5.25/5.47 => ~ ( ord_less_eq_real @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(8)
% 5.25/5.47 thf(fact_2676_minf_I8_J,axiom,
% 5.25/5.47 ! [T: rat] :
% 5.25/5.47 ? [Z2: rat] :
% 5.25/5.47 ! [X: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X @ Z2 )
% 5.25/5.47 => ~ ( ord_less_eq_rat @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(8)
% 5.25/5.47 thf(fact_2677_minf_I8_J,axiom,
% 5.25/5.47 ! [T: num] :
% 5.25/5.47 ? [Z2: num] :
% 5.25/5.47 ! [X: num] :
% 5.25/5.47 ( ( ord_less_num @ X @ Z2 )
% 5.25/5.47 => ~ ( ord_less_eq_num @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(8)
% 5.25/5.47 thf(fact_2678_minf_I8_J,axiom,
% 5.25/5.47 ! [T: nat] :
% 5.25/5.47 ? [Z2: nat] :
% 5.25/5.47 ! [X: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X @ Z2 )
% 5.25/5.47 => ~ ( ord_less_eq_nat @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(8)
% 5.25/5.47 thf(fact_2679_minf_I8_J,axiom,
% 5.25/5.47 ! [T: int] :
% 5.25/5.47 ? [Z2: int] :
% 5.25/5.47 ! [X: int] :
% 5.25/5.47 ( ( ord_less_int @ X @ Z2 )
% 5.25/5.47 => ~ ( ord_less_eq_int @ T @ X ) ) ).
% 5.25/5.47
% 5.25/5.47 % minf(8)
% 5.25/5.47 thf(fact_2680_imp__le__cong,axiom,
% 5.25/5.47 ! [X3: int,X6: int,P: $o,P3: $o] :
% 5.25/5.47 ( ( X3 = X6 )
% 5.25/5.47 => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 5.25/5.47 => ( P = P3 ) )
% 5.25/5.47 => ( ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.47 => P )
% 5.25/5.47 = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 5.25/5.47 => P3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % imp_le_cong
% 5.25/5.47 thf(fact_2681_conj__le__cong,axiom,
% 5.25/5.47 ! [X3: int,X6: int,P: $o,P3: $o] :
% 5.25/5.47 ( ( X3 = X6 )
% 5.25/5.47 => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 5.25/5.47 => ( P = P3 ) )
% 5.25/5.47 => ( ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.47 & P )
% 5.25/5.47 = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 5.25/5.47 & P3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % conj_le_cong
% 5.25/5.47 thf(fact_2682_eucl__rel__int__iff,axiom,
% 5.25/5.47 ! [K: int,L2: int,Q2: int,R2: int] :
% 5.25/5.47 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.25/5.47 = ( ( K
% 5.25/5.47 = ( plus_plus_int @ ( times_times_int @ L2 @ Q2 ) @ R2 ) )
% 5.25/5.47 & ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.25/5.47 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.25/5.47 & ( ord_less_int @ R2 @ L2 ) ) )
% 5.25/5.47 & ( ~ ( ord_less_int @ zero_zero_int @ L2 )
% 5.25/5.47 => ( ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.25/5.47 => ( ( ord_less_int @ L2 @ R2 )
% 5.25/5.47 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 5.25/5.47 & ( ~ ( ord_less_int @ L2 @ zero_zero_int )
% 5.25/5.47 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % eucl_rel_int_iff
% 5.25/5.47 thf(fact_2683_invar__vebt_Osimps,axiom,
% 5.25/5.47 ( vEBT_invar_vebt
% 5.25/5.47 = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 5.25/5.47 ( ( ? [A3: $o,B2: $o] :
% 5.25/5.47 ( A1
% 5.25/5.47 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.25/5.47 & ( A22
% 5.25/5.47 = ( suc @ zero_zero_nat ) ) )
% 5.25/5.47 | ? [TreeList2: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 5.25/5.47 ( ( A1
% 5.25/5.47 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList2 @ Summary3 ) )
% 5.25/5.47 & ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 5.25/5.47 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 5.25/5.47 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.47 & ( A22
% 5.25/5.47 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.25/5.47 & ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X4 )
% 5.25/5.47 & ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.47 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.47 | ? [TreeList2: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 5.25/5.47 ( ( A1
% 5.25/5.47 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList2 @ Summary3 ) )
% 5.25/5.47 & ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 5.25/5.47 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 5.25/5.47 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.25/5.47 & ( A22
% 5.25/5.47 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.25/5.47 & ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X4 )
% 5.25/5.47 & ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.47 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.47 | ? [TreeList2: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.25/5.47 ( ( A1
% 5.25/5.47 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList2 @ Summary3 ) )
% 5.25/5.47 & ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 5.25/5.47 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 5.25/5.47 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.47 & ( A22
% 5.25/5.47 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.25/5.47 & ! [I3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.47 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 5.25/5.47 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 5.25/5.47 & ( ( Mi3 = Ma3 )
% 5.25/5.47 => ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.47 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.47 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.25/5.47 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.25/5.47 & ( ( Mi3 != Ma3 )
% 5.25/5.47 => ! [I3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.47 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.25/5.47 = I3 )
% 5.25/5.47 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.25/5.47 & ! [X2: nat] :
% 5.25/5.47 ( ( ( ( vEBT_VEBT_high @ X2 @ N2 )
% 5.25/5.47 = I3 )
% 5.25/5.47 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) )
% 5.25/5.47 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.25/5.47 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) )
% 5.25/5.47 | ? [TreeList2: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.25/5.47 ( ( A1
% 5.25/5.47 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList2 @ Summary3 ) )
% 5.25/5.47 & ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 5.25/5.47 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 5.25/5.47 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.25/5.47 & ( A22
% 5.25/5.47 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.25/5.47 & ! [I3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.25/5.47 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 5.25/5.47 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 5.25/5.47 & ( ( Mi3 = Ma3 )
% 5.25/5.47 => ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.47 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.47 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.25/5.47 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.25/5.47 & ( ( Mi3 != Ma3 )
% 5.25/5.47 => ! [I3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.25/5.47 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.25/5.47 = I3 )
% 5.25/5.47 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.25/5.47 & ! [X2: nat] :
% 5.25/5.47 ( ( ( ( vEBT_VEBT_high @ X2 @ N2 )
% 5.25/5.47 = I3 )
% 5.25/5.47 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) )
% 5.25/5.47 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.25/5.47 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % invar_vebt.simps
% 5.25/5.47 thf(fact_2684_invar__vebt_Ocases,axiom,
% 5.25/5.47 ! [A12: vEBT_VEBT,A23: nat] :
% 5.25/5.47 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 5.25/5.47 => ( ( ? [A5: $o,B5: $o] :
% 5.25/5.47 ( A12
% 5.25/5.47 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.47 => ( A23
% 5.25/5.47 != ( suc @ zero_zero_nat ) ) )
% 5.25/5.47 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat] :
% 5.25/5.47 ( ( A12
% 5.25/5.47 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.25/5.47 => ( ( A23 = Deg2 )
% 5.25/5.47 => ( ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X @ N3 ) )
% 5.25/5.47 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.25/5.47 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.25/5.47 => ( ( M5 = N3 )
% 5.25/5.47 => ( ( Deg2
% 5.25/5.47 = ( plus_plus_nat @ N3 @ M5 ) )
% 5.25/5.47 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 5.25/5.47 => ~ ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_1 ) ) ) ) ) ) ) ) ) )
% 5.25/5.47 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat] :
% 5.25/5.47 ( ( A12
% 5.25/5.47 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.25/5.47 => ( ( A23 = Deg2 )
% 5.25/5.47 => ( ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X @ N3 ) )
% 5.25/5.47 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.25/5.47 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.25/5.47 => ( ( M5
% 5.25/5.47 = ( suc @ N3 ) )
% 5.25/5.47 => ( ( Deg2
% 5.25/5.47 = ( plus_plus_nat @ N3 @ M5 ) )
% 5.25/5.47 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 5.25/5.47 => ~ ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_1 ) ) ) ) ) ) ) ) ) )
% 5.25/5.47 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.25/5.47 ( ( A12
% 5.25/5.47 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.25/5.47 => ( ( A23 = Deg2 )
% 5.25/5.47 => ( ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X @ N3 ) )
% 5.25/5.47 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.25/5.47 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.25/5.47 => ( ( M5 = N3 )
% 5.25/5.47 => ( ( Deg2
% 5.25/5.47 = ( plus_plus_nat @ N3 @ M5 ) )
% 5.25/5.47 => ( ! [I: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.25/5.47 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X4 ) )
% 5.25/5.47 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.25/5.47 => ( ( ( Mi2 = Ma2 )
% 5.25/5.47 => ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_1 ) ) )
% 5.25/5.47 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.25/5.47 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.25/5.47 => ~ ( ( Mi2 != Ma2 )
% 5.25/5.47 => ! [I: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.25/5.47 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.25/5.47 = I )
% 5.25/5.47 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.25/5.47 & ! [X: nat] :
% 5.25/5.47 ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 5.25/5.47 = I )
% 5.25/5.47 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 5.25/5.47 => ( ( ord_less_nat @ Mi2 @ X )
% 5.25/5.47 & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.25/5.47 => ~ ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.25/5.47 ( ( A12
% 5.25/5.47 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.25/5.47 => ( ( A23 = Deg2 )
% 5.25/5.47 => ( ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X @ N3 ) )
% 5.25/5.47 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.25/5.47 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.25/5.47 => ( ( M5
% 5.25/5.47 = ( suc @ N3 ) )
% 5.25/5.47 => ( ( Deg2
% 5.25/5.47 = ( plus_plus_nat @ N3 @ M5 ) )
% 5.25/5.47 => ( ! [I: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.25/5.47 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X4 ) )
% 5.25/5.47 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.25/5.47 => ( ( ( Mi2 = Ma2 )
% 5.25/5.47 => ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_1 ) ) )
% 5.25/5.47 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.25/5.47 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.25/5.47 => ~ ( ( Mi2 != Ma2 )
% 5.25/5.47 => ! [I: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.25/5.47 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.25/5.47 = I )
% 5.25/5.47 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.25/5.47 & ! [X: nat] :
% 5.25/5.47 ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 5.25/5.47 = I )
% 5.25/5.47 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 5.25/5.47 => ( ( ord_less_nat @ Mi2 @ X )
% 5.25/5.47 & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % invar_vebt.cases
% 5.25/5.47 thf(fact_2685_invar__vebt_Ointros_I2_J,axiom,
% 5.25/5.47 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.25/5.47 ( ! [X5: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X5 @ N ) )
% 5.25/5.47 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.25/5.47 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.47 => ( ( M = N )
% 5.25/5.47 => ( ( Deg
% 5.25/5.47 = ( plus_plus_nat @ N @ M ) )
% 5.25/5.47 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 5.25/5.47 => ( ! [X5: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.47 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % invar_vebt.intros(2)
% 5.25/5.47 thf(fact_2686_member__valid__both__member__options,axiom,
% 5.25/5.47 ! [Tree: vEBT_VEBT,N: nat,X3: nat] :
% 5.25/5.47 ( ( vEBT_invar_vebt @ Tree @ N )
% 5.25/5.47 => ( ( vEBT_vebt_member @ Tree @ X3 )
% 5.25/5.47 => ( ( vEBT_V5719532721284313246member @ Tree @ X3 )
% 5.25/5.47 | ( vEBT_VEBT_membermima @ Tree @ X3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % member_valid_both_member_options
% 5.25/5.47 thf(fact_2687_max__less__iff__conj,axiom,
% 5.25/5.47 ! [X3: extended_enat,Y: extended_enat,Z: extended_enat] :
% 5.25/5.47 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X3 @ Y ) @ Z )
% 5.25/5.47 = ( ( ord_le72135733267957522d_enat @ X3 @ Z )
% 5.25/5.47 & ( ord_le72135733267957522d_enat @ Y @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_less_iff_conj
% 5.25/5.47 thf(fact_2688_max__less__iff__conj,axiom,
% 5.25/5.47 ! [X3: real,Y: real,Z: real] :
% 5.25/5.47 ( ( ord_less_real @ ( ord_max_real @ X3 @ Y ) @ Z )
% 5.25/5.47 = ( ( ord_less_real @ X3 @ Z )
% 5.25/5.47 & ( ord_less_real @ Y @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_less_iff_conj
% 5.25/5.47 thf(fact_2689_max__less__iff__conj,axiom,
% 5.25/5.47 ! [X3: rat,Y: rat,Z: rat] :
% 5.25/5.47 ( ( ord_less_rat @ ( ord_max_rat @ X3 @ Y ) @ Z )
% 5.25/5.47 = ( ( ord_less_rat @ X3 @ Z )
% 5.25/5.47 & ( ord_less_rat @ Y @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_less_iff_conj
% 5.25/5.47 thf(fact_2690_max__less__iff__conj,axiom,
% 5.25/5.47 ! [X3: num,Y: num,Z: num] :
% 5.25/5.47 ( ( ord_less_num @ ( ord_max_num @ X3 @ Y ) @ Z )
% 5.25/5.47 = ( ( ord_less_num @ X3 @ Z )
% 5.25/5.47 & ( ord_less_num @ Y @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_less_iff_conj
% 5.25/5.47 thf(fact_2691_max__less__iff__conj,axiom,
% 5.25/5.47 ! [X3: nat,Y: nat,Z: nat] :
% 5.25/5.47 ( ( ord_less_nat @ ( ord_max_nat @ X3 @ Y ) @ Z )
% 5.25/5.47 = ( ( ord_less_nat @ X3 @ Z )
% 5.25/5.47 & ( ord_less_nat @ Y @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_less_iff_conj
% 5.25/5.47 thf(fact_2692_max__less__iff__conj,axiom,
% 5.25/5.47 ! [X3: int,Y: int,Z: int] :
% 5.25/5.47 ( ( ord_less_int @ ( ord_max_int @ X3 @ Y ) @ Z )
% 5.25/5.47 = ( ( ord_less_int @ X3 @ Z )
% 5.25/5.47 & ( ord_less_int @ Y @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max_less_iff_conj
% 5.25/5.47 thf(fact_2693_max_Oabsorb4,axiom,
% 5.25/5.47 ! [A: extended_enat,B: extended_enat] :
% 5.25/5.47 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.25/5.47 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.25/5.47 = B ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb4
% 5.25/5.47 thf(fact_2694_max_Oabsorb4,axiom,
% 5.25/5.47 ! [A: real,B: real] :
% 5.25/5.47 ( ( ord_less_real @ A @ B )
% 5.25/5.47 => ( ( ord_max_real @ A @ B )
% 5.25/5.47 = B ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb4
% 5.25/5.47 thf(fact_2695_max_Oabsorb4,axiom,
% 5.25/5.47 ! [A: rat,B: rat] :
% 5.25/5.47 ( ( ord_less_rat @ A @ B )
% 5.25/5.47 => ( ( ord_max_rat @ A @ B )
% 5.25/5.47 = B ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb4
% 5.25/5.47 thf(fact_2696_max_Oabsorb4,axiom,
% 5.25/5.47 ! [A: num,B: num] :
% 5.25/5.47 ( ( ord_less_num @ A @ B )
% 5.25/5.47 => ( ( ord_max_num @ A @ B )
% 5.25/5.47 = B ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb4
% 5.25/5.47 thf(fact_2697_max_Oabsorb4,axiom,
% 5.25/5.47 ! [A: nat,B: nat] :
% 5.25/5.47 ( ( ord_less_nat @ A @ B )
% 5.25/5.47 => ( ( ord_max_nat @ A @ B )
% 5.25/5.47 = B ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb4
% 5.25/5.47 thf(fact_2698_max_Oabsorb4,axiom,
% 5.25/5.47 ! [A: int,B: int] :
% 5.25/5.47 ( ( ord_less_int @ A @ B )
% 5.25/5.47 => ( ( ord_max_int @ A @ B )
% 5.25/5.47 = B ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb4
% 5.25/5.47 thf(fact_2699_max_Oabsorb3,axiom,
% 5.25/5.47 ! [B: extended_enat,A: extended_enat] :
% 5.25/5.47 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.25/5.47 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.25/5.47 = A ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb3
% 5.25/5.47 thf(fact_2700_max_Oabsorb3,axiom,
% 5.25/5.47 ! [B: real,A: real] :
% 5.25/5.47 ( ( ord_less_real @ B @ A )
% 5.25/5.47 => ( ( ord_max_real @ A @ B )
% 5.25/5.47 = A ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb3
% 5.25/5.47 thf(fact_2701_max_Oabsorb3,axiom,
% 5.25/5.47 ! [B: rat,A: rat] :
% 5.25/5.47 ( ( ord_less_rat @ B @ A )
% 5.25/5.47 => ( ( ord_max_rat @ A @ B )
% 5.25/5.47 = A ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb3
% 5.25/5.47 thf(fact_2702_max_Oabsorb3,axiom,
% 5.25/5.47 ! [B: num,A: num] :
% 5.25/5.47 ( ( ord_less_num @ B @ A )
% 5.25/5.47 => ( ( ord_max_num @ A @ B )
% 5.25/5.47 = A ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb3
% 5.25/5.47 thf(fact_2703_max_Oabsorb3,axiom,
% 5.25/5.47 ! [B: nat,A: nat] :
% 5.25/5.47 ( ( ord_less_nat @ B @ A )
% 5.25/5.47 => ( ( ord_max_nat @ A @ B )
% 5.25/5.47 = A ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb3
% 5.25/5.47 thf(fact_2704_max_Oabsorb3,axiom,
% 5.25/5.47 ! [B: int,A: int] :
% 5.25/5.47 ( ( ord_less_int @ B @ A )
% 5.25/5.47 => ( ( ord_max_int @ A @ B )
% 5.25/5.47 = A ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb3
% 5.25/5.47 thf(fact_2705_max_Obounded__iff,axiom,
% 5.25/5.47 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.25/5.47 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.25/5.47 = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.25/5.47 & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.bounded_iff
% 5.25/5.47 thf(fact_2706_max_Obounded__iff,axiom,
% 5.25/5.47 ! [B: rat,C: rat,A: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.25/5.47 = ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.47 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.bounded_iff
% 5.25/5.47 thf(fact_2707_max_Obounded__iff,axiom,
% 5.25/5.47 ! [B: num,C: num,A: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.25/5.47 = ( ( ord_less_eq_num @ B @ A )
% 5.25/5.47 & ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.bounded_iff
% 5.25/5.47 thf(fact_2708_max_Obounded__iff,axiom,
% 5.25/5.47 ! [B: nat,C: nat,A: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.25/5.47 = ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.47 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.bounded_iff
% 5.25/5.47 thf(fact_2709_max_Obounded__iff,axiom,
% 5.25/5.47 ! [B: int,C: int,A: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.25/5.47 = ( ( ord_less_eq_int @ B @ A )
% 5.25/5.47 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.bounded_iff
% 5.25/5.47 thf(fact_2710_max_Oabsorb2,axiom,
% 5.25/5.47 ! [A: extended_enat,B: extended_enat] :
% 5.25/5.47 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.25/5.47 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.25/5.47 = B ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb2
% 5.25/5.47 thf(fact_2711_max_Oabsorb2,axiom,
% 5.25/5.47 ! [A: rat,B: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.47 => ( ( ord_max_rat @ A @ B )
% 5.25/5.47 = B ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb2
% 5.25/5.47 thf(fact_2712_max_Oabsorb2,axiom,
% 5.25/5.47 ! [A: num,B: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.47 => ( ( ord_max_num @ A @ B )
% 5.25/5.47 = B ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb2
% 5.25/5.47 thf(fact_2713_max_Oabsorb2,axiom,
% 5.25/5.47 ! [A: nat,B: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.47 => ( ( ord_max_nat @ A @ B )
% 5.25/5.47 = B ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb2
% 5.25/5.47 thf(fact_2714_max_Oabsorb2,axiom,
% 5.25/5.47 ! [A: int,B: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.47 => ( ( ord_max_int @ A @ B )
% 5.25/5.47 = B ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb2
% 5.25/5.47 thf(fact_2715_max_Oabsorb1,axiom,
% 5.25/5.47 ! [B: extended_enat,A: extended_enat] :
% 5.25/5.47 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.25/5.47 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.25/5.47 = A ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb1
% 5.25/5.47 thf(fact_2716_max_Oabsorb1,axiom,
% 5.25/5.47 ! [B: rat,A: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.47 => ( ( ord_max_rat @ A @ B )
% 5.25/5.47 = A ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb1
% 5.25/5.47 thf(fact_2717_max_Oabsorb1,axiom,
% 5.25/5.47 ! [B: num,A: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ B @ A )
% 5.25/5.47 => ( ( ord_max_num @ A @ B )
% 5.25/5.47 = A ) ) ).
% 5.25/5.47
% 5.25/5.47 % max.absorb1
% 5.25/5.47 thf(fact_2718_max_Oabsorb1,axiom,
% 5.25/5.47 ! [B: nat,A: nat] :
% 5.25/5.48 ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.48 => ( ( ord_max_nat @ A @ B )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.absorb1
% 5.25/5.48 thf(fact_2719_max_Oabsorb1,axiom,
% 5.25/5.48 ! [B: int,A: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.48 => ( ( ord_max_int @ A @ B )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.absorb1
% 5.25/5.48 thf(fact_2720_both__member__options__def,axiom,
% 5.25/5.48 ( vEBT_V8194947554948674370ptions
% 5.25/5.48 = ( ^ [T2: vEBT_VEBT,X2: nat] :
% 5.25/5.48 ( ( vEBT_V5719532721284313246member @ T2 @ X2 )
% 5.25/5.48 | ( vEBT_VEBT_membermima @ T2 @ X2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % both_member_options_def
% 5.25/5.48 thf(fact_2721_gcd__nat__induct,axiom,
% 5.25/5.48 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.25/5.48 ( ! [M5: nat] : ( P @ M5 @ zero_zero_nat )
% 5.25/5.48 => ( ! [M5: nat,N3: nat] :
% 5.25/5.48 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.25/5.48 => ( ( P @ N3 @ ( modulo_modulo_nat @ M5 @ N3 ) )
% 5.25/5.48 => ( P @ M5 @ N3 ) ) )
% 5.25/5.48 => ( P @ M @ N ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % gcd_nat_induct
% 5.25/5.48 thf(fact_2722_buildup__nothing__in__min__max,axiom,
% 5.25/5.48 ! [N: nat,X3: nat] :
% 5.25/5.48 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X3 ) ).
% 5.25/5.48
% 5.25/5.48 % buildup_nothing_in_min_max
% 5.25/5.48 thf(fact_2723_max__enat__simps_I3_J,axiom,
% 5.25/5.48 ! [Q2: extended_enat] :
% 5.25/5.48 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.25/5.48 = Q2 ) ).
% 5.25/5.48
% 5.25/5.48 % max_enat_simps(3)
% 5.25/5.48 thf(fact_2724_max__enat__simps_I2_J,axiom,
% 5.25/5.48 ! [Q2: extended_enat] :
% 5.25/5.48 ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.25/5.48 = Q2 ) ).
% 5.25/5.48
% 5.25/5.48 % max_enat_simps(2)
% 5.25/5.48 thf(fact_2725_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.25/5.48 ! [Ux2: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.25/5.48 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy ) @ Uz ) ).
% 5.25/5.48
% 5.25/5.48 % VEBT_internal.membermima.simps(2)
% 5.25/5.48 thf(fact_2726_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.25/5.48 ! [Mi: nat,Ma: nat,Va2: list_VEBT_VEBT,Vb: vEBT_VEBT,X3: nat] :
% 5.25/5.48 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va2 @ Vb ) @ X3 )
% 5.25/5.48 = ( ( X3 = Mi )
% 5.25/5.48 | ( X3 = Ma ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % VEBT_internal.membermima.simps(3)
% 5.25/5.48 thf(fact_2727_Euclid__induct,axiom,
% 5.25/5.48 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.25/5.48 ( ! [A5: nat,B5: nat] :
% 5.25/5.48 ( ( P @ A5 @ B5 )
% 5.25/5.48 = ( P @ B5 @ A5 ) )
% 5.25/5.48 => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 5.25/5.48 => ( ! [A5: nat,B5: nat] :
% 5.25/5.48 ( ( P @ A5 @ B5 )
% 5.25/5.48 => ( P @ A5 @ ( plus_plus_nat @ A5 @ B5 ) ) )
% 5.25/5.48 => ( P @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % Euclid_induct
% 5.25/5.48 thf(fact_2728_max_OcoboundedI2,axiom,
% 5.25/5.48 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.25/5.48 ( ( ord_le2932123472753598470d_enat @ C @ B )
% 5.25/5.48 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.coboundedI2
% 5.25/5.48 thf(fact_2729_max_OcoboundedI2,axiom,
% 5.25/5.48 ! [C: rat,B: rat,A: rat] :
% 5.25/5.48 ( ( ord_less_eq_rat @ C @ B )
% 5.25/5.48 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.coboundedI2
% 5.25/5.48 thf(fact_2730_max_OcoboundedI2,axiom,
% 5.25/5.48 ! [C: num,B: num,A: num] :
% 5.25/5.48 ( ( ord_less_eq_num @ C @ B )
% 5.25/5.48 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.coboundedI2
% 5.25/5.48 thf(fact_2731_max_OcoboundedI2,axiom,
% 5.25/5.48 ! [C: nat,B: nat,A: nat] :
% 5.25/5.48 ( ( ord_less_eq_nat @ C @ B )
% 5.25/5.48 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.coboundedI2
% 5.25/5.48 thf(fact_2732_max_OcoboundedI2,axiom,
% 5.25/5.48 ! [C: int,B: int,A: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ C @ B )
% 5.25/5.48 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.coboundedI2
% 5.25/5.48 thf(fact_2733_max_OcoboundedI1,axiom,
% 5.25/5.48 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.25/5.48 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.25/5.48 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.coboundedI1
% 5.25/5.48 thf(fact_2734_max_OcoboundedI1,axiom,
% 5.25/5.48 ! [C: rat,A: rat,B: rat] :
% 5.25/5.48 ( ( ord_less_eq_rat @ C @ A )
% 5.25/5.48 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.coboundedI1
% 5.25/5.48 thf(fact_2735_max_OcoboundedI1,axiom,
% 5.25/5.48 ! [C: num,A: num,B: num] :
% 5.25/5.48 ( ( ord_less_eq_num @ C @ A )
% 5.25/5.48 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.coboundedI1
% 5.25/5.48 thf(fact_2736_max_OcoboundedI1,axiom,
% 5.25/5.48 ! [C: nat,A: nat,B: nat] :
% 5.25/5.48 ( ( ord_less_eq_nat @ C @ A )
% 5.25/5.48 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.coboundedI1
% 5.25/5.48 thf(fact_2737_max_OcoboundedI1,axiom,
% 5.25/5.48 ! [C: int,A: int,B: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ C @ A )
% 5.25/5.48 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.coboundedI1
% 5.25/5.48 thf(fact_2738_max_Oabsorb__iff2,axiom,
% 5.25/5.48 ( ord_le2932123472753598470d_enat
% 5.25/5.48 = ( ^ [A3: extended_enat,B2: extended_enat] :
% 5.25/5.48 ( ( ord_ma741700101516333627d_enat @ A3 @ B2 )
% 5.25/5.48 = B2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.absorb_iff2
% 5.25/5.48 thf(fact_2739_max_Oabsorb__iff2,axiom,
% 5.25/5.48 ( ord_less_eq_rat
% 5.25/5.48 = ( ^ [A3: rat,B2: rat] :
% 5.25/5.48 ( ( ord_max_rat @ A3 @ B2 )
% 5.25/5.48 = B2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.absorb_iff2
% 5.25/5.48 thf(fact_2740_max_Oabsorb__iff2,axiom,
% 5.25/5.48 ( ord_less_eq_num
% 5.25/5.48 = ( ^ [A3: num,B2: num] :
% 5.25/5.48 ( ( ord_max_num @ A3 @ B2 )
% 5.25/5.48 = B2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.absorb_iff2
% 5.25/5.48 thf(fact_2741_max_Oabsorb__iff2,axiom,
% 5.25/5.48 ( ord_less_eq_nat
% 5.25/5.48 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.48 ( ( ord_max_nat @ A3 @ B2 )
% 5.25/5.48 = B2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.absorb_iff2
% 5.25/5.48 thf(fact_2742_max_Oabsorb__iff2,axiom,
% 5.25/5.48 ( ord_less_eq_int
% 5.25/5.48 = ( ^ [A3: int,B2: int] :
% 5.25/5.48 ( ( ord_max_int @ A3 @ B2 )
% 5.25/5.48 = B2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.absorb_iff2
% 5.25/5.48 thf(fact_2743_max_Oabsorb__iff1,axiom,
% 5.25/5.48 ( ord_le2932123472753598470d_enat
% 5.25/5.48 = ( ^ [B2: extended_enat,A3: extended_enat] :
% 5.25/5.48 ( ( ord_ma741700101516333627d_enat @ A3 @ B2 )
% 5.25/5.48 = A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.absorb_iff1
% 5.25/5.48 thf(fact_2744_max_Oabsorb__iff1,axiom,
% 5.25/5.48 ( ord_less_eq_rat
% 5.25/5.48 = ( ^ [B2: rat,A3: rat] :
% 5.25/5.48 ( ( ord_max_rat @ A3 @ B2 )
% 5.25/5.48 = A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.absorb_iff1
% 5.25/5.48 thf(fact_2745_max_Oabsorb__iff1,axiom,
% 5.25/5.48 ( ord_less_eq_num
% 5.25/5.48 = ( ^ [B2: num,A3: num] :
% 5.25/5.48 ( ( ord_max_num @ A3 @ B2 )
% 5.25/5.48 = A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.absorb_iff1
% 5.25/5.48 thf(fact_2746_max_Oabsorb__iff1,axiom,
% 5.25/5.48 ( ord_less_eq_nat
% 5.25/5.48 = ( ^ [B2: nat,A3: nat] :
% 5.25/5.48 ( ( ord_max_nat @ A3 @ B2 )
% 5.25/5.48 = A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.absorb_iff1
% 5.25/5.48 thf(fact_2747_max_Oabsorb__iff1,axiom,
% 5.25/5.48 ( ord_less_eq_int
% 5.25/5.48 = ( ^ [B2: int,A3: int] :
% 5.25/5.48 ( ( ord_max_int @ A3 @ B2 )
% 5.25/5.48 = A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.absorb_iff1
% 5.25/5.48 thf(fact_2748_le__max__iff__disj,axiom,
% 5.25/5.48 ! [Z: extended_enat,X3: extended_enat,Y: extended_enat] :
% 5.25/5.48 ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X3 @ Y ) )
% 5.25/5.48 = ( ( ord_le2932123472753598470d_enat @ Z @ X3 )
% 5.25/5.48 | ( ord_le2932123472753598470d_enat @ Z @ Y ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_max_iff_disj
% 5.25/5.48 thf(fact_2749_le__max__iff__disj,axiom,
% 5.25/5.48 ! [Z: rat,X3: rat,Y: rat] :
% 5.25/5.48 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X3 @ Y ) )
% 5.25/5.48 = ( ( ord_less_eq_rat @ Z @ X3 )
% 5.25/5.48 | ( ord_less_eq_rat @ Z @ Y ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_max_iff_disj
% 5.25/5.48 thf(fact_2750_le__max__iff__disj,axiom,
% 5.25/5.48 ! [Z: num,X3: num,Y: num] :
% 5.25/5.48 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X3 @ Y ) )
% 5.25/5.48 = ( ( ord_less_eq_num @ Z @ X3 )
% 5.25/5.48 | ( ord_less_eq_num @ Z @ Y ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_max_iff_disj
% 5.25/5.48 thf(fact_2751_le__max__iff__disj,axiom,
% 5.25/5.48 ! [Z: nat,X3: nat,Y: nat] :
% 5.25/5.48 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X3 @ Y ) )
% 5.25/5.48 = ( ( ord_less_eq_nat @ Z @ X3 )
% 5.25/5.48 | ( ord_less_eq_nat @ Z @ Y ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_max_iff_disj
% 5.25/5.48 thf(fact_2752_le__max__iff__disj,axiom,
% 5.25/5.48 ! [Z: int,X3: int,Y: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X3 @ Y ) )
% 5.25/5.48 = ( ( ord_less_eq_int @ Z @ X3 )
% 5.25/5.48 | ( ord_less_eq_int @ Z @ Y ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_max_iff_disj
% 5.25/5.48 thf(fact_2753_max_Ocobounded2,axiom,
% 5.25/5.48 ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.cobounded2
% 5.25/5.48 thf(fact_2754_max_Ocobounded2,axiom,
% 5.25/5.48 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.cobounded2
% 5.25/5.48 thf(fact_2755_max_Ocobounded2,axiom,
% 5.25/5.48 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.cobounded2
% 5.25/5.48 thf(fact_2756_max_Ocobounded2,axiom,
% 5.25/5.48 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.cobounded2
% 5.25/5.48 thf(fact_2757_max_Ocobounded2,axiom,
% 5.25/5.48 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.cobounded2
% 5.25/5.48 thf(fact_2758_max_Ocobounded1,axiom,
% 5.25/5.48 ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.cobounded1
% 5.25/5.48 thf(fact_2759_max_Ocobounded1,axiom,
% 5.25/5.48 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.cobounded1
% 5.25/5.48 thf(fact_2760_max_Ocobounded1,axiom,
% 5.25/5.48 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.cobounded1
% 5.25/5.48 thf(fact_2761_max_Ocobounded1,axiom,
% 5.25/5.48 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.cobounded1
% 5.25/5.48 thf(fact_2762_max_Ocobounded1,axiom,
% 5.25/5.48 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.cobounded1
% 5.25/5.48 thf(fact_2763_max_Oorder__iff,axiom,
% 5.25/5.48 ( ord_le2932123472753598470d_enat
% 5.25/5.48 = ( ^ [B2: extended_enat,A3: extended_enat] :
% 5.25/5.48 ( A3
% 5.25/5.48 = ( ord_ma741700101516333627d_enat @ A3 @ B2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.order_iff
% 5.25/5.48 thf(fact_2764_max_Oorder__iff,axiom,
% 5.25/5.48 ( ord_less_eq_rat
% 5.25/5.48 = ( ^ [B2: rat,A3: rat] :
% 5.25/5.48 ( A3
% 5.25/5.48 = ( ord_max_rat @ A3 @ B2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.order_iff
% 5.25/5.48 thf(fact_2765_max_Oorder__iff,axiom,
% 5.25/5.48 ( ord_less_eq_num
% 5.25/5.48 = ( ^ [B2: num,A3: num] :
% 5.25/5.48 ( A3
% 5.25/5.48 = ( ord_max_num @ A3 @ B2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.order_iff
% 5.25/5.48 thf(fact_2766_max_Oorder__iff,axiom,
% 5.25/5.48 ( ord_less_eq_nat
% 5.25/5.48 = ( ^ [B2: nat,A3: nat] :
% 5.25/5.48 ( A3
% 5.25/5.48 = ( ord_max_nat @ A3 @ B2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.order_iff
% 5.25/5.48 thf(fact_2767_max_Oorder__iff,axiom,
% 5.25/5.48 ( ord_less_eq_int
% 5.25/5.48 = ( ^ [B2: int,A3: int] :
% 5.25/5.48 ( A3
% 5.25/5.48 = ( ord_max_int @ A3 @ B2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.order_iff
% 5.25/5.48 thf(fact_2768_max_OboundedI,axiom,
% 5.25/5.48 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.25/5.48 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.25/5.48 => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.25/5.48 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.boundedI
% 5.25/5.48 thf(fact_2769_max_OboundedI,axiom,
% 5.25/5.48 ! [B: rat,A: rat,C: rat] :
% 5.25/5.48 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.48 => ( ( ord_less_eq_rat @ C @ A )
% 5.25/5.48 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.boundedI
% 5.25/5.48 thf(fact_2770_max_OboundedI,axiom,
% 5.25/5.48 ! [B: num,A: num,C: num] :
% 5.25/5.48 ( ( ord_less_eq_num @ B @ A )
% 5.25/5.48 => ( ( ord_less_eq_num @ C @ A )
% 5.25/5.48 => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.boundedI
% 5.25/5.48 thf(fact_2771_max_OboundedI,axiom,
% 5.25/5.48 ! [B: nat,A: nat,C: nat] :
% 5.25/5.48 ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.48 => ( ( ord_less_eq_nat @ C @ A )
% 5.25/5.48 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.boundedI
% 5.25/5.48 thf(fact_2772_max_OboundedI,axiom,
% 5.25/5.48 ! [B: int,A: int,C: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.48 => ( ( ord_less_eq_int @ C @ A )
% 5.25/5.48 => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.boundedI
% 5.25/5.48 thf(fact_2773_max_OboundedE,axiom,
% 5.25/5.48 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.25/5.48 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.25/5.48 => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.25/5.48 => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.boundedE
% 5.25/5.48 thf(fact_2774_max_OboundedE,axiom,
% 5.25/5.48 ! [B: rat,C: rat,A: rat] :
% 5.25/5.48 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.25/5.48 => ~ ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.48 => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.boundedE
% 5.25/5.48 thf(fact_2775_max_OboundedE,axiom,
% 5.25/5.48 ! [B: num,C: num,A: num] :
% 5.25/5.48 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.25/5.48 => ~ ( ( ord_less_eq_num @ B @ A )
% 5.25/5.48 => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.boundedE
% 5.25/5.48 thf(fact_2776_max_OboundedE,axiom,
% 5.25/5.48 ! [B: nat,C: nat,A: nat] :
% 5.25/5.48 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.25/5.48 => ~ ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.48 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.boundedE
% 5.25/5.48 thf(fact_2777_max_OboundedE,axiom,
% 5.25/5.48 ! [B: int,C: int,A: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.25/5.48 => ~ ( ( ord_less_eq_int @ B @ A )
% 5.25/5.48 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.boundedE
% 5.25/5.48 thf(fact_2778_max_OorderI,axiom,
% 5.25/5.48 ! [A: extended_enat,B: extended_enat] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 5.25/5.48 => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.orderI
% 5.25/5.48 thf(fact_2779_max_OorderI,axiom,
% 5.25/5.48 ! [A: rat,B: rat] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( ord_max_rat @ A @ B ) )
% 5.25/5.48 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.orderI
% 5.25/5.48 thf(fact_2780_max_OorderI,axiom,
% 5.25/5.48 ! [A: num,B: num] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( ord_max_num @ A @ B ) )
% 5.25/5.48 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.orderI
% 5.25/5.48 thf(fact_2781_max_OorderI,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( ord_max_nat @ A @ B ) )
% 5.25/5.48 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.orderI
% 5.25/5.48 thf(fact_2782_max_OorderI,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( ord_max_int @ A @ B ) )
% 5.25/5.48 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.orderI
% 5.25/5.48 thf(fact_2783_max_OorderE,axiom,
% 5.25/5.48 ! [B: extended_enat,A: extended_enat] :
% 5.25/5.48 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.25/5.48 => ( A
% 5.25/5.48 = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.orderE
% 5.25/5.48 thf(fact_2784_max_OorderE,axiom,
% 5.25/5.48 ! [B: rat,A: rat] :
% 5.25/5.48 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.48 => ( A
% 5.25/5.48 = ( ord_max_rat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.orderE
% 5.25/5.48 thf(fact_2785_max_OorderE,axiom,
% 5.25/5.48 ! [B: num,A: num] :
% 5.25/5.48 ( ( ord_less_eq_num @ B @ A )
% 5.25/5.48 => ( A
% 5.25/5.48 = ( ord_max_num @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.orderE
% 5.25/5.48 thf(fact_2786_max_OorderE,axiom,
% 5.25/5.48 ! [B: nat,A: nat] :
% 5.25/5.48 ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.48 => ( A
% 5.25/5.48 = ( ord_max_nat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.orderE
% 5.25/5.48 thf(fact_2787_max_OorderE,axiom,
% 5.25/5.48 ! [B: int,A: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.48 => ( A
% 5.25/5.48 = ( ord_max_int @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.orderE
% 5.25/5.48 thf(fact_2788_max_Omono,axiom,
% 5.25/5.48 ! [C: extended_enat,A: extended_enat,D: extended_enat,B: extended_enat] :
% 5.25/5.48 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.25/5.48 => ( ( ord_le2932123472753598470d_enat @ D @ B )
% 5.25/5.48 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.mono
% 5.25/5.48 thf(fact_2789_max_Omono,axiom,
% 5.25/5.48 ! [C: rat,A: rat,D: rat,B: rat] :
% 5.25/5.48 ( ( ord_less_eq_rat @ C @ A )
% 5.25/5.48 => ( ( ord_less_eq_rat @ D @ B )
% 5.25/5.48 => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.mono
% 5.25/5.48 thf(fact_2790_max_Omono,axiom,
% 5.25/5.48 ! [C: num,A: num,D: num,B: num] :
% 5.25/5.48 ( ( ord_less_eq_num @ C @ A )
% 5.25/5.48 => ( ( ord_less_eq_num @ D @ B )
% 5.25/5.48 => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.mono
% 5.25/5.48 thf(fact_2791_max_Omono,axiom,
% 5.25/5.48 ! [C: nat,A: nat,D: nat,B: nat] :
% 5.25/5.48 ( ( ord_less_eq_nat @ C @ A )
% 5.25/5.48 => ( ( ord_less_eq_nat @ D @ B )
% 5.25/5.48 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.mono
% 5.25/5.48 thf(fact_2792_max_Omono,axiom,
% 5.25/5.48 ! [C: int,A: int,D: int,B: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ C @ A )
% 5.25/5.48 => ( ( ord_less_eq_int @ D @ B )
% 5.25/5.48 => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.mono
% 5.25/5.48 thf(fact_2793_max_Ostrict__coboundedI2,axiom,
% 5.25/5.48 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.25/5.48 ( ( ord_le72135733267957522d_enat @ C @ B )
% 5.25/5.48 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_coboundedI2
% 5.25/5.48 thf(fact_2794_max_Ostrict__coboundedI2,axiom,
% 5.25/5.48 ! [C: real,B: real,A: real] :
% 5.25/5.48 ( ( ord_less_real @ C @ B )
% 5.25/5.48 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_coboundedI2
% 5.25/5.48 thf(fact_2795_max_Ostrict__coboundedI2,axiom,
% 5.25/5.48 ! [C: rat,B: rat,A: rat] :
% 5.25/5.48 ( ( ord_less_rat @ C @ B )
% 5.25/5.48 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_coboundedI2
% 5.25/5.48 thf(fact_2796_max_Ostrict__coboundedI2,axiom,
% 5.25/5.48 ! [C: num,B: num,A: num] :
% 5.25/5.48 ( ( ord_less_num @ C @ B )
% 5.25/5.48 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_coboundedI2
% 5.25/5.48 thf(fact_2797_max_Ostrict__coboundedI2,axiom,
% 5.25/5.48 ! [C: nat,B: nat,A: nat] :
% 5.25/5.48 ( ( ord_less_nat @ C @ B )
% 5.25/5.48 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_coboundedI2
% 5.25/5.48 thf(fact_2798_max_Ostrict__coboundedI2,axiom,
% 5.25/5.48 ! [C: int,B: int,A: int] :
% 5.25/5.48 ( ( ord_less_int @ C @ B )
% 5.25/5.48 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_coboundedI2
% 5.25/5.48 thf(fact_2799_max_Ostrict__coboundedI1,axiom,
% 5.25/5.48 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.25/5.48 ( ( ord_le72135733267957522d_enat @ C @ A )
% 5.25/5.48 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_coboundedI1
% 5.25/5.48 thf(fact_2800_max_Ostrict__coboundedI1,axiom,
% 5.25/5.48 ! [C: real,A: real,B: real] :
% 5.25/5.48 ( ( ord_less_real @ C @ A )
% 5.25/5.48 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_coboundedI1
% 5.25/5.48 thf(fact_2801_max_Ostrict__coboundedI1,axiom,
% 5.25/5.48 ! [C: rat,A: rat,B: rat] :
% 5.25/5.48 ( ( ord_less_rat @ C @ A )
% 5.25/5.48 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_coboundedI1
% 5.25/5.48 thf(fact_2802_max_Ostrict__coboundedI1,axiom,
% 5.25/5.48 ! [C: num,A: num,B: num] :
% 5.25/5.48 ( ( ord_less_num @ C @ A )
% 5.25/5.48 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_coboundedI1
% 5.25/5.48 thf(fact_2803_max_Ostrict__coboundedI1,axiom,
% 5.25/5.48 ! [C: nat,A: nat,B: nat] :
% 5.25/5.48 ( ( ord_less_nat @ C @ A )
% 5.25/5.48 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_coboundedI1
% 5.25/5.48 thf(fact_2804_max_Ostrict__coboundedI1,axiom,
% 5.25/5.48 ! [C: int,A: int,B: int] :
% 5.25/5.48 ( ( ord_less_int @ C @ A )
% 5.25/5.48 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_coboundedI1
% 5.25/5.48 thf(fact_2805_max_Ostrict__order__iff,axiom,
% 5.25/5.48 ( ord_le72135733267957522d_enat
% 5.25/5.48 = ( ^ [B2: extended_enat,A3: extended_enat] :
% 5.25/5.48 ( ( A3
% 5.25/5.48 = ( ord_ma741700101516333627d_enat @ A3 @ B2 ) )
% 5.25/5.48 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_order_iff
% 5.25/5.48 thf(fact_2806_max_Ostrict__order__iff,axiom,
% 5.25/5.48 ( ord_less_real
% 5.25/5.48 = ( ^ [B2: real,A3: real] :
% 5.25/5.48 ( ( A3
% 5.25/5.48 = ( ord_max_real @ A3 @ B2 ) )
% 5.25/5.48 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_order_iff
% 5.25/5.48 thf(fact_2807_max_Ostrict__order__iff,axiom,
% 5.25/5.48 ( ord_less_rat
% 5.25/5.48 = ( ^ [B2: rat,A3: rat] :
% 5.25/5.48 ( ( A3
% 5.25/5.48 = ( ord_max_rat @ A3 @ B2 ) )
% 5.25/5.48 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_order_iff
% 5.25/5.48 thf(fact_2808_max_Ostrict__order__iff,axiom,
% 5.25/5.48 ( ord_less_num
% 5.25/5.48 = ( ^ [B2: num,A3: num] :
% 5.25/5.48 ( ( A3
% 5.25/5.48 = ( ord_max_num @ A3 @ B2 ) )
% 5.25/5.48 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_order_iff
% 5.25/5.48 thf(fact_2809_max_Ostrict__order__iff,axiom,
% 5.25/5.48 ( ord_less_nat
% 5.25/5.48 = ( ^ [B2: nat,A3: nat] :
% 5.25/5.48 ( ( A3
% 5.25/5.48 = ( ord_max_nat @ A3 @ B2 ) )
% 5.25/5.48 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_order_iff
% 5.25/5.48 thf(fact_2810_max_Ostrict__order__iff,axiom,
% 5.25/5.48 ( ord_less_int
% 5.25/5.48 = ( ^ [B2: int,A3: int] :
% 5.25/5.48 ( ( A3
% 5.25/5.48 = ( ord_max_int @ A3 @ B2 ) )
% 5.25/5.48 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_order_iff
% 5.25/5.48 thf(fact_2811_max_Ostrict__boundedE,axiom,
% 5.25/5.48 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.25/5.48 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.25/5.48 => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.25/5.48 => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_boundedE
% 5.25/5.48 thf(fact_2812_max_Ostrict__boundedE,axiom,
% 5.25/5.48 ! [B: real,C: real,A: real] :
% 5.25/5.48 ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 5.25/5.48 => ~ ( ( ord_less_real @ B @ A )
% 5.25/5.48 => ~ ( ord_less_real @ C @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_boundedE
% 5.25/5.48 thf(fact_2813_max_Ostrict__boundedE,axiom,
% 5.25/5.48 ! [B: rat,C: rat,A: rat] :
% 5.25/5.48 ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.25/5.48 => ~ ( ( ord_less_rat @ B @ A )
% 5.25/5.48 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_boundedE
% 5.25/5.48 thf(fact_2814_max_Ostrict__boundedE,axiom,
% 5.25/5.48 ! [B: num,C: num,A: num] :
% 5.25/5.48 ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 5.25/5.48 => ~ ( ( ord_less_num @ B @ A )
% 5.25/5.48 => ~ ( ord_less_num @ C @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_boundedE
% 5.25/5.48 thf(fact_2815_max_Ostrict__boundedE,axiom,
% 5.25/5.48 ! [B: nat,C: nat,A: nat] :
% 5.25/5.48 ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.25/5.48 => ~ ( ( ord_less_nat @ B @ A )
% 5.25/5.48 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_boundedE
% 5.25/5.48 thf(fact_2816_max_Ostrict__boundedE,axiom,
% 5.25/5.48 ! [B: int,C: int,A: int] :
% 5.25/5.48 ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 5.25/5.48 => ~ ( ( ord_less_int @ B @ A )
% 5.25/5.48 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max.strict_boundedE
% 5.25/5.48 thf(fact_2817_less__max__iff__disj,axiom,
% 5.25/5.48 ! [Z: extended_enat,X3: extended_enat,Y: extended_enat] :
% 5.25/5.48 ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X3 @ Y ) )
% 5.25/5.48 = ( ( ord_le72135733267957522d_enat @ Z @ X3 )
% 5.25/5.48 | ( ord_le72135733267957522d_enat @ Z @ Y ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % less_max_iff_disj
% 5.25/5.48 thf(fact_2818_less__max__iff__disj,axiom,
% 5.25/5.48 ! [Z: real,X3: real,Y: real] :
% 5.25/5.48 ( ( ord_less_real @ Z @ ( ord_max_real @ X3 @ Y ) )
% 5.25/5.48 = ( ( ord_less_real @ Z @ X3 )
% 5.25/5.48 | ( ord_less_real @ Z @ Y ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % less_max_iff_disj
% 5.25/5.48 thf(fact_2819_less__max__iff__disj,axiom,
% 5.25/5.48 ! [Z: rat,X3: rat,Y: rat] :
% 5.25/5.48 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X3 @ Y ) )
% 5.25/5.48 = ( ( ord_less_rat @ Z @ X3 )
% 5.25/5.48 | ( ord_less_rat @ Z @ Y ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % less_max_iff_disj
% 5.25/5.48 thf(fact_2820_less__max__iff__disj,axiom,
% 5.25/5.48 ! [Z: num,X3: num,Y: num] :
% 5.25/5.48 ( ( ord_less_num @ Z @ ( ord_max_num @ X3 @ Y ) )
% 5.25/5.48 = ( ( ord_less_num @ Z @ X3 )
% 5.25/5.48 | ( ord_less_num @ Z @ Y ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % less_max_iff_disj
% 5.25/5.48 thf(fact_2821_less__max__iff__disj,axiom,
% 5.25/5.48 ! [Z: nat,X3: nat,Y: nat] :
% 5.25/5.48 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X3 @ Y ) )
% 5.25/5.48 = ( ( ord_less_nat @ Z @ X3 )
% 5.25/5.48 | ( ord_less_nat @ Z @ Y ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % less_max_iff_disj
% 5.25/5.48 thf(fact_2822_less__max__iff__disj,axiom,
% 5.25/5.48 ! [Z: int,X3: int,Y: int] :
% 5.25/5.48 ( ( ord_less_int @ Z @ ( ord_max_int @ X3 @ Y ) )
% 5.25/5.48 = ( ( ord_less_int @ Z @ X3 )
% 5.25/5.48 | ( ord_less_int @ Z @ Y ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % less_max_iff_disj
% 5.25/5.48 thf(fact_2823_concat__bit__Suc,axiom,
% 5.25/5.48 ! [N: nat,K: int,L2: int] :
% 5.25/5.48 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L2 )
% 5.25/5.48 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % concat_bit_Suc
% 5.25/5.48 thf(fact_2824_option_Osize_I3_J,axiom,
% 5.25/5.48 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.25/5.48 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % option.size(3)
% 5.25/5.48 thf(fact_2825_option_Osize_I3_J,axiom,
% 5.25/5.48 ( ( size_size_option_num @ none_num )
% 5.25/5.48 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % option.size(3)
% 5.25/5.48 thf(fact_2826_option_Osize_I4_J,axiom,
% 5.25/5.48 ! [X22: product_prod_nat_nat] :
% 5.25/5.48 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.25/5.48 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % option.size(4)
% 5.25/5.48 thf(fact_2827_option_Osize_I4_J,axiom,
% 5.25/5.48 ! [X22: num] :
% 5.25/5.48 ( ( size_size_option_num @ ( some_num @ X22 ) )
% 5.25/5.48 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % option.size(4)
% 5.25/5.48 thf(fact_2828_neg__eucl__rel__int__mult__2,axiom,
% 5.25/5.48 ! [B: int,A: int,Q2: int,R2: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.25/5.48 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.25/5.48 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % neg_eucl_rel_int_mult_2
% 5.25/5.48 thf(fact_2829_even__succ__mod__exp,axiom,
% 5.25/5.48 ! [A: nat,N: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.48 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.48 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_succ_mod_exp
% 5.25/5.48 thf(fact_2830_even__succ__mod__exp,axiom,
% 5.25/5.48 ! [A: int,N: nat] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.48 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.48 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_succ_mod_exp
% 5.25/5.48 thf(fact_2831_even__succ__mod__exp,axiom,
% 5.25/5.48 ! [A: code_integer,N: nat] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.48 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.48 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_succ_mod_exp
% 5.25/5.48 thf(fact_2832_even__succ__div__exp,axiom,
% 5.25/5.48 ! [A: code_integer,N: nat] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.48 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_succ_div_exp
% 5.25/5.48 thf(fact_2833_even__succ__div__exp,axiom,
% 5.25/5.48 ! [A: nat,N: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.48 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.48 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_succ_div_exp
% 5.25/5.48 thf(fact_2834_even__succ__div__exp,axiom,
% 5.25/5.48 ! [A: int,N: nat] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.48 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.48 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_succ_div_exp
% 5.25/5.48 thf(fact_2835_vebt__insert_Oelims,axiom,
% 5.25/5.48 ! [X3: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.25/5.48 ( ( ( vEBT_vebt_insert @ X3 @ Xa2 )
% 5.25/5.48 = Y )
% 5.25/5.48 => ( ! [A5: $o,B5: $o] :
% 5.25/5.48 ( ( X3
% 5.25/5.48 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.48 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.48 => ( Y
% 5.25/5.48 = ( vEBT_Leaf @ $true @ B5 ) ) )
% 5.25/5.48 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.48 => ( ( ( Xa2 = one_one_nat )
% 5.25/5.48 => ( Y
% 5.25/5.48 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 5.25/5.48 & ( ( Xa2 != one_one_nat )
% 5.25/5.48 => ( Y
% 5.25/5.48 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) ) )
% 5.25/5.48 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.25/5.48 ( ( X3
% 5.25/5.48 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.25/5.48 => ( Y
% 5.25/5.48 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) ) )
% 5.25/5.48 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.25/5.48 ( ( X3
% 5.25/5.48 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.25/5.48 => ( Y
% 5.25/5.48 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) ) )
% 5.25/5.48 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.25/5.48 ( ( X3
% 5.25/5.48 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.25/5.48 => ( Y
% 5.25/5.48 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.25/5.48 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.25/5.48 ( ( X3
% 5.25/5.48 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.25/5.48 => ( Y
% 5.25/5.48 != ( if_VEBT_VEBT
% 5.25/5.48 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.48 & ~ ( ( Xa2 = Mi2 )
% 5.25/5.48 | ( Xa2 = Ma2 ) ) )
% 5.25/5.48 @ ( 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 @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.25/5.48 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % vebt_insert.elims
% 5.25/5.48 thf(fact_2836_add__scale__eq__noteq,axiom,
% 5.25/5.48 ! [R2: complex,A: complex,B: complex,C: complex,D: complex] :
% 5.25/5.48 ( ( R2 != zero_zero_complex )
% 5.25/5.48 => ( ( ( A = B )
% 5.25/5.48 & ( C != D ) )
% 5.25/5.48 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R2 @ C ) )
% 5.25/5.48 != ( plus_plus_complex @ B @ ( times_times_complex @ R2 @ D ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % add_scale_eq_noteq
% 5.25/5.48 thf(fact_2837_add__scale__eq__noteq,axiom,
% 5.25/5.48 ! [R2: real,A: real,B: real,C: real,D: real] :
% 5.25/5.48 ( ( R2 != zero_zero_real )
% 5.25/5.48 => ( ( ( A = B )
% 5.25/5.48 & ( C != D ) )
% 5.25/5.48 => ( ( plus_plus_real @ A @ ( times_times_real @ R2 @ C ) )
% 5.25/5.48 != ( plus_plus_real @ B @ ( times_times_real @ R2 @ D ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % add_scale_eq_noteq
% 5.25/5.48 thf(fact_2838_add__scale__eq__noteq,axiom,
% 5.25/5.48 ! [R2: rat,A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.48 ( ( R2 != zero_zero_rat )
% 5.25/5.48 => ( ( ( A = B )
% 5.25/5.48 & ( C != D ) )
% 5.25/5.48 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 5.25/5.48 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % add_scale_eq_noteq
% 5.25/5.48 thf(fact_2839_add__scale__eq__noteq,axiom,
% 5.25/5.48 ! [R2: nat,A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.48 ( ( R2 != zero_zero_nat )
% 5.25/5.48 => ( ( ( A = B )
% 5.25/5.48 & ( C != D ) )
% 5.25/5.48 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 5.25/5.48 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % add_scale_eq_noteq
% 5.25/5.48 thf(fact_2840_add__scale__eq__noteq,axiom,
% 5.25/5.48 ! [R2: int,A: int,B: int,C: int,D: int] :
% 5.25/5.48 ( ( R2 != zero_zero_int )
% 5.25/5.48 => ( ( ( A = B )
% 5.25/5.48 & ( C != D ) )
% 5.25/5.48 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 5.25/5.48 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % add_scale_eq_noteq
% 5.25/5.48 thf(fact_2841_signed__take__bit__Suc__bit1,axiom,
% 5.25/5.48 ! [N: nat,K: num] :
% 5.25/5.48 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.25/5.48 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.25/5.48
% 5.25/5.48 % signed_take_bit_Suc_bit1
% 5.25/5.48 thf(fact_2842_set__vebt_H__def,axiom,
% 5.25/5.48 ( vEBT_VEBT_set_vebt
% 5.25/5.48 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % set_vebt'_def
% 5.25/5.48 thf(fact_2843_semiring__norm_I90_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( ( bit1 @ M )
% 5.25/5.48 = ( bit1 @ N ) )
% 5.25/5.48 = ( M = N ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(90)
% 5.25/5.48 thf(fact_2844_nat__dvd__1__iff__1,axiom,
% 5.25/5.48 ! [M: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.25/5.48 = ( M = one_one_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % nat_dvd_1_iff_1
% 5.25/5.48 thf(fact_2845_diff__self,axiom,
% 5.25/5.48 ! [A: complex] :
% 5.25/5.48 ( ( minus_minus_complex @ A @ A )
% 5.25/5.48 = zero_zero_complex ) ).
% 5.25/5.48
% 5.25/5.48 % diff_self
% 5.25/5.48 thf(fact_2846_diff__self,axiom,
% 5.25/5.48 ! [A: real] :
% 5.25/5.48 ( ( minus_minus_real @ A @ A )
% 5.25/5.48 = zero_zero_real ) ).
% 5.25/5.48
% 5.25/5.48 % diff_self
% 5.25/5.48 thf(fact_2847_diff__self,axiom,
% 5.25/5.48 ! [A: rat] :
% 5.25/5.48 ( ( minus_minus_rat @ A @ A )
% 5.25/5.48 = zero_zero_rat ) ).
% 5.25/5.48
% 5.25/5.48 % diff_self
% 5.25/5.48 thf(fact_2848_diff__self,axiom,
% 5.25/5.48 ! [A: int] :
% 5.25/5.48 ( ( minus_minus_int @ A @ A )
% 5.25/5.48 = zero_zero_int ) ).
% 5.25/5.48
% 5.25/5.48 % diff_self
% 5.25/5.48 thf(fact_2849_diff__0__right,axiom,
% 5.25/5.48 ! [A: complex] :
% 5.25/5.48 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % diff_0_right
% 5.25/5.48 thf(fact_2850_diff__0__right,axiom,
% 5.25/5.48 ! [A: real] :
% 5.25/5.48 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % diff_0_right
% 5.25/5.48 thf(fact_2851_diff__0__right,axiom,
% 5.25/5.48 ! [A: rat] :
% 5.25/5.48 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % diff_0_right
% 5.25/5.48 thf(fact_2852_diff__0__right,axiom,
% 5.25/5.48 ! [A: int] :
% 5.25/5.48 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % diff_0_right
% 5.25/5.48 thf(fact_2853_zero__diff,axiom,
% 5.25/5.48 ! [A: nat] :
% 5.25/5.48 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 5.25/5.48 = zero_zero_nat ) ).
% 5.25/5.48
% 5.25/5.48 % zero_diff
% 5.25/5.48 thf(fact_2854_diff__zero,axiom,
% 5.25/5.48 ! [A: complex] :
% 5.25/5.48 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % diff_zero
% 5.25/5.48 thf(fact_2855_diff__zero,axiom,
% 5.25/5.48 ! [A: real] :
% 5.25/5.48 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % diff_zero
% 5.25/5.48 thf(fact_2856_diff__zero,axiom,
% 5.25/5.48 ! [A: rat] :
% 5.25/5.48 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % diff_zero
% 5.25/5.48 thf(fact_2857_diff__zero,axiom,
% 5.25/5.48 ! [A: nat] :
% 5.25/5.48 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % diff_zero
% 5.25/5.48 thf(fact_2858_diff__zero,axiom,
% 5.25/5.48 ! [A: int] :
% 5.25/5.48 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % diff_zero
% 5.25/5.48 thf(fact_2859_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.25/5.48 ! [A: complex] :
% 5.25/5.48 ( ( minus_minus_complex @ A @ A )
% 5.25/5.48 = zero_zero_complex ) ).
% 5.25/5.48
% 5.25/5.48 % cancel_comm_monoid_add_class.diff_cancel
% 5.25/5.48 thf(fact_2860_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.25/5.48 ! [A: real] :
% 5.25/5.48 ( ( minus_minus_real @ A @ A )
% 5.25/5.48 = zero_zero_real ) ).
% 5.25/5.48
% 5.25/5.48 % cancel_comm_monoid_add_class.diff_cancel
% 5.25/5.48 thf(fact_2861_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.25/5.48 ! [A: rat] :
% 5.25/5.48 ( ( minus_minus_rat @ A @ A )
% 5.25/5.48 = zero_zero_rat ) ).
% 5.25/5.48
% 5.25/5.48 % cancel_comm_monoid_add_class.diff_cancel
% 5.25/5.48 thf(fact_2862_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.25/5.48 ! [A: nat] :
% 5.25/5.48 ( ( minus_minus_nat @ A @ A )
% 5.25/5.48 = zero_zero_nat ) ).
% 5.25/5.48
% 5.25/5.48 % cancel_comm_monoid_add_class.diff_cancel
% 5.25/5.48 thf(fact_2863_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.25/5.48 ! [A: int] :
% 5.25/5.48 ( ( minus_minus_int @ A @ A )
% 5.25/5.48 = zero_zero_int ) ).
% 5.25/5.48
% 5.25/5.48 % cancel_comm_monoid_add_class.diff_cancel
% 5.25/5.48 thf(fact_2864_add__diff__cancel__right_H,axiom,
% 5.25/5.48 ! [A: real,B: real] :
% 5.25/5.48 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_right'
% 5.25/5.48 thf(fact_2865_add__diff__cancel__right_H,axiom,
% 5.25/5.48 ! [A: rat,B: rat] :
% 5.25/5.48 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_right'
% 5.25/5.48 thf(fact_2866_add__diff__cancel__right_H,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_right'
% 5.25/5.48 thf(fact_2867_add__diff__cancel__right_H,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_right'
% 5.25/5.48 thf(fact_2868_add__diff__cancel__right,axiom,
% 5.25/5.48 ! [A: real,C: real,B: real] :
% 5.25/5.48 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.25/5.48 = ( minus_minus_real @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_right
% 5.25/5.48 thf(fact_2869_add__diff__cancel__right,axiom,
% 5.25/5.48 ! [A: rat,C: rat,B: rat] :
% 5.25/5.48 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.48 = ( minus_minus_rat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_right
% 5.25/5.48 thf(fact_2870_add__diff__cancel__right,axiom,
% 5.25/5.48 ! [A: nat,C: nat,B: nat] :
% 5.25/5.48 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.48 = ( minus_minus_nat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_right
% 5.25/5.48 thf(fact_2871_add__diff__cancel__right,axiom,
% 5.25/5.48 ! [A: int,C: int,B: int] :
% 5.25/5.48 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.25/5.48 = ( minus_minus_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_right
% 5.25/5.48 thf(fact_2872_add__diff__cancel__left_H,axiom,
% 5.25/5.48 ! [A: real,B: real] :
% 5.25/5.48 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 5.25/5.48 = B ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_left'
% 5.25/5.48 thf(fact_2873_add__diff__cancel__left_H,axiom,
% 5.25/5.48 ! [A: rat,B: rat] :
% 5.25/5.48 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 5.25/5.48 = B ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_left'
% 5.25/5.48 thf(fact_2874_add__diff__cancel__left_H,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 5.25/5.48 = B ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_left'
% 5.25/5.48 thf(fact_2875_add__diff__cancel__left_H,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 5.25/5.48 = B ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_left'
% 5.25/5.48 thf(fact_2876_add__diff__cancel__left,axiom,
% 5.25/5.48 ! [C: real,A: real,B: real] :
% 5.25/5.48 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.25/5.48 = ( minus_minus_real @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_left
% 5.25/5.48 thf(fact_2877_add__diff__cancel__left,axiom,
% 5.25/5.48 ! [C: rat,A: rat,B: rat] :
% 5.25/5.48 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.25/5.48 = ( minus_minus_rat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_left
% 5.25/5.48 thf(fact_2878_add__diff__cancel__left,axiom,
% 5.25/5.48 ! [C: nat,A: nat,B: nat] :
% 5.25/5.48 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.25/5.48 = ( minus_minus_nat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_left
% 5.25/5.48 thf(fact_2879_add__diff__cancel__left,axiom,
% 5.25/5.48 ! [C: int,A: int,B: int] :
% 5.25/5.48 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.25/5.48 = ( minus_minus_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel_left
% 5.25/5.48 thf(fact_2880_diff__add__cancel,axiom,
% 5.25/5.48 ! [A: real,B: real] :
% 5.25/5.48 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % diff_add_cancel
% 5.25/5.48 thf(fact_2881_diff__add__cancel,axiom,
% 5.25/5.48 ! [A: rat,B: rat] :
% 5.25/5.48 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % diff_add_cancel
% 5.25/5.48 thf(fact_2882_diff__add__cancel,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % diff_add_cancel
% 5.25/5.48 thf(fact_2883_add__diff__cancel,axiom,
% 5.25/5.48 ! [A: real,B: real] :
% 5.25/5.48 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel
% 5.25/5.48 thf(fact_2884_add__diff__cancel,axiom,
% 5.25/5.48 ! [A: rat,B: rat] :
% 5.25/5.48 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel
% 5.25/5.48 thf(fact_2885_add__diff__cancel,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.25/5.48 = A ) ).
% 5.25/5.48
% 5.25/5.48 % add_diff_cancel
% 5.25/5.48 thf(fact_2886_dvd__0__right,axiom,
% 5.25/5.48 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_right
% 5.25/5.48 thf(fact_2887_dvd__0__right,axiom,
% 5.25/5.48 ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_right
% 5.25/5.48 thf(fact_2888_dvd__0__right,axiom,
% 5.25/5.48 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_right
% 5.25/5.48 thf(fact_2889_dvd__0__right,axiom,
% 5.25/5.48 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_right
% 5.25/5.48 thf(fact_2890_dvd__0__right,axiom,
% 5.25/5.48 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_right
% 5.25/5.48 thf(fact_2891_dvd__0__right,axiom,
% 5.25/5.48 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_right
% 5.25/5.48 thf(fact_2892_dvd__0__left__iff,axiom,
% 5.25/5.48 ! [A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.25/5.48 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_left_iff
% 5.25/5.48 thf(fact_2893_dvd__0__left__iff,axiom,
% 5.25/5.48 ! [A: complex] :
% 5.25/5.48 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.25/5.48 = ( A = zero_zero_complex ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_left_iff
% 5.25/5.48 thf(fact_2894_dvd__0__left__iff,axiom,
% 5.25/5.48 ! [A: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.25/5.48 = ( A = zero_zero_real ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_left_iff
% 5.25/5.48 thf(fact_2895_dvd__0__left__iff,axiom,
% 5.25/5.48 ! [A: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.25/5.48 = ( A = zero_zero_rat ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_left_iff
% 5.25/5.48 thf(fact_2896_dvd__0__left__iff,axiom,
% 5.25/5.48 ! [A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.25/5.48 = ( A = zero_zero_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_left_iff
% 5.25/5.48 thf(fact_2897_dvd__0__left__iff,axiom,
% 5.25/5.48 ! [A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.25/5.48 = ( A = zero_zero_int ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_left_iff
% 5.25/5.48 thf(fact_2898_dvd__add__triv__right__iff,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_triv_right_iff
% 5.25/5.48 thf(fact_2899_dvd__add__triv__right__iff,axiom,
% 5.25/5.48 ! [A: real,B: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.25/5.48 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_triv_right_iff
% 5.25/5.48 thf(fact_2900_dvd__add__triv__right__iff,axiom,
% 5.25/5.48 ! [A: rat,B: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.25/5.48 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_triv_right_iff
% 5.25/5.48 thf(fact_2901_dvd__add__triv__right__iff,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.25/5.48 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_triv_right_iff
% 5.25/5.48 thf(fact_2902_dvd__add__triv__right__iff,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.25/5.48 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_triv_right_iff
% 5.25/5.48 thf(fact_2903_dvd__add__triv__left__iff,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_triv_left_iff
% 5.25/5.48 thf(fact_2904_dvd__add__triv__left__iff,axiom,
% 5.25/5.48 ! [A: real,B: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.25/5.48 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_triv_left_iff
% 5.25/5.48 thf(fact_2905_dvd__add__triv__left__iff,axiom,
% 5.25/5.48 ! [A: rat,B: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.25/5.48 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_triv_left_iff
% 5.25/5.48 thf(fact_2906_dvd__add__triv__left__iff,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.25/5.48 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_triv_left_iff
% 5.25/5.48 thf(fact_2907_dvd__add__triv__left__iff,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.25/5.48 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_triv_left_iff
% 5.25/5.48 thf(fact_2908_dvd__1__iff__1,axiom,
% 5.25/5.48 ! [M: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.25/5.48 = ( M
% 5.25/5.48 = ( suc @ zero_zero_nat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_1_iff_1
% 5.25/5.48 thf(fact_2909_dvd__1__left,axiom,
% 5.25/5.48 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_1_left
% 5.25/5.48 thf(fact_2910_div__dvd__div,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_dvd_div
% 5.25/5.48 thf(fact_2911_div__dvd__div,axiom,
% 5.25/5.48 ! [A: nat,B: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_nat @ A @ C )
% 5.25/5.48 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.25/5.48 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_dvd_div
% 5.25/5.48 thf(fact_2912_div__dvd__div,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_int @ A @ C )
% 5.25/5.48 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.25/5.48 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_dvd_div
% 5.25/5.48 thf(fact_2913_semiring__norm_I88_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( bit0 @ M )
% 5.25/5.48 != ( bit1 @ N ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(88)
% 5.25/5.48 thf(fact_2914_semiring__norm_I89_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( bit1 @ M )
% 5.25/5.48 != ( bit0 @ N ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(89)
% 5.25/5.48 thf(fact_2915_semiring__norm_I84_J,axiom,
% 5.25/5.48 ! [N: num] :
% 5.25/5.48 ( one
% 5.25/5.48 != ( bit1 @ N ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(84)
% 5.25/5.48 thf(fact_2916_semiring__norm_I86_J,axiom,
% 5.25/5.48 ! [M: num] :
% 5.25/5.48 ( ( bit1 @ M )
% 5.25/5.48 != one ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(86)
% 5.25/5.48 thf(fact_2917_minus__mod__self2,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.25/5.48 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % minus_mod_self2
% 5.25/5.48 thf(fact_2918_minus__mod__self2,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 5.25/5.48 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % minus_mod_self2
% 5.25/5.48 thf(fact_2919_nat__mult__dvd__cancel__disj,axiom,
% 5.25/5.48 ! [K: nat,M: nat,N: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.25/5.48 = ( ( K = zero_zero_nat )
% 5.25/5.48 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nat_mult_dvd_cancel_disj
% 5.25/5.48 thf(fact_2920_concat__bit__0,axiom,
% 5.25/5.48 ! [K: int,L2: int] :
% 5.25/5.48 ( ( bit_concat_bit @ zero_zero_nat @ K @ L2 )
% 5.25/5.48 = L2 ) ).
% 5.25/5.48
% 5.25/5.48 % concat_bit_0
% 5.25/5.48 thf(fact_2921_semiring__norm_I80_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.25/5.48 = ( ord_less_num @ M @ N ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(80)
% 5.25/5.48 thf(fact_2922_semiring__norm_I73_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.25/5.48 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(73)
% 5.25/5.48 thf(fact_2923_diff__ge__0__iff__ge,axiom,
% 5.25/5.48 ! [A: real,B: real] :
% 5.25/5.48 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.25/5.48 = ( ord_less_eq_real @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_ge_0_iff_ge
% 5.25/5.48 thf(fact_2924_diff__ge__0__iff__ge,axiom,
% 5.25/5.48 ! [A: rat,B: rat] :
% 5.25/5.48 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.25/5.48 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_ge_0_iff_ge
% 5.25/5.48 thf(fact_2925_diff__ge__0__iff__ge,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.25/5.48 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_ge_0_iff_ge
% 5.25/5.48 thf(fact_2926_diff__gt__0__iff__gt,axiom,
% 5.25/5.48 ! [A: real,B: real] :
% 5.25/5.48 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.25/5.48 = ( ord_less_real @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_gt_0_iff_gt
% 5.25/5.48 thf(fact_2927_diff__gt__0__iff__gt,axiom,
% 5.25/5.48 ! [A: rat,B: rat] :
% 5.25/5.48 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.25/5.48 = ( ord_less_rat @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_gt_0_iff_gt
% 5.25/5.48 thf(fact_2928_diff__gt__0__iff__gt,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.25/5.48 = ( ord_less_int @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_gt_0_iff_gt
% 5.25/5.48 thf(fact_2929_le__add__diff__inverse,axiom,
% 5.25/5.48 ! [B: real,A: real] :
% 5.25/5.48 ( ( ord_less_eq_real @ B @ A )
% 5.25/5.48 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_add_diff_inverse
% 5.25/5.48 thf(fact_2930_le__add__diff__inverse,axiom,
% 5.25/5.48 ! [B: rat,A: rat] :
% 5.25/5.48 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.48 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_add_diff_inverse
% 5.25/5.48 thf(fact_2931_le__add__diff__inverse,axiom,
% 5.25/5.48 ! [B: nat,A: nat] :
% 5.25/5.48 ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.48 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_add_diff_inverse
% 5.25/5.48 thf(fact_2932_le__add__diff__inverse,axiom,
% 5.25/5.48 ! [B: int,A: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.48 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_add_diff_inverse
% 5.25/5.48 thf(fact_2933_le__add__diff__inverse2,axiom,
% 5.25/5.48 ! [B: real,A: real] :
% 5.25/5.48 ( ( ord_less_eq_real @ B @ A )
% 5.25/5.48 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_add_diff_inverse2
% 5.25/5.48 thf(fact_2934_le__add__diff__inverse2,axiom,
% 5.25/5.48 ! [B: rat,A: rat] :
% 5.25/5.48 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.48 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_add_diff_inverse2
% 5.25/5.48 thf(fact_2935_le__add__diff__inverse2,axiom,
% 5.25/5.48 ! [B: nat,A: nat] :
% 5.25/5.48 ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.48 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_add_diff_inverse2
% 5.25/5.48 thf(fact_2936_le__add__diff__inverse2,axiom,
% 5.25/5.48 ! [B: int,A: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.48 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_add_diff_inverse2
% 5.25/5.48 thf(fact_2937_diff__numeral__special_I9_J,axiom,
% 5.25/5.48 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.25/5.48 = zero_zero_complex ) ).
% 5.25/5.48
% 5.25/5.48 % diff_numeral_special(9)
% 5.25/5.48 thf(fact_2938_diff__numeral__special_I9_J,axiom,
% 5.25/5.48 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.25/5.48 = zero_zero_real ) ).
% 5.25/5.48
% 5.25/5.48 % diff_numeral_special(9)
% 5.25/5.48 thf(fact_2939_diff__numeral__special_I9_J,axiom,
% 5.25/5.48 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.25/5.48 = zero_zero_rat ) ).
% 5.25/5.48
% 5.25/5.48 % diff_numeral_special(9)
% 5.25/5.48 thf(fact_2940_diff__numeral__special_I9_J,axiom,
% 5.25/5.48 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.25/5.48 = zero_zero_int ) ).
% 5.25/5.48
% 5.25/5.48 % diff_numeral_special(9)
% 5.25/5.48 thf(fact_2941_diff__add__zero,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.25/5.48 = zero_zero_nat ) ).
% 5.25/5.48
% 5.25/5.48 % diff_add_zero
% 5.25/5.48 thf(fact_2942_left__diff__distrib__numeral,axiom,
% 5.25/5.48 ! [A: complex,B: complex,V: num] :
% 5.25/5.48 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.25/5.48 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % left_diff_distrib_numeral
% 5.25/5.48 thf(fact_2943_left__diff__distrib__numeral,axiom,
% 5.25/5.48 ! [A: real,B: real,V: num] :
% 5.25/5.48 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.25/5.48 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % left_diff_distrib_numeral
% 5.25/5.48 thf(fact_2944_left__diff__distrib__numeral,axiom,
% 5.25/5.48 ! [A: rat,B: rat,V: num] :
% 5.25/5.48 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.25/5.48 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % left_diff_distrib_numeral
% 5.25/5.48 thf(fact_2945_left__diff__distrib__numeral,axiom,
% 5.25/5.48 ! [A: int,B: int,V: num] :
% 5.25/5.48 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.25/5.48 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % left_diff_distrib_numeral
% 5.25/5.48 thf(fact_2946_right__diff__distrib__numeral,axiom,
% 5.25/5.48 ! [V: num,B: complex,C: complex] :
% 5.25/5.48 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 5.25/5.48 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % right_diff_distrib_numeral
% 5.25/5.48 thf(fact_2947_right__diff__distrib__numeral,axiom,
% 5.25/5.48 ! [V: num,B: real,C: real] :
% 5.25/5.48 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 5.25/5.48 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % right_diff_distrib_numeral
% 5.25/5.48 thf(fact_2948_right__diff__distrib__numeral,axiom,
% 5.25/5.48 ! [V: num,B: rat,C: rat] :
% 5.25/5.48 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 5.25/5.48 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % right_diff_distrib_numeral
% 5.25/5.48 thf(fact_2949_right__diff__distrib__numeral,axiom,
% 5.25/5.48 ! [V: num,B: int,C: int] :
% 5.25/5.48 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 5.25/5.48 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % right_diff_distrib_numeral
% 5.25/5.48 thf(fact_2950_dvd__mult__cancel__left,axiom,
% 5.25/5.48 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.25/5.48 = ( ( C = zero_z3403309356797280102nteger )
% 5.25/5.48 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_cancel_left
% 5.25/5.48 thf(fact_2951_dvd__mult__cancel__left,axiom,
% 5.25/5.48 ! [C: complex,A: complex,B: complex] :
% 5.25/5.48 ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.25/5.48 = ( ( C = zero_zero_complex )
% 5.25/5.48 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_cancel_left
% 5.25/5.48 thf(fact_2952_dvd__mult__cancel__left,axiom,
% 5.25/5.48 ! [C: real,A: real,B: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.48 = ( ( C = zero_zero_real )
% 5.25/5.48 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_cancel_left
% 5.25/5.48 thf(fact_2953_dvd__mult__cancel__left,axiom,
% 5.25/5.48 ! [C: rat,A: rat,B: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.48 = ( ( C = zero_zero_rat )
% 5.25/5.48 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_cancel_left
% 5.25/5.48 thf(fact_2954_dvd__mult__cancel__left,axiom,
% 5.25/5.48 ! [C: int,A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.48 = ( ( C = zero_zero_int )
% 5.25/5.48 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_cancel_left
% 5.25/5.48 thf(fact_2955_dvd__mult__cancel__right,axiom,
% 5.25/5.48 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.25/5.48 = ( ( C = zero_z3403309356797280102nteger )
% 5.25/5.48 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_cancel_right
% 5.25/5.48 thf(fact_2956_dvd__mult__cancel__right,axiom,
% 5.25/5.48 ! [A: complex,C: complex,B: complex] :
% 5.25/5.48 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.25/5.48 = ( ( C = zero_zero_complex )
% 5.25/5.48 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_cancel_right
% 5.25/5.48 thf(fact_2957_dvd__mult__cancel__right,axiom,
% 5.25/5.48 ! [A: real,C: real,B: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.25/5.48 = ( ( C = zero_zero_real )
% 5.25/5.48 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_cancel_right
% 5.25/5.48 thf(fact_2958_dvd__mult__cancel__right,axiom,
% 5.25/5.48 ! [A: rat,C: rat,B: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.48 = ( ( C = zero_zero_rat )
% 5.25/5.48 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_cancel_right
% 5.25/5.48 thf(fact_2959_dvd__mult__cancel__right,axiom,
% 5.25/5.48 ! [A: int,C: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.48 = ( ( C = zero_zero_int )
% 5.25/5.48 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_cancel_right
% 5.25/5.48 thf(fact_2960_dvd__times__left__cancel__iff,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.48 ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_times_left_cancel_iff
% 5.25/5.48 thf(fact_2961_dvd__times__left__cancel__iff,axiom,
% 5.25/5.48 ! [A: nat,B: nat,C: nat] :
% 5.25/5.48 ( ( A != zero_zero_nat )
% 5.25/5.48 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 5.25/5.48 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_times_left_cancel_iff
% 5.25/5.48 thf(fact_2962_dvd__times__left__cancel__iff,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int] :
% 5.25/5.48 ( ( A != zero_zero_int )
% 5.25/5.48 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 5.25/5.48 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_times_left_cancel_iff
% 5.25/5.48 thf(fact_2963_dvd__times__right__cancel__iff,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.48 ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_times_right_cancel_iff
% 5.25/5.48 thf(fact_2964_dvd__times__right__cancel__iff,axiom,
% 5.25/5.48 ! [A: nat,B: nat,C: nat] :
% 5.25/5.48 ( ( A != zero_zero_nat )
% 5.25/5.48 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 5.25/5.48 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_times_right_cancel_iff
% 5.25/5.48 thf(fact_2965_dvd__times__right__cancel__iff,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int] :
% 5.25/5.48 ( ( A != zero_zero_int )
% 5.25/5.48 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 5.25/5.48 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_times_right_cancel_iff
% 5.25/5.48 thf(fact_2966_unit__prod,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.48 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_prod
% 5.25/5.48 thf(fact_2967_unit__prod,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.48 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.48 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_prod
% 5.25/5.48 thf(fact_2968_unit__prod,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.48 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.48 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_prod
% 5.25/5.48 thf(fact_2969_dvd__add__times__triv__left__iff,axiom,
% 5.25/5.48 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_times_triv_left_iff
% 5.25/5.48 thf(fact_2970_dvd__add__times__triv__left__iff,axiom,
% 5.25/5.48 ! [A: real,C: real,B: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 5.25/5.48 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_times_triv_left_iff
% 5.25/5.48 thf(fact_2971_dvd__add__times__triv__left__iff,axiom,
% 5.25/5.48 ! [A: rat,C: rat,B: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 5.25/5.48 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_times_triv_left_iff
% 5.25/5.48 thf(fact_2972_dvd__add__times__triv__left__iff,axiom,
% 5.25/5.48 ! [A: nat,C: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 5.25/5.48 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_times_triv_left_iff
% 5.25/5.48 thf(fact_2973_dvd__add__times__triv__left__iff,axiom,
% 5.25/5.48 ! [A: int,C: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 5.25/5.48 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_times_triv_left_iff
% 5.25/5.48 thf(fact_2974_dvd__add__times__triv__right__iff,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_times_triv_right_iff
% 5.25/5.48 thf(fact_2975_dvd__add__times__triv__right__iff,axiom,
% 5.25/5.48 ! [A: real,B: real,C: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 5.25/5.48 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_times_triv_right_iff
% 5.25/5.48 thf(fact_2976_dvd__add__times__triv__right__iff,axiom,
% 5.25/5.48 ! [A: rat,B: rat,C: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 5.25/5.48 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_times_triv_right_iff
% 5.25/5.48 thf(fact_2977_dvd__add__times__triv__right__iff,axiom,
% 5.25/5.48 ! [A: nat,B: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 5.25/5.48 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_times_triv_right_iff
% 5.25/5.48 thf(fact_2978_dvd__add__times__triv__right__iff,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 5.25/5.48 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_times_triv_right_iff
% 5.25/5.48 thf(fact_2979_dvd__div__mult__self,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.48 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_mult_self
% 5.25/5.48 thf(fact_2980_dvd__div__mult__self,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.48 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_mult_self
% 5.25/5.48 thf(fact_2981_dvd__div__mult__self,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ B )
% 5.25/5.48 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_mult_self
% 5.25/5.48 thf(fact_2982_dvd__mult__div__cancel,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.48 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_div_cancel
% 5.25/5.48 thf(fact_2983_dvd__mult__div__cancel,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.48 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_div_cancel
% 5.25/5.48 thf(fact_2984_dvd__mult__div__cancel,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ B )
% 5.25/5.48 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_div_cancel
% 5.25/5.48 thf(fact_2985_unit__div,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.48 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div
% 5.25/5.48 thf(fact_2986_unit__div,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.48 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.48 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div
% 5.25/5.48 thf(fact_2987_unit__div,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.48 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.48 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div
% 5.25/5.48 thf(fact_2988_unit__div__1__unit,axiom,
% 5.25/5.48 ! [A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.48 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_1_unit
% 5.25/5.48 thf(fact_2989_unit__div__1__unit,axiom,
% 5.25/5.48 ! [A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.48 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_1_unit
% 5.25/5.48 thf(fact_2990_unit__div__1__unit,axiom,
% 5.25/5.48 ! [A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.48 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_1_unit
% 5.25/5.48 thf(fact_2991_unit__div__1__div__1,axiom,
% 5.25/5.48 ! [A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_1_div_1
% 5.25/5.48 thf(fact_2992_unit__div__1__div__1,axiom,
% 5.25/5.48 ! [A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.48 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_1_div_1
% 5.25/5.48 thf(fact_2993_unit__div__1__div__1,axiom,
% 5.25/5.48 ! [A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.48 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_1_div_1
% 5.25/5.48 thf(fact_2994_div__add,axiom,
% 5.25/5.48 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.25/5.48 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_add
% 5.25/5.48 thf(fact_2995_div__add,axiom,
% 5.25/5.48 ! [C: nat,A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ C @ A )
% 5.25/5.48 => ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.48 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.48 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_add
% 5.25/5.48 thf(fact_2996_div__add,axiom,
% 5.25/5.48 ! [C: int,A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ C @ A )
% 5.25/5.48 => ( ( dvd_dvd_int @ C @ B )
% 5.25/5.48 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.48 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_add
% 5.25/5.48 thf(fact_2997_div__diff,axiom,
% 5.25/5.48 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.25/5.48 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_diff
% 5.25/5.48 thf(fact_2998_div__diff,axiom,
% 5.25/5.48 ! [C: int,A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ C @ A )
% 5.25/5.48 => ( ( dvd_dvd_int @ C @ B )
% 5.25/5.48 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.25/5.48 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_diff
% 5.25/5.48 thf(fact_2999_dvd__imp__mod__0,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.48 => ( ( modulo_modulo_nat @ B @ A )
% 5.25/5.48 = zero_zero_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_imp_mod_0
% 5.25/5.48 thf(fact_3000_dvd__imp__mod__0,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ B )
% 5.25/5.48 => ( ( modulo_modulo_int @ B @ A )
% 5.25/5.48 = zero_zero_int ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_imp_mod_0
% 5.25/5.48 thf(fact_3001_dvd__imp__mod__0,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.48 => ( ( modulo364778990260209775nteger @ B @ A )
% 5.25/5.48 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_imp_mod_0
% 5.25/5.48 thf(fact_3002_semiring__norm_I9_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.25/5.48 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(9)
% 5.25/5.48 thf(fact_3003_semiring__norm_I7_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.25/5.48 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(7)
% 5.25/5.48 thf(fact_3004_semiring__norm_I15_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.25/5.48 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(15)
% 5.25/5.48 thf(fact_3005_semiring__norm_I14_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.25/5.48 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(14)
% 5.25/5.48 thf(fact_3006_semiring__norm_I81_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.25/5.48 = ( ord_less_num @ M @ N ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(81)
% 5.25/5.48 thf(fact_3007_semiring__norm_I72_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.25/5.48 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(72)
% 5.25/5.48 thf(fact_3008_semiring__norm_I77_J,axiom,
% 5.25/5.48 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(77)
% 5.25/5.48 thf(fact_3009_semiring__norm_I70_J,axiom,
% 5.25/5.48 ! [M: num] :
% 5.25/5.48 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(70)
% 5.25/5.48 thf(fact_3010_concat__bit__nonnegative__iff,axiom,
% 5.25/5.48 ! [N: nat,K: int,L2: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L2 ) )
% 5.25/5.48 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ).
% 5.25/5.48
% 5.25/5.48 % concat_bit_nonnegative_iff
% 5.25/5.48 thf(fact_3011_concat__bit__negative__iff,axiom,
% 5.25/5.48 ! [N: nat,K: int,L2: int] :
% 5.25/5.48 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L2 ) @ zero_zero_int )
% 5.25/5.48 = ( ord_less_int @ L2 @ zero_zero_int ) ) ).
% 5.25/5.48
% 5.25/5.48 % concat_bit_negative_iff
% 5.25/5.48 thf(fact_3012_unit__mult__div__div,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.48 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.25/5.48 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_mult_div_div
% 5.25/5.48 thf(fact_3013_unit__mult__div__div,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.48 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.25/5.48 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_mult_div_div
% 5.25/5.48 thf(fact_3014_unit__mult__div__div,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.48 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.25/5.48 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_mult_div_div
% 5.25/5.48 thf(fact_3015_unit__div__mult__self,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.48 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_mult_self
% 5.25/5.48 thf(fact_3016_unit__div__mult__self,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.48 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_mult_self
% 5.25/5.48 thf(fact_3017_unit__div__mult__self,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.48 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_mult_self
% 5.25/5.48 thf(fact_3018_even__Suc__Suc__iff,axiom,
% 5.25/5.48 ! [N: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 5.25/5.48 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_Suc_Suc_iff
% 5.25/5.48 thf(fact_3019_even__Suc,axiom,
% 5.25/5.48 ! [N: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 5.25/5.48 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_Suc
% 5.25/5.48 thf(fact_3020_pow__divides__pow__iff,axiom,
% 5.25/5.48 ! [N: nat,A: nat,B: nat] :
% 5.25/5.48 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.48 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.25/5.48 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % pow_divides_pow_iff
% 5.25/5.48 thf(fact_3021_pow__divides__pow__iff,axiom,
% 5.25/5.48 ! [N: nat,A: int,B: int] :
% 5.25/5.48 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.48 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.25/5.48 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % pow_divides_pow_iff
% 5.25/5.48 thf(fact_3022_zdiv__numeral__Bit1,axiom,
% 5.25/5.48 ! [V: num,W: num] :
% 5.25/5.48 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.25/5.48 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zdiv_numeral_Bit1
% 5.25/5.48 thf(fact_3023_semiring__norm_I3_J,axiom,
% 5.25/5.48 ! [N: num] :
% 5.25/5.48 ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 5.25/5.48 = ( bit1 @ N ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(3)
% 5.25/5.48 thf(fact_3024_semiring__norm_I4_J,axiom,
% 5.25/5.48 ! [N: num] :
% 5.25/5.48 ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 5.25/5.48 = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(4)
% 5.25/5.48 thf(fact_3025_semiring__norm_I5_J,axiom,
% 5.25/5.48 ! [M: num] :
% 5.25/5.48 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.25/5.48 = ( bit1 @ M ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(5)
% 5.25/5.48 thf(fact_3026_semiring__norm_I8_J,axiom,
% 5.25/5.48 ! [M: num] :
% 5.25/5.48 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.25/5.48 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(8)
% 5.25/5.48 thf(fact_3027_semiring__norm_I10_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.25/5.48 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(10)
% 5.25/5.48 thf(fact_3028_zle__diff1__eq,axiom,
% 5.25/5.48 ! [W: int,Z: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 5.25/5.48 = ( ord_less_int @ W @ Z ) ) ).
% 5.25/5.48
% 5.25/5.48 % zle_diff1_eq
% 5.25/5.48 thf(fact_3029_semiring__norm_I16_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.25/5.48 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(16)
% 5.25/5.48 thf(fact_3030_semiring__norm_I79_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.25/5.48 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(79)
% 5.25/5.48 thf(fact_3031_semiring__norm_I74_J,axiom,
% 5.25/5.48 ! [M: num,N: num] :
% 5.25/5.48 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.25/5.48 = ( ord_less_num @ M @ N ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_norm(74)
% 5.25/5.48 thf(fact_3032_even__mult__iff,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.25/5.48 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_mult_iff
% 5.25/5.48 thf(fact_3033_even__mult__iff,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 5.25/5.48 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_mult_iff
% 5.25/5.48 thf(fact_3034_even__mult__iff,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 5.25/5.48 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_mult_iff
% 5.25/5.48 thf(fact_3035_even__add,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.25/5.48 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_add
% 5.25/5.48 thf(fact_3036_even__add,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 5.25/5.48 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_add
% 5.25/5.48 thf(fact_3037_even__add,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 5.25/5.48 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_add
% 5.25/5.48 thf(fact_3038_odd__add,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 5.25/5.48 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.48 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % odd_add
% 5.25/5.48 thf(fact_3039_odd__add,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 5.25/5.48 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.48 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % odd_add
% 5.25/5.48 thf(fact_3040_odd__add,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 5.25/5.48 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.48 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % odd_add
% 5.25/5.48 thf(fact_3041_even__mod__2__iff,axiom,
% 5.25/5.48 ! [A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.48 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_mod_2_iff
% 5.25/5.48 thf(fact_3042_even__mod__2__iff,axiom,
% 5.25/5.48 ! [A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.25/5.48 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_mod_2_iff
% 5.25/5.48 thf(fact_3043_even__mod__2__iff,axiom,
% 5.25/5.48 ! [A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_mod_2_iff
% 5.25/5.48 thf(fact_3044_even__Suc__div__two,axiom,
% 5.25/5.48 ! [N: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.48 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.48 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_Suc_div_two
% 5.25/5.48 thf(fact_3045_odd__Suc__div__two,axiom,
% 5.25/5.48 ! [N: nat] :
% 5.25/5.48 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.48 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.48 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % odd_Suc_div_two
% 5.25/5.48 thf(fact_3046_zero__le__power__eq__numeral,axiom,
% 5.25/5.48 ! [A: real,W: num] :
% 5.25/5.48 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.25/5.48 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zero_le_power_eq_numeral
% 5.25/5.48 thf(fact_3047_zero__le__power__eq__numeral,axiom,
% 5.25/5.48 ! [A: rat,W: num] :
% 5.25/5.48 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.25/5.48 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zero_le_power_eq_numeral
% 5.25/5.48 thf(fact_3048_zero__le__power__eq__numeral,axiom,
% 5.25/5.48 ! [A: int,W: num] :
% 5.25/5.48 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.25/5.48 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zero_le_power_eq_numeral
% 5.25/5.48 thf(fact_3049_power__less__zero__eq__numeral,axiom,
% 5.25/5.48 ! [A: real,W: num] :
% 5.25/5.48 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.25/5.48 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_less_zero_eq_numeral
% 5.25/5.48 thf(fact_3050_power__less__zero__eq__numeral,axiom,
% 5.25/5.48 ! [A: rat,W: num] :
% 5.25/5.48 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.25/5.48 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_less_zero_eq_numeral
% 5.25/5.48 thf(fact_3051_power__less__zero__eq__numeral,axiom,
% 5.25/5.48 ! [A: int,W: num] :
% 5.25/5.48 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.25/5.48 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_less_zero_eq_numeral
% 5.25/5.48 thf(fact_3052_power__less__zero__eq,axiom,
% 5.25/5.48 ! [A: real,N: nat] :
% 5.25/5.48 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.25/5.48 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.48 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_less_zero_eq
% 5.25/5.48 thf(fact_3053_power__less__zero__eq,axiom,
% 5.25/5.48 ! [A: rat,N: nat] :
% 5.25/5.48 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.25/5.48 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.48 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_less_zero_eq
% 5.25/5.48 thf(fact_3054_power__less__zero__eq,axiom,
% 5.25/5.48 ! [A: int,N: nat] :
% 5.25/5.48 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.25/5.48 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.48 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_less_zero_eq
% 5.25/5.48 thf(fact_3055_even__plus__one__iff,axiom,
% 5.25/5.48 ! [A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 5.25/5.48 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_plus_one_iff
% 5.25/5.48 thf(fact_3056_even__plus__one__iff,axiom,
% 5.25/5.48 ! [A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 5.25/5.48 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_plus_one_iff
% 5.25/5.48 thf(fact_3057_even__plus__one__iff,axiom,
% 5.25/5.48 ! [A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 5.25/5.48 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_plus_one_iff
% 5.25/5.48 thf(fact_3058_even__diff,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_diff
% 5.25/5.48 thf(fact_3059_even__diff,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 5.25/5.48 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_diff
% 5.25/5.48 thf(fact_3060_div__Suc__eq__div__add3,axiom,
% 5.25/5.48 ! [M: nat,N: nat] :
% 5.25/5.48 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.25/5.48 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_Suc_eq_div_add3
% 5.25/5.48 thf(fact_3061_Suc__div__eq__add3__div__numeral,axiom,
% 5.25/5.48 ! [M: nat,V: num] :
% 5.25/5.48 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.25/5.48 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % Suc_div_eq_add3_div_numeral
% 5.25/5.48 thf(fact_3062_mod__Suc__eq__mod__add3,axiom,
% 5.25/5.48 ! [M: nat,N: nat] :
% 5.25/5.48 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.25/5.48 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_Suc_eq_mod_add3
% 5.25/5.48 thf(fact_3063_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.25/5.48 ! [M: nat,V: num] :
% 5.25/5.48 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.25/5.48 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % Suc_mod_eq_add3_mod_numeral
% 5.25/5.48 thf(fact_3064_zero__less__power__eq__numeral,axiom,
% 5.25/5.48 ! [A: real,W: num] :
% 5.25/5.48 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.25/5.48 = ( ( ( numeral_numeral_nat @ W )
% 5.25/5.48 = zero_zero_nat )
% 5.25/5.48 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( A != zero_zero_real ) )
% 5.25/5.48 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zero_less_power_eq_numeral
% 5.25/5.48 thf(fact_3065_zero__less__power__eq__numeral,axiom,
% 5.25/5.48 ! [A: rat,W: num] :
% 5.25/5.48 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.25/5.48 = ( ( ( numeral_numeral_nat @ W )
% 5.25/5.48 = zero_zero_nat )
% 5.25/5.48 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( A != zero_zero_rat ) )
% 5.25/5.48 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zero_less_power_eq_numeral
% 5.25/5.48 thf(fact_3066_zero__less__power__eq__numeral,axiom,
% 5.25/5.48 ! [A: int,W: num] :
% 5.25/5.48 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.25/5.48 = ( ( ( numeral_numeral_nat @ W )
% 5.25/5.48 = zero_zero_nat )
% 5.25/5.48 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( A != zero_zero_int ) )
% 5.25/5.48 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zero_less_power_eq_numeral
% 5.25/5.48 thf(fact_3067_even__succ__div__two,axiom,
% 5.25/5.48 ! [A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.48 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_succ_div_two
% 5.25/5.48 thf(fact_3068_even__succ__div__two,axiom,
% 5.25/5.48 ! [A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.48 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_succ_div_two
% 5.25/5.48 thf(fact_3069_even__succ__div__two,axiom,
% 5.25/5.48 ! [A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.48 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_succ_div_two
% 5.25/5.48 thf(fact_3070_odd__succ__div__two,axiom,
% 5.25/5.48 ! [A: code_integer] :
% 5.25/5.48 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.48 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % odd_succ_div_two
% 5.25/5.48 thf(fact_3071_odd__succ__div__two,axiom,
% 5.25/5.48 ! [A: nat] :
% 5.25/5.48 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.48 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % odd_succ_div_two
% 5.25/5.48 thf(fact_3072_odd__succ__div__two,axiom,
% 5.25/5.48 ! [A: int] :
% 5.25/5.48 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.48 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % odd_succ_div_two
% 5.25/5.48 thf(fact_3073_even__succ__div__2,axiom,
% 5.25/5.48 ! [A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.48 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_succ_div_2
% 5.25/5.48 thf(fact_3074_even__succ__div__2,axiom,
% 5.25/5.48 ! [A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.48 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_succ_div_2
% 5.25/5.48 thf(fact_3075_even__succ__div__2,axiom,
% 5.25/5.48 ! [A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.48 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_succ_div_2
% 5.25/5.48 thf(fact_3076_even__power,axiom,
% 5.25/5.48 ! [A: code_integer,N: nat] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.25/5.48 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_power
% 5.25/5.48 thf(fact_3077_even__power,axiom,
% 5.25/5.48 ! [A: nat,N: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 5.25/5.48 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_power
% 5.25/5.48 thf(fact_3078_even__power,axiom,
% 5.25/5.48 ! [A: int,N: nat] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 5.25/5.48 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_power
% 5.25/5.48 thf(fact_3079_odd__two__times__div__two__succ,axiom,
% 5.25/5.48 ! [A: code_integer] :
% 5.25/5.48 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % odd_two_times_div_two_succ
% 5.25/5.48 thf(fact_3080_odd__two__times__div__two__succ,axiom,
% 5.25/5.48 ! [A: nat] :
% 5.25/5.48 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % odd_two_times_div_two_succ
% 5.25/5.48 thf(fact_3081_odd__two__times__div__two__succ,axiom,
% 5.25/5.48 ! [A: int] :
% 5.25/5.48 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % odd_two_times_div_two_succ
% 5.25/5.48 thf(fact_3082_power__le__zero__eq__numeral,axiom,
% 5.25/5.48 ! [A: real,W: num] :
% 5.25/5.48 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.25/5.48 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.25/5.48 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_le_zero_eq_numeral
% 5.25/5.48 thf(fact_3083_power__le__zero__eq__numeral,axiom,
% 5.25/5.48 ! [A: rat,W: num] :
% 5.25/5.48 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.25/5.48 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.25/5.48 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_le_zero_eq_numeral
% 5.25/5.48 thf(fact_3084_power__le__zero__eq__numeral,axiom,
% 5.25/5.48 ! [A: int,W: num] :
% 5.25/5.48 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.25/5.48 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.25/5.48 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.48 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_le_zero_eq_numeral
% 5.25/5.48 thf(fact_3085_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.25/5.48 ! [N: nat] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 5.25/5.48 = ( N = zero_zero_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_parity_class.even_mask_iff
% 5.25/5.48 thf(fact_3086_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.25/5.48 ! [N: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 5.25/5.48 = ( N = zero_zero_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_parity_class.even_mask_iff
% 5.25/5.48 thf(fact_3087_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.25/5.48 ! [N: nat] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.25/5.48 = ( N = zero_zero_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % semiring_parity_class.even_mask_iff
% 5.25/5.48 thf(fact_3088_zmod__numeral__Bit1,axiom,
% 5.25/5.48 ! [V: num,W: num] :
% 5.25/5.48 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.25/5.48 = ( 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 ) ) ).
% 5.25/5.48
% 5.25/5.48 % zmod_numeral_Bit1
% 5.25/5.48 thf(fact_3089_subset__divisors__dvd,axiom,
% 5.25/5.48 ! [A: complex,B: complex] :
% 5.25/5.48 ( ( ord_le211207098394363844omplex
% 5.25/5.48 @ ( collect_complex
% 5.25/5.48 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ A ) )
% 5.25/5.48 @ ( collect_complex
% 5.25/5.48 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ B ) ) )
% 5.25/5.48 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % subset_divisors_dvd
% 5.25/5.48 thf(fact_3090_subset__divisors__dvd,axiom,
% 5.25/5.48 ! [A: real,B: real] :
% 5.25/5.48 ( ( ord_less_eq_set_real
% 5.25/5.48 @ ( collect_real
% 5.25/5.48 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 5.25/5.48 @ ( collect_real
% 5.25/5.48 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 5.25/5.48 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % subset_divisors_dvd
% 5.25/5.48 thf(fact_3091_subset__divisors__dvd,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( ord_less_eq_set_nat
% 5.25/5.48 @ ( collect_nat
% 5.25/5.48 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 5.25/5.48 @ ( collect_nat
% 5.25/5.48 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 5.25/5.48 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % subset_divisors_dvd
% 5.25/5.48 thf(fact_3092_subset__divisors__dvd,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( ord_le7084787975880047091nteger
% 5.25/5.48 @ ( collect_Code_integer
% 5.25/5.48 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 5.25/5.48 @ ( collect_Code_integer
% 5.25/5.48 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B ) ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % subset_divisors_dvd
% 5.25/5.48 thf(fact_3093_subset__divisors__dvd,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( ord_less_eq_set_int
% 5.25/5.48 @ ( collect_int
% 5.25/5.48 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 5.25/5.48 @ ( collect_int
% 5.25/5.48 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 5.25/5.48 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % subset_divisors_dvd
% 5.25/5.48 thf(fact_3094_strict__subset__divisors__dvd,axiom,
% 5.25/5.48 ! [A: complex,B: complex] :
% 5.25/5.48 ( ( ord_less_set_complex
% 5.25/5.48 @ ( collect_complex
% 5.25/5.48 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ A ) )
% 5.25/5.48 @ ( collect_complex
% 5.25/5.48 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ B ) ) )
% 5.25/5.48 = ( ( dvd_dvd_complex @ A @ B )
% 5.25/5.48 & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % strict_subset_divisors_dvd
% 5.25/5.48 thf(fact_3095_strict__subset__divisors__dvd,axiom,
% 5.25/5.48 ! [A: real,B: real] :
% 5.25/5.48 ( ( ord_less_set_real
% 5.25/5.48 @ ( collect_real
% 5.25/5.48 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 5.25/5.48 @ ( collect_real
% 5.25/5.48 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 5.25/5.48 = ( ( dvd_dvd_real @ A @ B )
% 5.25/5.48 & ~ ( dvd_dvd_real @ B @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % strict_subset_divisors_dvd
% 5.25/5.48 thf(fact_3096_strict__subset__divisors__dvd,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( ord_less_set_nat
% 5.25/5.48 @ ( collect_nat
% 5.25/5.48 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 5.25/5.48 @ ( collect_nat
% 5.25/5.48 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 5.25/5.48 = ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.48 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % strict_subset_divisors_dvd
% 5.25/5.48 thf(fact_3097_strict__subset__divisors__dvd,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( ord_less_set_int
% 5.25/5.48 @ ( collect_int
% 5.25/5.48 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 5.25/5.48 @ ( collect_int
% 5.25/5.48 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 5.25/5.48 = ( ( dvd_dvd_int @ A @ B )
% 5.25/5.48 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % strict_subset_divisors_dvd
% 5.25/5.48 thf(fact_3098_strict__subset__divisors__dvd,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( ord_le1307284697595431911nteger
% 5.25/5.48 @ ( collect_Code_integer
% 5.25/5.48 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 5.25/5.48 @ ( collect_Code_integer
% 5.25/5.48 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B ) ) )
% 5.25/5.48 = ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.48 & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % strict_subset_divisors_dvd
% 5.25/5.48 thf(fact_3099_dvd__minus__mod,axiom,
% 5.25/5.48 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_minus_mod
% 5.25/5.48 thf(fact_3100_dvd__minus__mod,axiom,
% 5.25/5.48 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_minus_mod
% 5.25/5.48 thf(fact_3101_dvd__minus__mod,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_minus_mod
% 5.25/5.48 thf(fact_3102_mod__eq__dvd__iff,axiom,
% 5.25/5.48 ! [A: int,C: int,B: int] :
% 5.25/5.48 ( ( ( modulo_modulo_int @ A @ C )
% 5.25/5.48 = ( modulo_modulo_int @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_eq_dvd_iff
% 5.25/5.48 thf(fact_3103_mod__eq__dvd__iff,axiom,
% 5.25/5.48 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.48 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.25/5.48 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_eq_dvd_iff
% 5.25/5.48 thf(fact_3104_dvd__diff__commute,axiom,
% 5.25/5.48 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_diff_commute
% 5.25/5.48 thf(fact_3105_dvd__diff__commute,axiom,
% 5.25/5.48 ! [A: int,C: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.25/5.48 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_diff_commute
% 5.25/5.48 thf(fact_3106_dvd__diff,axiom,
% 5.25/5.48 ! [X3: code_integer,Y: code_integer,Z: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ X3 @ Y )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ X3 @ Z )
% 5.25/5.48 => ( dvd_dvd_Code_integer @ X3 @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_diff
% 5.25/5.48 thf(fact_3107_dvd__diff,axiom,
% 5.25/5.48 ! [X3: real,Y: real,Z: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ X3 @ Y )
% 5.25/5.48 => ( ( dvd_dvd_real @ X3 @ Z )
% 5.25/5.48 => ( dvd_dvd_real @ X3 @ ( minus_minus_real @ Y @ Z ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_diff
% 5.25/5.48 thf(fact_3108_dvd__diff,axiom,
% 5.25/5.48 ! [X3: rat,Y: rat,Z: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ X3 @ Y )
% 5.25/5.48 => ( ( dvd_dvd_rat @ X3 @ Z )
% 5.25/5.48 => ( dvd_dvd_rat @ X3 @ ( minus_minus_rat @ Y @ Z ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_diff
% 5.25/5.48 thf(fact_3109_dvd__diff,axiom,
% 5.25/5.48 ! [X3: int,Y: int,Z: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ X3 @ Y )
% 5.25/5.48 => ( ( dvd_dvd_int @ X3 @ Z )
% 5.25/5.48 => ( dvd_dvd_int @ X3 @ ( minus_minus_int @ Y @ Z ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_diff
% 5.25/5.48 thf(fact_3110_dvd__refl,axiom,
% 5.25/5.48 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_refl
% 5.25/5.48 thf(fact_3111_dvd__refl,axiom,
% 5.25/5.48 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_refl
% 5.25/5.48 thf(fact_3112_dvd__refl,axiom,
% 5.25/5.48 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_refl
% 5.25/5.48 thf(fact_3113_diff__eq__diff__eq,axiom,
% 5.25/5.48 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.48 ( ( ( minus_minus_real @ A @ B )
% 5.25/5.48 = ( minus_minus_real @ C @ D ) )
% 5.25/5.48 => ( ( A = B )
% 5.25/5.48 = ( C = D ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_eq_diff_eq
% 5.25/5.48 thf(fact_3114_diff__eq__diff__eq,axiom,
% 5.25/5.48 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.48 ( ( ( minus_minus_rat @ A @ B )
% 5.25/5.48 = ( minus_minus_rat @ C @ D ) )
% 5.25/5.48 => ( ( A = B )
% 5.25/5.48 = ( C = D ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_eq_diff_eq
% 5.25/5.48 thf(fact_3115_diff__eq__diff__eq,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.48 ( ( ( minus_minus_int @ A @ B )
% 5.25/5.48 = ( minus_minus_int @ C @ D ) )
% 5.25/5.48 => ( ( A = B )
% 5.25/5.48 = ( C = D ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_eq_diff_eq
% 5.25/5.48 thf(fact_3116_dvd__trans,axiom,
% 5.25/5.48 ! [A: nat,B: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_nat @ B @ C )
% 5.25/5.48 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_trans
% 5.25/5.48 thf(fact_3117_dvd__trans,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_int @ B @ C )
% 5.25/5.48 => ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_trans
% 5.25/5.48 thf(fact_3118_dvd__trans,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ B @ C )
% 5.25/5.48 => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_trans
% 5.25/5.48 thf(fact_3119_diff__right__commute,axiom,
% 5.25/5.48 ! [A: real,C: real,B: real] :
% 5.25/5.48 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 5.25/5.48 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_right_commute
% 5.25/5.48 thf(fact_3120_diff__right__commute,axiom,
% 5.25/5.48 ! [A: rat,C: rat,B: rat] :
% 5.25/5.48 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 5.25/5.48 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_right_commute
% 5.25/5.48 thf(fact_3121_diff__right__commute,axiom,
% 5.25/5.48 ! [A: nat,C: nat,B: nat] :
% 5.25/5.48 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 5.25/5.48 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_right_commute
% 5.25/5.48 thf(fact_3122_diff__right__commute,axiom,
% 5.25/5.48 ! [A: int,C: int,B: int] :
% 5.25/5.48 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 5.25/5.48 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_right_commute
% 5.25/5.48 thf(fact_3123_numeral__code_I3_J,axiom,
% 5.25/5.48 ! [N: num] :
% 5.25/5.48 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.25/5.48 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.25/5.48
% 5.25/5.48 % numeral_code(3)
% 5.25/5.48 thf(fact_3124_numeral__code_I3_J,axiom,
% 5.25/5.48 ! [N: num] :
% 5.25/5.48 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.25/5.48 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.25/5.48
% 5.25/5.48 % numeral_code(3)
% 5.25/5.48 thf(fact_3125_numeral__code_I3_J,axiom,
% 5.25/5.48 ! [N: num] :
% 5.25/5.48 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.25/5.48 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.25/5.48
% 5.25/5.48 % numeral_code(3)
% 5.25/5.48 thf(fact_3126_numeral__code_I3_J,axiom,
% 5.25/5.48 ! [N: num] :
% 5.25/5.48 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.25/5.48 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % numeral_code(3)
% 5.25/5.48 thf(fact_3127_numeral__code_I3_J,axiom,
% 5.25/5.48 ! [N: num] :
% 5.25/5.48 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.25/5.48 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.25/5.48
% 5.25/5.48 % numeral_code(3)
% 5.25/5.48 thf(fact_3128_power__numeral__odd,axiom,
% 5.25/5.48 ! [Z: complex,W: num] :
% 5.25/5.48 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.25/5.48 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_numeral_odd
% 5.25/5.48 thf(fact_3129_power__numeral__odd,axiom,
% 5.25/5.48 ! [Z: real,W: num] :
% 5.25/5.48 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.25/5.48 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_numeral_odd
% 5.25/5.48 thf(fact_3130_power__numeral__odd,axiom,
% 5.25/5.48 ! [Z: rat,W: num] :
% 5.25/5.48 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.25/5.48 = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_numeral_odd
% 5.25/5.48 thf(fact_3131_power__numeral__odd,axiom,
% 5.25/5.48 ! [Z: nat,W: num] :
% 5.25/5.48 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.25/5.48 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_numeral_odd
% 5.25/5.48 thf(fact_3132_power__numeral__odd,axiom,
% 5.25/5.48 ! [Z: int,W: num] :
% 5.25/5.48 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.25/5.48 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_numeral_odd
% 5.25/5.48 thf(fact_3133_lambda__zero,axiom,
% 5.25/5.48 ( ( ^ [H: complex] : zero_zero_complex )
% 5.25/5.48 = ( times_times_complex @ zero_zero_complex ) ) ).
% 5.25/5.48
% 5.25/5.48 % lambda_zero
% 5.25/5.48 thf(fact_3134_lambda__zero,axiom,
% 5.25/5.48 ( ( ^ [H: real] : zero_zero_real )
% 5.25/5.48 = ( times_times_real @ zero_zero_real ) ) ).
% 5.25/5.48
% 5.25/5.48 % lambda_zero
% 5.25/5.48 thf(fact_3135_lambda__zero,axiom,
% 5.25/5.48 ( ( ^ [H: rat] : zero_zero_rat )
% 5.25/5.48 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.25/5.48
% 5.25/5.48 % lambda_zero
% 5.25/5.48 thf(fact_3136_lambda__zero,axiom,
% 5.25/5.48 ( ( ^ [H: nat] : zero_zero_nat )
% 5.25/5.48 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % lambda_zero
% 5.25/5.48 thf(fact_3137_lambda__zero,axiom,
% 5.25/5.48 ( ( ^ [H: int] : zero_zero_int )
% 5.25/5.48 = ( times_times_int @ zero_zero_int ) ) ).
% 5.25/5.48
% 5.25/5.48 % lambda_zero
% 5.25/5.48 thf(fact_3138_lambda__one,axiom,
% 5.25/5.48 ( ( ^ [X2: complex] : X2 )
% 5.25/5.48 = ( times_times_complex @ one_one_complex ) ) ).
% 5.25/5.48
% 5.25/5.48 % lambda_one
% 5.25/5.48 thf(fact_3139_lambda__one,axiom,
% 5.25/5.48 ( ( ^ [X2: real] : X2 )
% 5.25/5.48 = ( times_times_real @ one_one_real ) ) ).
% 5.25/5.48
% 5.25/5.48 % lambda_one
% 5.25/5.48 thf(fact_3140_lambda__one,axiom,
% 5.25/5.48 ( ( ^ [X2: rat] : X2 )
% 5.25/5.48 = ( times_times_rat @ one_one_rat ) ) ).
% 5.25/5.48
% 5.25/5.48 % lambda_one
% 5.25/5.48 thf(fact_3141_lambda__one,axiom,
% 5.25/5.48 ( ( ^ [X2: nat] : X2 )
% 5.25/5.48 = ( times_times_nat @ one_one_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % lambda_one
% 5.25/5.48 thf(fact_3142_lambda__one,axiom,
% 5.25/5.48 ( ( ^ [X2: int] : X2 )
% 5.25/5.48 = ( times_times_int @ one_one_int ) ) ).
% 5.25/5.48
% 5.25/5.48 % lambda_one
% 5.25/5.48 thf(fact_3143_max__def__raw,axiom,
% 5.25/5.48 ( ord_ma741700101516333627d_enat
% 5.25/5.48 = ( ^ [A3: extended_enat,B2: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max_def_raw
% 5.25/5.48 thf(fact_3144_max__def__raw,axiom,
% 5.25/5.48 ( ord_max_set_int
% 5.25/5.48 = ( ^ [A3: set_int,B2: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max_def_raw
% 5.25/5.48 thf(fact_3145_max__def__raw,axiom,
% 5.25/5.48 ( ord_max_rat
% 5.25/5.48 = ( ^ [A3: rat,B2: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max_def_raw
% 5.25/5.48 thf(fact_3146_max__def__raw,axiom,
% 5.25/5.48 ( ord_max_num
% 5.25/5.48 = ( ^ [A3: num,B2: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max_def_raw
% 5.25/5.48 thf(fact_3147_max__def__raw,axiom,
% 5.25/5.48 ( ord_max_nat
% 5.25/5.48 = ( ^ [A3: nat,B2: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max_def_raw
% 5.25/5.48 thf(fact_3148_max__def__raw,axiom,
% 5.25/5.48 ( ord_max_int
% 5.25/5.48 = ( ^ [A3: int,B2: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % max_def_raw
% 5.25/5.48 thf(fact_3149_inf__period_I4_J,axiom,
% 5.25/5.48 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.25/5.48 => ! [X: code_integer,K4: code_integer] :
% 5.25/5.48 ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ T ) ) )
% 5.25/5.48 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % inf_period(4)
% 5.25/5.48 thf(fact_3150_inf__period_I4_J,axiom,
% 5.25/5.48 ! [D: real,D4: real,T: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ D @ D4 )
% 5.25/5.48 => ! [X: real,K4: real] :
% 5.25/5.48 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ T ) ) )
% 5.25/5.48 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % inf_period(4)
% 5.25/5.48 thf(fact_3151_inf__period_I4_J,axiom,
% 5.25/5.48 ! [D: rat,D4: rat,T: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ D @ D4 )
% 5.25/5.48 => ! [X: rat,K4: rat] :
% 5.25/5.48 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ T ) ) )
% 5.25/5.48 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % inf_period(4)
% 5.25/5.48 thf(fact_3152_inf__period_I4_J,axiom,
% 5.25/5.48 ! [D: int,D4: int,T: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ D @ D4 )
% 5.25/5.48 => ! [X: int,K4: int] :
% 5.25/5.48 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) ) )
% 5.25/5.48 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % inf_period(4)
% 5.25/5.48 thf(fact_3153_inf__period_I3_J,axiom,
% 5.25/5.48 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.25/5.48 => ! [X: code_integer,K4: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ T ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % inf_period(3)
% 5.25/5.48 thf(fact_3154_inf__period_I3_J,axiom,
% 5.25/5.48 ! [D: real,D4: real,T: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ D @ D4 )
% 5.25/5.48 => ! [X: real,K4: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ T ) )
% 5.25/5.48 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % inf_period(3)
% 5.25/5.48 thf(fact_3155_inf__period_I3_J,axiom,
% 5.25/5.48 ! [D: rat,D4: rat,T: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ D @ D4 )
% 5.25/5.48 => ! [X: rat,K4: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ T ) )
% 5.25/5.48 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % inf_period(3)
% 5.25/5.48 thf(fact_3156_inf__period_I3_J,axiom,
% 5.25/5.48 ! [D: int,D4: int,T: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ D @ D4 )
% 5.25/5.48 => ! [X: int,K4: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) )
% 5.25/5.48 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % inf_period(3)
% 5.25/5.48 thf(fact_3157_dvd__field__iff,axiom,
% 5.25/5.48 ( dvd_dvd_complex
% 5.25/5.48 = ( ^ [A3: complex,B2: complex] :
% 5.25/5.48 ( ( A3 = zero_zero_complex )
% 5.25/5.48 => ( B2 = zero_zero_complex ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_field_iff
% 5.25/5.48 thf(fact_3158_dvd__field__iff,axiom,
% 5.25/5.48 ( dvd_dvd_real
% 5.25/5.48 = ( ^ [A3: real,B2: real] :
% 5.25/5.48 ( ( A3 = zero_zero_real )
% 5.25/5.48 => ( B2 = zero_zero_real ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_field_iff
% 5.25/5.48 thf(fact_3159_dvd__field__iff,axiom,
% 5.25/5.48 ( dvd_dvd_rat
% 5.25/5.48 = ( ^ [A3: rat,B2: rat] :
% 5.25/5.48 ( ( A3 = zero_zero_rat )
% 5.25/5.48 => ( B2 = zero_zero_rat ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_field_iff
% 5.25/5.48 thf(fact_3160_dvd__0__left,axiom,
% 5.25/5.48 ! [A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.25/5.48 => ( A = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_left
% 5.25/5.48 thf(fact_3161_dvd__0__left,axiom,
% 5.25/5.48 ! [A: complex] :
% 5.25/5.48 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.25/5.48 => ( A = zero_zero_complex ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_left
% 5.25/5.48 thf(fact_3162_dvd__0__left,axiom,
% 5.25/5.48 ! [A: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.25/5.48 => ( A = zero_zero_real ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_left
% 5.25/5.48 thf(fact_3163_dvd__0__left,axiom,
% 5.25/5.48 ! [A: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.25/5.48 => ( A = zero_zero_rat ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_left
% 5.25/5.48 thf(fact_3164_dvd__0__left,axiom,
% 5.25/5.48 ! [A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.25/5.48 => ( A = zero_zero_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_left
% 5.25/5.48 thf(fact_3165_dvd__0__left,axiom,
% 5.25/5.48 ! [A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.25/5.48 => ( A = zero_zero_int ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_0_left
% 5.25/5.48 thf(fact_3166_diff__eq__diff__less__eq,axiom,
% 5.25/5.48 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.48 ( ( ( minus_minus_real @ A @ B )
% 5.25/5.48 = ( minus_minus_real @ C @ D ) )
% 5.25/5.48 => ( ( ord_less_eq_real @ A @ B )
% 5.25/5.48 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_eq_diff_less_eq
% 5.25/5.48 thf(fact_3167_diff__eq__diff__less__eq,axiom,
% 5.25/5.48 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.48 ( ( ( minus_minus_rat @ A @ B )
% 5.25/5.48 = ( minus_minus_rat @ C @ D ) )
% 5.25/5.48 => ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.48 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_eq_diff_less_eq
% 5.25/5.48 thf(fact_3168_diff__eq__diff__less__eq,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.48 ( ( ( minus_minus_int @ A @ B )
% 5.25/5.48 = ( minus_minus_int @ C @ D ) )
% 5.25/5.48 => ( ( ord_less_eq_int @ A @ B )
% 5.25/5.48 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_eq_diff_less_eq
% 5.25/5.48 thf(fact_3169_diff__right__mono,axiom,
% 5.25/5.48 ! [A: real,B: real,C: real] :
% 5.25/5.48 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.48 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_right_mono
% 5.25/5.48 thf(fact_3170_diff__right__mono,axiom,
% 5.25/5.48 ! [A: rat,B: rat,C: rat] :
% 5.25/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.48 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_right_mono
% 5.25/5.48 thf(fact_3171_diff__right__mono,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.48 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_right_mono
% 5.25/5.48 thf(fact_3172_diff__left__mono,axiom,
% 5.25/5.48 ! [B: real,A: real,C: real] :
% 5.25/5.48 ( ( ord_less_eq_real @ B @ A )
% 5.25/5.48 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_left_mono
% 5.25/5.48 thf(fact_3173_diff__left__mono,axiom,
% 5.25/5.48 ! [B: rat,A: rat,C: rat] :
% 5.25/5.48 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.48 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_left_mono
% 5.25/5.48 thf(fact_3174_diff__left__mono,axiom,
% 5.25/5.48 ! [B: int,A: int,C: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.48 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_left_mono
% 5.25/5.48 thf(fact_3175_diff__mono,axiom,
% 5.25/5.48 ! [A: real,B: real,D: real,C: real] :
% 5.25/5.48 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.48 => ( ( ord_less_eq_real @ D @ C )
% 5.25/5.48 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_mono
% 5.25/5.48 thf(fact_3176_diff__mono,axiom,
% 5.25/5.48 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.25/5.48 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.48 => ( ( ord_less_eq_rat @ D @ C )
% 5.25/5.48 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_mono
% 5.25/5.48 thf(fact_3177_diff__mono,axiom,
% 5.25/5.48 ! [A: int,B: int,D: int,C: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.48 => ( ( ord_less_eq_int @ D @ C )
% 5.25/5.48 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % diff_mono
% 5.25/5.48 thf(fact_3178_eq__iff__diff__eq__0,axiom,
% 5.25/5.48 ( ( ^ [Y5: complex,Z3: complex] : ( Y5 = Z3 ) )
% 5.25/5.48 = ( ^ [A3: complex,B2: complex] :
% 5.25/5.48 ( ( minus_minus_complex @ A3 @ B2 )
% 5.25/5.48 = zero_zero_complex ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % eq_iff_diff_eq_0
% 5.25/5.48 thf(fact_3179_eq__iff__diff__eq__0,axiom,
% 5.25/5.48 ( ( ^ [Y5: real,Z3: real] : ( Y5 = Z3 ) )
% 5.25/5.48 = ( ^ [A3: real,B2: real] :
% 5.25/5.48 ( ( minus_minus_real @ A3 @ B2 )
% 5.25/5.48 = zero_zero_real ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % eq_iff_diff_eq_0
% 5.25/5.48 thf(fact_3180_eq__iff__diff__eq__0,axiom,
% 5.25/5.48 ( ( ^ [Y5: rat,Z3: rat] : ( Y5 = Z3 ) )
% 5.25/5.48 = ( ^ [A3: rat,B2: rat] :
% 5.25/5.48 ( ( minus_minus_rat @ A3 @ B2 )
% 5.25/5.48 = zero_zero_rat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_iff_diff_eq_0
% 5.25/5.49 thf(fact_3181_eq__iff__diff__eq__0,axiom,
% 5.25/5.49 ( ( ^ [Y5: int,Z3: int] : ( Y5 = Z3 ) )
% 5.25/5.49 = ( ^ [A3: int,B2: int] :
% 5.25/5.49 ( ( minus_minus_int @ A3 @ B2 )
% 5.25/5.49 = zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_iff_diff_eq_0
% 5.25/5.49 thf(fact_3182_dvd__triv__right,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_triv_right
% 5.25/5.49 thf(fact_3183_dvd__triv__right,axiom,
% 5.25/5.49 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_triv_right
% 5.25/5.49 thf(fact_3184_dvd__triv__right,axiom,
% 5.25/5.49 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_triv_right
% 5.25/5.49 thf(fact_3185_dvd__triv__right,axiom,
% 5.25/5.49 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_triv_right
% 5.25/5.49 thf(fact_3186_dvd__triv__right,axiom,
% 5.25/5.49 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_triv_right
% 5.25/5.49 thf(fact_3187_dvd__mult__right,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_right
% 5.25/5.49 thf(fact_3188_dvd__mult__right,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.25/5.49 => ( dvd_dvd_real @ B @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_right
% 5.25/5.49 thf(fact_3189_dvd__mult__right,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.25/5.49 => ( dvd_dvd_rat @ B @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_right
% 5.25/5.49 thf(fact_3190_dvd__mult__right,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.49 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_right
% 5.25/5.49 thf(fact_3191_dvd__mult__right,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.49 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_right
% 5.25/5.49 thf(fact_3192_mult__dvd__mono,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_dvd_mono
% 5.25/5.49 thf(fact_3193_mult__dvd__mono,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.49 ( ( dvd_dvd_real @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_real @ C @ D )
% 5.25/5.49 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_dvd_mono
% 5.25/5.49 thf(fact_3194_mult__dvd__mono,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.49 ( ( dvd_dvd_rat @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_rat @ C @ D )
% 5.25/5.49 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_dvd_mono
% 5.25/5.49 thf(fact_3195_mult__dvd__mono,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_nat @ C @ D )
% 5.25/5.49 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_dvd_mono
% 5.25/5.49 thf(fact_3196_mult__dvd__mono,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_int @ C @ D )
% 5.25/5.49 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_dvd_mono
% 5.25/5.49 thf(fact_3197_dvd__triv__left,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_triv_left
% 5.25/5.49 thf(fact_3198_dvd__triv__left,axiom,
% 5.25/5.49 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_triv_left
% 5.25/5.49 thf(fact_3199_dvd__triv__left,axiom,
% 5.25/5.49 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_triv_left
% 5.25/5.49 thf(fact_3200_dvd__triv__left,axiom,
% 5.25/5.49 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_triv_left
% 5.25/5.49 thf(fact_3201_dvd__triv__left,axiom,
% 5.25/5.49 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_triv_left
% 5.25/5.49 thf(fact_3202_dvd__mult__left,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_left
% 5.25/5.49 thf(fact_3203_dvd__mult__left,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.25/5.49 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_left
% 5.25/5.49 thf(fact_3204_dvd__mult__left,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.25/5.49 => ( dvd_dvd_rat @ A @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_left
% 5.25/5.49 thf(fact_3205_dvd__mult__left,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.49 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_left
% 5.25/5.49 thf(fact_3206_dvd__mult__left,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.49 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_left
% 5.25/5.49 thf(fact_3207_dvd__mult2,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult2
% 5.25/5.49 thf(fact_3208_dvd__mult2,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( dvd_dvd_real @ A @ B )
% 5.25/5.49 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult2
% 5.25/5.49 thf(fact_3209_dvd__mult2,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( dvd_dvd_rat @ A @ B )
% 5.25/5.49 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult2
% 5.25/5.49 thf(fact_3210_dvd__mult2,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.49 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult2
% 5.25/5.49 thf(fact_3211_dvd__mult2,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ B )
% 5.25/5.49 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult2
% 5.25/5.49 thf(fact_3212_dvd__mult,axiom,
% 5.25/5.49 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult
% 5.25/5.49 thf(fact_3213_dvd__mult,axiom,
% 5.25/5.49 ! [A: real,C: real,B: real] :
% 5.25/5.49 ( ( dvd_dvd_real @ A @ C )
% 5.25/5.49 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult
% 5.25/5.49 thf(fact_3214_dvd__mult,axiom,
% 5.25/5.49 ! [A: rat,C: rat,B: rat] :
% 5.25/5.49 ( ( dvd_dvd_rat @ A @ C )
% 5.25/5.49 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult
% 5.25/5.49 thf(fact_3215_dvd__mult,axiom,
% 5.25/5.49 ! [A: nat,C: nat,B: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ A @ C )
% 5.25/5.49 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult
% 5.25/5.49 thf(fact_3216_dvd__mult,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ C )
% 5.25/5.49 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult
% 5.25/5.49 thf(fact_3217_dvd__def,axiom,
% 5.25/5.49 ( dvd_dvd_Code_integer
% 5.25/5.49 = ( ^ [B2: code_integer,A3: code_integer] :
% 5.25/5.49 ? [K3: code_integer] :
% 5.25/5.49 ( A3
% 5.25/5.49 = ( times_3573771949741848930nteger @ B2 @ K3 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_def
% 5.25/5.49 thf(fact_3218_dvd__def,axiom,
% 5.25/5.49 ( dvd_dvd_real
% 5.25/5.49 = ( ^ [B2: real,A3: real] :
% 5.25/5.49 ? [K3: real] :
% 5.25/5.49 ( A3
% 5.25/5.49 = ( times_times_real @ B2 @ K3 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_def
% 5.25/5.49 thf(fact_3219_dvd__def,axiom,
% 5.25/5.49 ( dvd_dvd_rat
% 5.25/5.49 = ( ^ [B2: rat,A3: rat] :
% 5.25/5.49 ? [K3: rat] :
% 5.25/5.49 ( A3
% 5.25/5.49 = ( times_times_rat @ B2 @ K3 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_def
% 5.25/5.49 thf(fact_3220_dvd__def,axiom,
% 5.25/5.49 ( dvd_dvd_nat
% 5.25/5.49 = ( ^ [B2: nat,A3: nat] :
% 5.25/5.49 ? [K3: nat] :
% 5.25/5.49 ( A3
% 5.25/5.49 = ( times_times_nat @ B2 @ K3 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_def
% 5.25/5.49 thf(fact_3221_dvd__def,axiom,
% 5.25/5.49 ( dvd_dvd_int
% 5.25/5.49 = ( ^ [B2: int,A3: int] :
% 5.25/5.49 ? [K3: int] :
% 5.25/5.49 ( A3
% 5.25/5.49 = ( times_times_int @ B2 @ K3 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_def
% 5.25/5.49 thf(fact_3222_dvdI,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvdI
% 5.25/5.49 thf(fact_3223_dvdI,axiom,
% 5.25/5.49 ! [A: real,B: real,K: real] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( times_times_real @ B @ K ) )
% 5.25/5.49 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvdI
% 5.25/5.49 thf(fact_3224_dvdI,axiom,
% 5.25/5.49 ! [A: rat,B: rat,K: rat] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( times_times_rat @ B @ K ) )
% 5.25/5.49 => ( dvd_dvd_rat @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvdI
% 5.25/5.49 thf(fact_3225_dvdI,axiom,
% 5.25/5.49 ! [A: nat,B: nat,K: nat] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( times_times_nat @ B @ K ) )
% 5.25/5.49 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvdI
% 5.25/5.49 thf(fact_3226_dvdI,axiom,
% 5.25/5.49 ! [A: int,B: int,K: int] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( times_times_int @ B @ K ) )
% 5.25/5.49 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvdI
% 5.25/5.49 thf(fact_3227_dvdE,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.49 => ~ ! [K2: code_integer] :
% 5.25/5.49 ( A
% 5.25/5.49 != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvdE
% 5.25/5.49 thf(fact_3228_dvdE,axiom,
% 5.25/5.49 ! [B: real,A: real] :
% 5.25/5.49 ( ( dvd_dvd_real @ B @ A )
% 5.25/5.49 => ~ ! [K2: real] :
% 5.25/5.49 ( A
% 5.25/5.49 != ( times_times_real @ B @ K2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvdE
% 5.25/5.49 thf(fact_3229_dvdE,axiom,
% 5.25/5.49 ! [B: rat,A: rat] :
% 5.25/5.49 ( ( dvd_dvd_rat @ B @ A )
% 5.25/5.49 => ~ ! [K2: rat] :
% 5.25/5.49 ( A
% 5.25/5.49 != ( times_times_rat @ B @ K2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvdE
% 5.25/5.49 thf(fact_3230_dvdE,axiom,
% 5.25/5.49 ! [B: nat,A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.49 => ~ ! [K2: nat] :
% 5.25/5.49 ( A
% 5.25/5.49 != ( times_times_nat @ B @ K2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvdE
% 5.25/5.49 thf(fact_3231_dvdE,axiom,
% 5.25/5.49 ! [B: int,A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ A )
% 5.25/5.49 => ~ ! [K2: int] :
% 5.25/5.49 ( A
% 5.25/5.49 != ( times_times_int @ B @ K2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvdE
% 5.25/5.49 thf(fact_3232_dvd__productE,axiom,
% 5.25/5.49 ! [P2: nat,A: nat,B: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ P2 @ ( times_times_nat @ A @ B ) )
% 5.25/5.49 => ~ ! [X5: nat,Y3: nat] :
% 5.25/5.49 ( ( P2
% 5.25/5.49 = ( times_times_nat @ X5 @ Y3 ) )
% 5.25/5.49 => ( ( dvd_dvd_nat @ X5 @ A )
% 5.25/5.49 => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_productE
% 5.25/5.49 thf(fact_3233_dvd__productE,axiom,
% 5.25/5.49 ! [P2: int,A: int,B: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ P2 @ ( times_times_int @ A @ B ) )
% 5.25/5.49 => ~ ! [X5: int,Y3: int] :
% 5.25/5.49 ( ( P2
% 5.25/5.49 = ( times_times_int @ X5 @ Y3 ) )
% 5.25/5.49 => ( ( dvd_dvd_int @ X5 @ A )
% 5.25/5.49 => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_productE
% 5.25/5.49 thf(fact_3234_division__decomp,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.25/5.49 => ? [B6: nat,C4: nat] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( times_times_nat @ B6 @ C4 ) )
% 5.25/5.49 & ( dvd_dvd_nat @ B6 @ B )
% 5.25/5.49 & ( dvd_dvd_nat @ C4 @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % division_decomp
% 5.25/5.49 thf(fact_3235_division__decomp,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.25/5.49 => ? [B6: int,C4: int] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( times_times_int @ B6 @ C4 ) )
% 5.25/5.49 & ( dvd_dvd_int @ B6 @ B )
% 5.25/5.49 & ( dvd_dvd_int @ C4 @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % division_decomp
% 5.25/5.49 thf(fact_3236_diff__strict__right__mono,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( ord_less_real @ A @ B )
% 5.25/5.49 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_strict_right_mono
% 5.25/5.49 thf(fact_3237_diff__strict__right__mono,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( ord_less_rat @ A @ B )
% 5.25/5.49 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_strict_right_mono
% 5.25/5.49 thf(fact_3238_diff__strict__right__mono,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( ord_less_int @ A @ B )
% 5.25/5.49 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_strict_right_mono
% 5.25/5.49 thf(fact_3239_diff__strict__left__mono,axiom,
% 5.25/5.49 ! [B: real,A: real,C: real] :
% 5.25/5.49 ( ( ord_less_real @ B @ A )
% 5.25/5.49 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_strict_left_mono
% 5.25/5.49 thf(fact_3240_diff__strict__left__mono,axiom,
% 5.25/5.49 ! [B: rat,A: rat,C: rat] :
% 5.25/5.49 ( ( ord_less_rat @ B @ A )
% 5.25/5.49 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_strict_left_mono
% 5.25/5.49 thf(fact_3241_diff__strict__left__mono,axiom,
% 5.25/5.49 ! [B: int,A: int,C: int] :
% 5.25/5.49 ( ( ord_less_int @ B @ A )
% 5.25/5.49 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_strict_left_mono
% 5.25/5.49 thf(fact_3242_diff__eq__diff__less,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.49 ( ( ( minus_minus_real @ A @ B )
% 5.25/5.49 = ( minus_minus_real @ C @ D ) )
% 5.25/5.49 => ( ( ord_less_real @ A @ B )
% 5.25/5.49 = ( ord_less_real @ C @ D ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_eq_diff_less
% 5.25/5.49 thf(fact_3243_diff__eq__diff__less,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.49 ( ( ( minus_minus_rat @ A @ B )
% 5.25/5.49 = ( minus_minus_rat @ C @ D ) )
% 5.25/5.49 => ( ( ord_less_rat @ A @ B )
% 5.25/5.49 = ( ord_less_rat @ C @ D ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_eq_diff_less
% 5.25/5.49 thf(fact_3244_diff__eq__diff__less,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.49 ( ( ( minus_minus_int @ A @ B )
% 5.25/5.49 = ( minus_minus_int @ C @ D ) )
% 5.25/5.49 => ( ( ord_less_int @ A @ B )
% 5.25/5.49 = ( ord_less_int @ C @ D ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_eq_diff_less
% 5.25/5.49 thf(fact_3245_diff__strict__mono,axiom,
% 5.25/5.49 ! [A: real,B: real,D: real,C: real] :
% 5.25/5.49 ( ( ord_less_real @ A @ B )
% 5.25/5.49 => ( ( ord_less_real @ D @ C )
% 5.25/5.49 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_strict_mono
% 5.25/5.49 thf(fact_3246_diff__strict__mono,axiom,
% 5.25/5.49 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.25/5.49 ( ( ord_less_rat @ A @ B )
% 5.25/5.49 => ( ( ord_less_rat @ D @ C )
% 5.25/5.49 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_strict_mono
% 5.25/5.49 thf(fact_3247_diff__strict__mono,axiom,
% 5.25/5.49 ! [A: int,B: int,D: int,C: int] :
% 5.25/5.49 ( ( ord_less_int @ A @ B )
% 5.25/5.49 => ( ( ord_less_int @ D @ C )
% 5.25/5.49 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_strict_mono
% 5.25/5.49 thf(fact_3248_dvd__unit__imp__unit,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_unit_imp_unit
% 5.25/5.49 thf(fact_3249_dvd__unit__imp__unit,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.49 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_unit_imp_unit
% 5.25/5.49 thf(fact_3250_dvd__unit__imp__unit,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.49 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_unit_imp_unit
% 5.25/5.49 thf(fact_3251_unit__imp__dvd,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_imp_dvd
% 5.25/5.49 thf(fact_3252_unit__imp__dvd,axiom,
% 5.25/5.49 ! [B: nat,A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.49 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_imp_dvd
% 5.25/5.49 thf(fact_3253_unit__imp__dvd,axiom,
% 5.25/5.49 ! [B: int,A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.49 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_imp_dvd
% 5.25/5.49 thf(fact_3254_one__dvd,axiom,
% 5.25/5.49 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.25/5.49
% 5.25/5.49 % one_dvd
% 5.25/5.49 thf(fact_3255_one__dvd,axiom,
% 5.25/5.49 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.25/5.49
% 5.25/5.49 % one_dvd
% 5.25/5.49 thf(fact_3256_one__dvd,axiom,
% 5.25/5.49 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.25/5.49
% 5.25/5.49 % one_dvd
% 5.25/5.49 thf(fact_3257_one__dvd,axiom,
% 5.25/5.49 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 5.25/5.49
% 5.25/5.49 % one_dvd
% 5.25/5.49 thf(fact_3258_one__dvd,axiom,
% 5.25/5.49 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.25/5.49
% 5.25/5.49 % one_dvd
% 5.25/5.49 thf(fact_3259_one__dvd,axiom,
% 5.25/5.49 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.25/5.49
% 5.25/5.49 % one_dvd
% 5.25/5.49 thf(fact_3260_dvd__add__right__iff,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add_right_iff
% 5.25/5.49 thf(fact_3261_dvd__add__right__iff,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( dvd_dvd_real @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add_right_iff
% 5.25/5.49 thf(fact_3262_dvd__add__right__iff,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( dvd_dvd_rat @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add_right_iff
% 5.25/5.49 thf(fact_3263_dvd__add__right__iff,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add_right_iff
% 5.25/5.49 thf(fact_3264_dvd__add__right__iff,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add_right_iff
% 5.25/5.49 thf(fact_3265_dvd__add__left__iff,axiom,
% 5.25/5.49 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add_left_iff
% 5.25/5.49 thf(fact_3266_dvd__add__left__iff,axiom,
% 5.25/5.49 ! [A: real,C: real,B: real] :
% 5.25/5.49 ( ( dvd_dvd_real @ A @ C )
% 5.25/5.49 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add_left_iff
% 5.25/5.49 thf(fact_3267_dvd__add__left__iff,axiom,
% 5.25/5.49 ! [A: rat,C: rat,B: rat] :
% 5.25/5.49 ( ( dvd_dvd_rat @ A @ C )
% 5.25/5.49 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add_left_iff
% 5.25/5.49 thf(fact_3268_dvd__add__left__iff,axiom,
% 5.25/5.49 ! [A: nat,C: nat,B: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ A @ C )
% 5.25/5.49 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add_left_iff
% 5.25/5.49 thf(fact_3269_dvd__add__left__iff,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ C )
% 5.25/5.49 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add_left_iff
% 5.25/5.49 thf(fact_3270_dvd__add,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add
% 5.25/5.49 thf(fact_3271_dvd__add,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( dvd_dvd_real @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_real @ A @ C )
% 5.25/5.49 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add
% 5.25/5.49 thf(fact_3272_dvd__add,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( dvd_dvd_rat @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_rat @ A @ C )
% 5.25/5.49 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add
% 5.25/5.49 thf(fact_3273_dvd__add,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_nat @ A @ C )
% 5.25/5.49 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add
% 5.25/5.49 thf(fact_3274_dvd__add,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_int @ A @ C )
% 5.25/5.49 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_add
% 5.25/5.49 thf(fact_3275_inf__period_I2_J,axiom,
% 5.25/5.49 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.25/5.49 ( ! [X5: real,K2: real] :
% 5.25/5.49 ( ( P @ X5 )
% 5.25/5.49 = ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.25/5.49 => ( ! [X5: real,K2: real] :
% 5.25/5.49 ( ( Q @ X5 )
% 5.25/5.49 = ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.25/5.49 => ! [X: real,K4: real] :
% 5.25/5.49 ( ( ( P @ X )
% 5.25/5.49 | ( Q @ X ) )
% 5.25/5.49 = ( ( P @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D4 ) ) )
% 5.25/5.49 | ( Q @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % inf_period(2)
% 5.25/5.49 thf(fact_3276_inf__period_I2_J,axiom,
% 5.25/5.49 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.25/5.49 ( ! [X5: rat,K2: rat] :
% 5.25/5.49 ( ( P @ X5 )
% 5.25/5.49 = ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.25/5.49 => ( ! [X5: rat,K2: rat] :
% 5.25/5.49 ( ( Q @ X5 )
% 5.25/5.49 = ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.25/5.49 => ! [X: rat,K4: rat] :
% 5.25/5.49 ( ( ( P @ X )
% 5.25/5.49 | ( Q @ X ) )
% 5.25/5.49 = ( ( P @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.25/5.49 | ( Q @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % inf_period(2)
% 5.25/5.49 thf(fact_3277_inf__period_I2_J,axiom,
% 5.25/5.49 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.25/5.49 ( ! [X5: int,K2: int] :
% 5.25/5.49 ( ( P @ X5 )
% 5.25/5.49 = ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.25/5.49 => ( ! [X5: int,K2: int] :
% 5.25/5.49 ( ( Q @ X5 )
% 5.25/5.49 = ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.25/5.49 => ! [X: int,K4: int] :
% 5.25/5.49 ( ( ( P @ X )
% 5.25/5.49 | ( Q @ X ) )
% 5.25/5.49 = ( ( P @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D4 ) ) )
% 5.25/5.49 | ( Q @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % inf_period(2)
% 5.25/5.49 thf(fact_3278_inf__period_I1_J,axiom,
% 5.25/5.49 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.25/5.49 ( ! [X5: real,K2: real] :
% 5.25/5.49 ( ( P @ X5 )
% 5.25/5.49 = ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.25/5.49 => ( ! [X5: real,K2: real] :
% 5.25/5.49 ( ( Q @ X5 )
% 5.25/5.49 = ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.25/5.49 => ! [X: real,K4: real] :
% 5.25/5.49 ( ( ( P @ X )
% 5.25/5.49 & ( Q @ X ) )
% 5.25/5.49 = ( ( P @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D4 ) ) )
% 5.25/5.49 & ( Q @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % inf_period(1)
% 5.25/5.49 thf(fact_3279_inf__period_I1_J,axiom,
% 5.25/5.49 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.25/5.49 ( ! [X5: rat,K2: rat] :
% 5.25/5.49 ( ( P @ X5 )
% 5.25/5.49 = ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.25/5.49 => ( ! [X5: rat,K2: rat] :
% 5.25/5.49 ( ( Q @ X5 )
% 5.25/5.49 = ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.25/5.49 => ! [X: rat,K4: rat] :
% 5.25/5.49 ( ( ( P @ X )
% 5.25/5.49 & ( Q @ X ) )
% 5.25/5.49 = ( ( P @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.25/5.49 & ( Q @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % inf_period(1)
% 5.25/5.49 thf(fact_3280_inf__period_I1_J,axiom,
% 5.25/5.49 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.25/5.49 ( ! [X5: int,K2: int] :
% 5.25/5.49 ( ( P @ X5 )
% 5.25/5.49 = ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.25/5.49 => ( ! [X5: int,K2: int] :
% 5.25/5.49 ( ( Q @ X5 )
% 5.25/5.49 = ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.25/5.49 => ! [X: int,K4: int] :
% 5.25/5.49 ( ( ( P @ X )
% 5.25/5.49 & ( Q @ X ) )
% 5.25/5.49 = ( ( P @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D4 ) ) )
% 5.25/5.49 & ( Q @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % inf_period(1)
% 5.25/5.49 thf(fact_3281_right__diff__distrib_H,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.25/5.49 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % right_diff_distrib'
% 5.25/5.49 thf(fact_3282_right__diff__distrib_H,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.25/5.49 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % right_diff_distrib'
% 5.25/5.49 thf(fact_3283_right__diff__distrib_H,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 5.25/5.49 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % right_diff_distrib'
% 5.25/5.49 thf(fact_3284_right__diff__distrib_H,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.25/5.49 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % right_diff_distrib'
% 5.25/5.49 thf(fact_3285_left__diff__distrib_H,axiom,
% 5.25/5.49 ! [B: real,C: real,A: real] :
% 5.25/5.49 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 5.25/5.49 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % left_diff_distrib'
% 5.25/5.49 thf(fact_3286_left__diff__distrib_H,axiom,
% 5.25/5.49 ! [B: rat,C: rat,A: rat] :
% 5.25/5.49 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 5.25/5.49 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % left_diff_distrib'
% 5.25/5.49 thf(fact_3287_left__diff__distrib_H,axiom,
% 5.25/5.49 ! [B: nat,C: nat,A: nat] :
% 5.25/5.49 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 5.25/5.49 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % left_diff_distrib'
% 5.25/5.49 thf(fact_3288_left__diff__distrib_H,axiom,
% 5.25/5.49 ! [B: int,C: int,A: int] :
% 5.25/5.49 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 5.25/5.49 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % left_diff_distrib'
% 5.25/5.49 thf(fact_3289_right__diff__distrib,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.25/5.49 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % right_diff_distrib
% 5.25/5.49 thf(fact_3290_right__diff__distrib,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.25/5.49 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % right_diff_distrib
% 5.25/5.49 thf(fact_3291_right__diff__distrib,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.25/5.49 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % right_diff_distrib
% 5.25/5.49 thf(fact_3292_left__diff__distrib,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.25/5.49 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % left_diff_distrib
% 5.25/5.49 thf(fact_3293_left__diff__distrib,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.25/5.49 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % left_diff_distrib
% 5.25/5.49 thf(fact_3294_left__diff__distrib,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.25/5.49 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % left_diff_distrib
% 5.25/5.49 thf(fact_3295_verit__eq__simplify_I14_J,axiom,
% 5.25/5.49 ! [X22: num,X32: num] :
% 5.25/5.49 ( ( bit0 @ X22 )
% 5.25/5.49 != ( bit1 @ X32 ) ) ).
% 5.25/5.49
% 5.25/5.49 % verit_eq_simplify(14)
% 5.25/5.49 thf(fact_3296_div__div__div__same,axiom,
% 5.25/5.49 ! [D: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ D @ B )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.49 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 5.25/5.49 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_div_div_same
% 5.25/5.49 thf(fact_3297_div__div__div__same,axiom,
% 5.25/5.49 ! [D: nat,B: nat,A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ D @ B )
% 5.25/5.49 => ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.49 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 5.25/5.49 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_div_div_same
% 5.25/5.49 thf(fact_3298_div__div__div__same,axiom,
% 5.25/5.49 ! [D: int,B: int,A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ D @ B )
% 5.25/5.49 => ( ( dvd_dvd_int @ B @ A )
% 5.25/5.49 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 5.25/5.49 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_div_div_same
% 5.25/5.49 thf(fact_3299_dvd__div__eq__cancel,axiom,
% 5.25/5.49 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.49 ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.25/5.49 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ C @ A )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.49 => ( A = B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_cancel
% 5.25/5.49 thf(fact_3300_dvd__div__eq__cancel,axiom,
% 5.25/5.49 ! [A: complex,C: complex,B: complex] :
% 5.25/5.49 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.25/5.49 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.49 => ( ( dvd_dvd_complex @ C @ A )
% 5.25/5.49 => ( ( dvd_dvd_complex @ C @ B )
% 5.25/5.49 => ( A = B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_cancel
% 5.25/5.49 thf(fact_3301_dvd__div__eq__cancel,axiom,
% 5.25/5.49 ! [A: real,C: real,B: real] :
% 5.25/5.49 ( ( ( divide_divide_real @ A @ C )
% 5.25/5.49 = ( divide_divide_real @ B @ C ) )
% 5.25/5.49 => ( ( dvd_dvd_real @ C @ A )
% 5.25/5.49 => ( ( dvd_dvd_real @ C @ B )
% 5.25/5.49 => ( A = B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_cancel
% 5.25/5.49 thf(fact_3302_dvd__div__eq__cancel,axiom,
% 5.25/5.49 ! [A: rat,C: rat,B: rat] :
% 5.25/5.49 ( ( ( divide_divide_rat @ A @ C )
% 5.25/5.49 = ( divide_divide_rat @ B @ C ) )
% 5.25/5.49 => ( ( dvd_dvd_rat @ C @ A )
% 5.25/5.49 => ( ( dvd_dvd_rat @ C @ B )
% 5.25/5.49 => ( A = B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_cancel
% 5.25/5.49 thf(fact_3303_dvd__div__eq__cancel,axiom,
% 5.25/5.49 ! [A: nat,C: nat,B: nat] :
% 5.25/5.49 ( ( ( divide_divide_nat @ A @ C )
% 5.25/5.49 = ( divide_divide_nat @ B @ C ) )
% 5.25/5.49 => ( ( dvd_dvd_nat @ C @ A )
% 5.25/5.49 => ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.49 => ( A = B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_cancel
% 5.25/5.49 thf(fact_3304_dvd__div__eq__cancel,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int] :
% 5.25/5.49 ( ( ( divide_divide_int @ A @ C )
% 5.25/5.49 = ( divide_divide_int @ B @ C ) )
% 5.25/5.49 => ( ( dvd_dvd_int @ C @ A )
% 5.25/5.49 => ( ( dvd_dvd_int @ C @ B )
% 5.25/5.49 => ( A = B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_cancel
% 5.25/5.49 thf(fact_3305_dvd__div__eq__iff,axiom,
% 5.25/5.49 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.49 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.25/5.49 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.25/5.49 = ( A = B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_iff
% 5.25/5.49 thf(fact_3306_dvd__div__eq__iff,axiom,
% 5.25/5.49 ! [C: complex,A: complex,B: complex] :
% 5.25/5.49 ( ( dvd_dvd_complex @ C @ A )
% 5.25/5.49 => ( ( dvd_dvd_complex @ C @ B )
% 5.25/5.49 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.25/5.49 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.49 = ( A = B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_iff
% 5.25/5.49 thf(fact_3307_dvd__div__eq__iff,axiom,
% 5.25/5.49 ! [C: real,A: real,B: real] :
% 5.25/5.49 ( ( dvd_dvd_real @ C @ A )
% 5.25/5.49 => ( ( dvd_dvd_real @ C @ B )
% 5.25/5.49 => ( ( ( divide_divide_real @ A @ C )
% 5.25/5.49 = ( divide_divide_real @ B @ C ) )
% 5.25/5.49 = ( A = B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_iff
% 5.25/5.49 thf(fact_3308_dvd__div__eq__iff,axiom,
% 5.25/5.49 ! [C: rat,A: rat,B: rat] :
% 5.25/5.49 ( ( dvd_dvd_rat @ C @ A )
% 5.25/5.49 => ( ( dvd_dvd_rat @ C @ B )
% 5.25/5.49 => ( ( ( divide_divide_rat @ A @ C )
% 5.25/5.49 = ( divide_divide_rat @ B @ C ) )
% 5.25/5.49 = ( A = B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_iff
% 5.25/5.49 thf(fact_3309_dvd__div__eq__iff,axiom,
% 5.25/5.49 ! [C: nat,A: nat,B: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ C @ A )
% 5.25/5.49 => ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.49 => ( ( ( divide_divide_nat @ A @ C )
% 5.25/5.49 = ( divide_divide_nat @ B @ C ) )
% 5.25/5.49 = ( A = B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_iff
% 5.25/5.49 thf(fact_3310_dvd__div__eq__iff,axiom,
% 5.25/5.49 ! [C: int,A: int,B: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ C @ A )
% 5.25/5.49 => ( ( dvd_dvd_int @ C @ B )
% 5.25/5.49 => ( ( ( divide_divide_int @ A @ C )
% 5.25/5.49 = ( divide_divide_int @ B @ C ) )
% 5.25/5.49 = ( A = B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_iff
% 5.25/5.49 thf(fact_3311_diff__diff__eq,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.25/5.49 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_diff_eq
% 5.25/5.49 thf(fact_3312_diff__diff__eq,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.25/5.49 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_diff_eq
% 5.25/5.49 thf(fact_3313_diff__diff__eq,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 5.25/5.49 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_diff_eq
% 5.25/5.49 thf(fact_3314_diff__diff__eq,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.25/5.49 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_diff_eq
% 5.25/5.49 thf(fact_3315_add__implies__diff,axiom,
% 5.25/5.49 ! [C: real,B: real,A: real] :
% 5.25/5.49 ( ( ( plus_plus_real @ C @ B )
% 5.25/5.49 = A )
% 5.25/5.49 => ( C
% 5.25/5.49 = ( minus_minus_real @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_implies_diff
% 5.25/5.49 thf(fact_3316_add__implies__diff,axiom,
% 5.25/5.49 ! [C: rat,B: rat,A: rat] :
% 5.25/5.49 ( ( ( plus_plus_rat @ C @ B )
% 5.25/5.49 = A )
% 5.25/5.49 => ( C
% 5.25/5.49 = ( minus_minus_rat @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_implies_diff
% 5.25/5.49 thf(fact_3317_add__implies__diff,axiom,
% 5.25/5.49 ! [C: nat,B: nat,A: nat] :
% 5.25/5.49 ( ( ( plus_plus_nat @ C @ B )
% 5.25/5.49 = A )
% 5.25/5.49 => ( C
% 5.25/5.49 = ( minus_minus_nat @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_implies_diff
% 5.25/5.49 thf(fact_3318_add__implies__diff,axiom,
% 5.25/5.49 ! [C: int,B: int,A: int] :
% 5.25/5.49 ( ( ( plus_plus_int @ C @ B )
% 5.25/5.49 = A )
% 5.25/5.49 => ( C
% 5.25/5.49 = ( minus_minus_int @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_implies_diff
% 5.25/5.49 thf(fact_3319_diff__add__eq__diff__diff__swap,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.25/5.49 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_add_eq_diff_diff_swap
% 5.25/5.49 thf(fact_3320_diff__add__eq__diff__diff__swap,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.49 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_add_eq_diff_diff_swap
% 5.25/5.49 thf(fact_3321_diff__add__eq__diff__diff__swap,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.25/5.49 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_add_eq_diff_diff_swap
% 5.25/5.49 thf(fact_3322_diff__add__eq,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.25/5.49 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_add_eq
% 5.25/5.49 thf(fact_3323_diff__add__eq,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.25/5.49 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_add_eq
% 5.25/5.49 thf(fact_3324_diff__add__eq,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.25/5.49 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_add_eq
% 5.25/5.49 thf(fact_3325_diff__diff__eq2,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.25/5.49 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_diff_eq2
% 5.25/5.49 thf(fact_3326_diff__diff__eq2,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.25/5.49 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_diff_eq2
% 5.25/5.49 thf(fact_3327_diff__diff__eq2,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.25/5.49 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_diff_eq2
% 5.25/5.49 thf(fact_3328_add__diff__eq,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.25/5.49 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_diff_eq
% 5.25/5.49 thf(fact_3329_add__diff__eq,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.25/5.49 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_diff_eq
% 5.25/5.49 thf(fact_3330_add__diff__eq,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.25/5.49 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_diff_eq
% 5.25/5.49 thf(fact_3331_eq__diff__eq,axiom,
% 5.25/5.49 ! [A: real,C: real,B: real] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( minus_minus_real @ C @ B ) )
% 5.25/5.49 = ( ( plus_plus_real @ A @ B )
% 5.25/5.49 = C ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_diff_eq
% 5.25/5.49 thf(fact_3332_eq__diff__eq,axiom,
% 5.25/5.49 ! [A: rat,C: rat,B: rat] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( minus_minus_rat @ C @ B ) )
% 5.25/5.49 = ( ( plus_plus_rat @ A @ B )
% 5.25/5.49 = C ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_diff_eq
% 5.25/5.49 thf(fact_3333_eq__diff__eq,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( minus_minus_int @ C @ B ) )
% 5.25/5.49 = ( ( plus_plus_int @ A @ B )
% 5.25/5.49 = C ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_diff_eq
% 5.25/5.49 thf(fact_3334_diff__eq__eq,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( ( minus_minus_real @ A @ B )
% 5.25/5.49 = C )
% 5.25/5.49 = ( A
% 5.25/5.49 = ( plus_plus_real @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_eq_eq
% 5.25/5.49 thf(fact_3335_diff__eq__eq,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( ( minus_minus_rat @ A @ B )
% 5.25/5.49 = C )
% 5.25/5.49 = ( A
% 5.25/5.49 = ( plus_plus_rat @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_eq_eq
% 5.25/5.49 thf(fact_3336_diff__eq__eq,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( ( minus_minus_int @ A @ B )
% 5.25/5.49 = C )
% 5.25/5.49 = ( A
% 5.25/5.49 = ( plus_plus_int @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_eq_eq
% 5.25/5.49 thf(fact_3337_group__cancel_Osub1,axiom,
% 5.25/5.49 ! [A2: real,K: real,A: real,B: real] :
% 5.25/5.49 ( ( A2
% 5.25/5.49 = ( plus_plus_real @ K @ A ) )
% 5.25/5.49 => ( ( minus_minus_real @ A2 @ B )
% 5.25/5.49 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % group_cancel.sub1
% 5.25/5.49 thf(fact_3338_group__cancel_Osub1,axiom,
% 5.25/5.49 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.25/5.49 ( ( A2
% 5.25/5.49 = ( plus_plus_rat @ K @ A ) )
% 5.25/5.49 => ( ( minus_minus_rat @ A2 @ B )
% 5.25/5.49 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % group_cancel.sub1
% 5.25/5.49 thf(fact_3339_group__cancel_Osub1,axiom,
% 5.25/5.49 ! [A2: int,K: int,A: int,B: int] :
% 5.25/5.49 ( ( A2
% 5.25/5.49 = ( plus_plus_int @ K @ A ) )
% 5.25/5.49 => ( ( minus_minus_int @ A2 @ B )
% 5.25/5.49 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % group_cancel.sub1
% 5.25/5.49 thf(fact_3340_add__diff__add,axiom,
% 5.25/5.49 ! [A: real,C: real,B: real,D: real] :
% 5.25/5.49 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 5.25/5.49 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_diff_add
% 5.25/5.49 thf(fact_3341_add__diff__add,axiom,
% 5.25/5.49 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.25/5.49 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 5.25/5.49 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_diff_add
% 5.25/5.49 thf(fact_3342_add__diff__add,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int,D: int] :
% 5.25/5.49 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 5.25/5.49 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_diff_add
% 5.25/5.49 thf(fact_3343_verit__eq__simplify_I12_J,axiom,
% 5.25/5.49 ! [X32: num] :
% 5.25/5.49 ( one
% 5.25/5.49 != ( bit1 @ X32 ) ) ).
% 5.25/5.49
% 5.25/5.49 % verit_eq_simplify(12)
% 5.25/5.49 thf(fact_3344_dvd__power__same,axiom,
% 5.25/5.49 ! [X3: code_integer,Y: code_integer,N: nat] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ X3 @ Y )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X3 @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_same
% 5.25/5.49 thf(fact_3345_dvd__power__same,axiom,
% 5.25/5.49 ! [X3: nat,Y: nat,N: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ X3 @ Y )
% 5.25/5.49 => ( dvd_dvd_nat @ ( power_power_nat @ X3 @ N ) @ ( power_power_nat @ Y @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_same
% 5.25/5.49 thf(fact_3346_dvd__power__same,axiom,
% 5.25/5.49 ! [X3: real,Y: real,N: nat] :
% 5.25/5.49 ( ( dvd_dvd_real @ X3 @ Y )
% 5.25/5.49 => ( dvd_dvd_real @ ( power_power_real @ X3 @ N ) @ ( power_power_real @ Y @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_same
% 5.25/5.49 thf(fact_3347_dvd__power__same,axiom,
% 5.25/5.49 ! [X3: int,Y: int,N: nat] :
% 5.25/5.49 ( ( dvd_dvd_int @ X3 @ Y )
% 5.25/5.49 => ( dvd_dvd_int @ ( power_power_int @ X3 @ N ) @ ( power_power_int @ Y @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_same
% 5.25/5.49 thf(fact_3348_dvd__power__same,axiom,
% 5.25/5.49 ! [X3: complex,Y: complex,N: nat] :
% 5.25/5.49 ( ( dvd_dvd_complex @ X3 @ Y )
% 5.25/5.49 => ( dvd_dvd_complex @ ( power_power_complex @ X3 @ N ) @ ( power_power_complex @ Y @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_same
% 5.25/5.49 thf(fact_3349_diff__divide__distrib,axiom,
% 5.25/5.49 ! [A: complex,B: complex,C: complex] :
% 5.25/5.49 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.25/5.49 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_divide_distrib
% 5.25/5.49 thf(fact_3350_diff__divide__distrib,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.25/5.49 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_divide_distrib
% 5.25/5.49 thf(fact_3351_diff__divide__distrib,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.25/5.49 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_divide_distrib
% 5.25/5.49 thf(fact_3352_dvd__mod,axiom,
% 5.25/5.49 ! [K: nat,M: nat,N: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ K @ M )
% 5.25/5.49 => ( ( dvd_dvd_nat @ K @ N )
% 5.25/5.49 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mod
% 5.25/5.49 thf(fact_3353_dvd__mod,axiom,
% 5.25/5.49 ! [K: int,M: int,N: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ K @ M )
% 5.25/5.49 => ( ( dvd_dvd_int @ K @ N )
% 5.25/5.49 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mod
% 5.25/5.49 thf(fact_3354_dvd__mod,axiom,
% 5.25/5.49 ! [K: code_integer,M: code_integer,N: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ K @ M )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ K @ N )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mod
% 5.25/5.49 thf(fact_3355_mod__mod__cancel,axiom,
% 5.25/5.49 ! [C: nat,B: nat,A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.49 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 5.25/5.49 = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mod_cancel
% 5.25/5.49 thf(fact_3356_mod__mod__cancel,axiom,
% 5.25/5.49 ! [C: int,B: int,A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ C @ B )
% 5.25/5.49 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 5.25/5.49 = ( modulo_modulo_int @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mod_cancel
% 5.25/5.49 thf(fact_3357_mod__mod__cancel,axiom,
% 5.25/5.49 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.49 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 5.25/5.49 = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mod_cancel
% 5.25/5.49 thf(fact_3358_dvd__mod__iff,axiom,
% 5.25/5.49 ! [C: nat,B: nat,A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.49 => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.25/5.49 = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mod_iff
% 5.25/5.49 thf(fact_3359_dvd__mod__iff,axiom,
% 5.25/5.49 ! [C: int,B: int,A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ C @ B )
% 5.25/5.49 => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.25/5.49 = ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mod_iff
% 5.25/5.49 thf(fact_3360_dvd__mod__iff,axiom,
% 5.25/5.49 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.25/5.49 = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mod_iff
% 5.25/5.49 thf(fact_3361_dvd__mod__imp__dvd,axiom,
% 5.25/5.49 ! [C: nat,A: nat,B: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.25/5.49 => ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.49 => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mod_imp_dvd
% 5.25/5.49 thf(fact_3362_dvd__mod__imp__dvd,axiom,
% 5.25/5.49 ! [C: int,A: int,B: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.25/5.49 => ( ( dvd_dvd_int @ C @ B )
% 5.25/5.49 => ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mod_imp_dvd
% 5.25/5.49 thf(fact_3363_dvd__mod__imp__dvd,axiom,
% 5.25/5.49 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mod_imp_dvd
% 5.25/5.49 thf(fact_3364_mod__diff__eq,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int] :
% 5.25/5.49 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.25/5.49 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_diff_eq
% 5.25/5.49 thf(fact_3365_mod__diff__eq,axiom,
% 5.25/5.49 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.49 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.25/5.49 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_diff_eq
% 5.25/5.49 thf(fact_3366_mod__diff__cong,axiom,
% 5.25/5.49 ! [A: int,C: int,A4: int,B: int,B4: int] :
% 5.25/5.49 ( ( ( modulo_modulo_int @ A @ C )
% 5.25/5.49 = ( modulo_modulo_int @ A4 @ C ) )
% 5.25/5.49 => ( ( ( modulo_modulo_int @ B @ C )
% 5.25/5.49 = ( modulo_modulo_int @ B4 @ C ) )
% 5.25/5.49 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.25/5.49 = ( modulo_modulo_int @ ( minus_minus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_diff_cong
% 5.25/5.49 thf(fact_3367_mod__diff__cong,axiom,
% 5.25/5.49 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 5.25/5.49 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.25/5.49 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 5.25/5.49 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.25/5.49 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.25/5.49 => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.25/5.49 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_diff_cong
% 5.25/5.49 thf(fact_3368_mod__diff__left__eq,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int] :
% 5.25/5.49 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.25/5.49 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_diff_left_eq
% 5.25/5.49 thf(fact_3369_mod__diff__left__eq,axiom,
% 5.25/5.49 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.49 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.25/5.49 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_diff_left_eq
% 5.25/5.49 thf(fact_3370_mod__diff__right__eq,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.25/5.49 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_diff_right_eq
% 5.25/5.49 thf(fact_3371_mod__diff__right__eq,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.49 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.25/5.49 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_diff_right_eq
% 5.25/5.49 thf(fact_3372_int__distrib_I4_J,axiom,
% 5.25/5.49 ! [W: int,Z1: int,Z22: int] :
% 5.25/5.49 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 5.25/5.49 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % int_distrib(4)
% 5.25/5.49 thf(fact_3373_int__distrib_I3_J,axiom,
% 5.25/5.49 ! [Z1: int,Z22: int,W: int] :
% 5.25/5.49 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 5.25/5.49 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % int_distrib(3)
% 5.25/5.49 thf(fact_3374_max__diff__distrib__left,axiom,
% 5.25/5.49 ! [X3: real,Y: real,Z: real] :
% 5.25/5.49 ( ( minus_minus_real @ ( ord_max_real @ X3 @ Y ) @ Z )
% 5.25/5.49 = ( ord_max_real @ ( minus_minus_real @ X3 @ Z ) @ ( minus_minus_real @ Y @ Z ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % max_diff_distrib_left
% 5.25/5.49 thf(fact_3375_max__diff__distrib__left,axiom,
% 5.25/5.49 ! [X3: rat,Y: rat,Z: rat] :
% 5.25/5.49 ( ( minus_minus_rat @ ( ord_max_rat @ X3 @ Y ) @ Z )
% 5.25/5.49 = ( ord_max_rat @ ( minus_minus_rat @ X3 @ Z ) @ ( minus_minus_rat @ Y @ Z ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % max_diff_distrib_left
% 5.25/5.49 thf(fact_3376_max__diff__distrib__left,axiom,
% 5.25/5.49 ! [X3: int,Y: int,Z: int] :
% 5.25/5.49 ( ( minus_minus_int @ ( ord_max_int @ X3 @ Y ) @ Z )
% 5.25/5.49 = ( ord_max_int @ ( minus_minus_int @ X3 @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % max_diff_distrib_left
% 5.25/5.49 thf(fact_3377_numeral__code_I2_J,axiom,
% 5.25/5.49 ! [N: num] :
% 5.25/5.49 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.25/5.49 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % numeral_code(2)
% 5.25/5.49 thf(fact_3378_numeral__code_I2_J,axiom,
% 5.25/5.49 ! [N: num] :
% 5.25/5.49 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.25/5.49 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % numeral_code(2)
% 5.25/5.49 thf(fact_3379_numeral__code_I2_J,axiom,
% 5.25/5.49 ! [N: num] :
% 5.25/5.49 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.25/5.49 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % numeral_code(2)
% 5.25/5.49 thf(fact_3380_numeral__code_I2_J,axiom,
% 5.25/5.49 ! [N: num] :
% 5.25/5.49 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.25/5.49 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % numeral_code(2)
% 5.25/5.49 thf(fact_3381_numeral__code_I2_J,axiom,
% 5.25/5.49 ! [N: num] :
% 5.25/5.49 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.25/5.49 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % numeral_code(2)
% 5.25/5.49 thf(fact_3382_set__vebt__def,axiom,
% 5.25/5.49 ( vEBT_set_vebt
% 5.25/5.49 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % set_vebt_def
% 5.25/5.49 thf(fact_3383_signed__take__bit__diff,axiom,
% 5.25/5.49 ! [N: nat,K: int,L2: int] :
% 5.25/5.49 ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.25/5.49 = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % signed_take_bit_diff
% 5.25/5.49 thf(fact_3384_odd__numeral,axiom,
% 5.25/5.49 ! [N: num] :
% 5.25/5.49 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % odd_numeral
% 5.25/5.49 thf(fact_3385_odd__numeral,axiom,
% 5.25/5.49 ! [N: num] :
% 5.25/5.49 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % odd_numeral
% 5.25/5.49 thf(fact_3386_odd__numeral,axiom,
% 5.25/5.49 ! [N: num] :
% 5.25/5.49 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % odd_numeral
% 5.25/5.49 thf(fact_3387_concat__bit__assoc,axiom,
% 5.25/5.49 ! [N: nat,K: int,M: nat,L2: int,R2: int] :
% 5.25/5.49 ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L2 @ R2 ) )
% 5.25/5.49 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L2 ) @ R2 ) ) ).
% 5.25/5.49
% 5.25/5.49 % concat_bit_assoc
% 5.25/5.49 thf(fact_3388_power__numeral__even,axiom,
% 5.25/5.49 ! [Z: complex,W: num] :
% 5.25/5.49 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.25/5.49 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_numeral_even
% 5.25/5.49 thf(fact_3389_power__numeral__even,axiom,
% 5.25/5.49 ! [Z: real,W: num] :
% 5.25/5.49 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.25/5.49 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_numeral_even
% 5.25/5.49 thf(fact_3390_power__numeral__even,axiom,
% 5.25/5.49 ! [Z: rat,W: num] :
% 5.25/5.49 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.25/5.49 = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_numeral_even
% 5.25/5.49 thf(fact_3391_power__numeral__even,axiom,
% 5.25/5.49 ! [Z: nat,W: num] :
% 5.25/5.49 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.25/5.49 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_numeral_even
% 5.25/5.49 thf(fact_3392_power__numeral__even,axiom,
% 5.25/5.49 ! [Z: int,W: num] :
% 5.25/5.49 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.25/5.49 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_numeral_even
% 5.25/5.49 thf(fact_3393_even__diff__iff,axiom,
% 5.25/5.49 ! [K: int,L2: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L2 ) )
% 5.25/5.49 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % even_diff_iff
% 5.25/5.49 thf(fact_3394_le__iff__diff__le__0,axiom,
% 5.25/5.49 ( ord_less_eq_real
% 5.25/5.49 = ( ^ [A3: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_iff_diff_le_0
% 5.25/5.49 thf(fact_3395_le__iff__diff__le__0,axiom,
% 5.25/5.49 ( ord_less_eq_rat
% 5.25/5.49 = ( ^ [A3: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_iff_diff_le_0
% 5.25/5.49 thf(fact_3396_le__iff__diff__le__0,axiom,
% 5.25/5.49 ( ord_less_eq_int
% 5.25/5.49 = ( ^ [A3: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_iff_diff_le_0
% 5.25/5.49 thf(fact_3397_not__is__unit__0,axiom,
% 5.25/5.49 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 5.25/5.49
% 5.25/5.49 % not_is_unit_0
% 5.25/5.49 thf(fact_3398_not__is__unit__0,axiom,
% 5.25/5.49 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.25/5.49
% 5.25/5.49 % not_is_unit_0
% 5.25/5.49 thf(fact_3399_not__is__unit__0,axiom,
% 5.25/5.49 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.25/5.49
% 5.25/5.49 % not_is_unit_0
% 5.25/5.49 thf(fact_3400_less__iff__diff__less__0,axiom,
% 5.25/5.49 ( ord_less_real
% 5.25/5.49 = ( ^ [A3: real,B2: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % less_iff_diff_less_0
% 5.25/5.49 thf(fact_3401_less__iff__diff__less__0,axiom,
% 5.25/5.49 ( ord_less_rat
% 5.25/5.49 = ( ^ [A3: rat,B2: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % less_iff_diff_less_0
% 5.25/5.49 thf(fact_3402_less__iff__diff__less__0,axiom,
% 5.25/5.49 ( ord_less_int
% 5.25/5.49 = ( ^ [A3: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % less_iff_diff_less_0
% 5.25/5.49 thf(fact_3403_minf_I10_J,axiom,
% 5.25/5.49 ! [D: code_integer,S: code_integer] :
% 5.25/5.49 ? [Z2: code_integer] :
% 5.25/5.49 ! [X: code_integer] :
% 5.25/5.49 ( ( ord_le6747313008572928689nteger @ X @ Z2 )
% 5.25/5.49 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S ) ) )
% 5.25/5.49 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % minf(10)
% 5.25/5.49 thf(fact_3404_minf_I10_J,axiom,
% 5.25/5.49 ! [D: real,S: real] :
% 5.25/5.49 ? [Z2: real] :
% 5.25/5.49 ! [X: real] :
% 5.25/5.49 ( ( ord_less_real @ X @ Z2 )
% 5.25/5.49 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) )
% 5.25/5.49 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % minf(10)
% 5.25/5.49 thf(fact_3405_minf_I10_J,axiom,
% 5.25/5.49 ! [D: rat,S: rat] :
% 5.25/5.49 ? [Z2: rat] :
% 5.25/5.49 ! [X: rat] :
% 5.25/5.49 ( ( ord_less_rat @ X @ Z2 )
% 5.25/5.49 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) )
% 5.25/5.49 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % minf(10)
% 5.25/5.49 thf(fact_3406_minf_I10_J,axiom,
% 5.25/5.49 ! [D: nat,S: nat] :
% 5.25/5.49 ? [Z2: nat] :
% 5.25/5.49 ! [X: nat] :
% 5.25/5.49 ( ( ord_less_nat @ X @ Z2 )
% 5.25/5.49 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) )
% 5.25/5.49 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % minf(10)
% 5.25/5.49 thf(fact_3407_minf_I10_J,axiom,
% 5.25/5.49 ! [D: int,S: int] :
% 5.25/5.49 ? [Z2: int] :
% 5.25/5.49 ! [X: int] :
% 5.25/5.49 ( ( ord_less_int @ X @ Z2 )
% 5.25/5.49 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) )
% 5.25/5.49 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % minf(10)
% 5.25/5.49 thf(fact_3408_minf_I9_J,axiom,
% 5.25/5.49 ! [D: code_integer,S: code_integer] :
% 5.25/5.49 ? [Z2: code_integer] :
% 5.25/5.49 ! [X: code_integer] :
% 5.25/5.49 ( ( ord_le6747313008572928689nteger @ X @ Z2 )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S ) )
% 5.25/5.49 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % minf(9)
% 5.25/5.49 thf(fact_3409_minf_I9_J,axiom,
% 5.25/5.49 ! [D: real,S: real] :
% 5.25/5.49 ? [Z2: real] :
% 5.25/5.49 ! [X: real] :
% 5.25/5.49 ( ( ord_less_real @ X @ Z2 )
% 5.25/5.49 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) )
% 5.25/5.49 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % minf(9)
% 5.25/5.49 thf(fact_3410_minf_I9_J,axiom,
% 5.25/5.49 ! [D: rat,S: rat] :
% 5.25/5.49 ? [Z2: rat] :
% 5.25/5.49 ! [X: rat] :
% 5.25/5.49 ( ( ord_less_rat @ X @ Z2 )
% 5.25/5.49 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) )
% 5.25/5.49 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % minf(9)
% 5.25/5.49 thf(fact_3411_minf_I9_J,axiom,
% 5.25/5.49 ! [D: nat,S: nat] :
% 5.25/5.49 ? [Z2: nat] :
% 5.25/5.49 ! [X: nat] :
% 5.25/5.49 ( ( ord_less_nat @ X @ Z2 )
% 5.25/5.49 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) )
% 5.25/5.49 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % minf(9)
% 5.25/5.49 thf(fact_3412_minf_I9_J,axiom,
% 5.25/5.49 ! [D: int,S: int] :
% 5.25/5.49 ? [Z2: int] :
% 5.25/5.49 ! [X: int] :
% 5.25/5.49 ( ( ord_less_int @ X @ Z2 )
% 5.25/5.49 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) )
% 5.25/5.49 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % minf(9)
% 5.25/5.49 thf(fact_3413_pinf_I10_J,axiom,
% 5.25/5.49 ! [D: code_integer,S: code_integer] :
% 5.25/5.49 ? [Z2: code_integer] :
% 5.25/5.49 ! [X: code_integer] :
% 5.25/5.49 ( ( ord_le6747313008572928689nteger @ Z2 @ X )
% 5.25/5.49 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S ) ) )
% 5.25/5.49 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % pinf(10)
% 5.25/5.49 thf(fact_3414_pinf_I10_J,axiom,
% 5.25/5.49 ! [D: real,S: real] :
% 5.25/5.49 ? [Z2: real] :
% 5.25/5.49 ! [X: real] :
% 5.25/5.49 ( ( ord_less_real @ Z2 @ X )
% 5.25/5.49 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) )
% 5.25/5.49 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % pinf(10)
% 5.25/5.49 thf(fact_3415_pinf_I10_J,axiom,
% 5.25/5.49 ! [D: rat,S: rat] :
% 5.25/5.49 ? [Z2: rat] :
% 5.25/5.49 ! [X: rat] :
% 5.25/5.49 ( ( ord_less_rat @ Z2 @ X )
% 5.25/5.49 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) )
% 5.25/5.49 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % pinf(10)
% 5.25/5.49 thf(fact_3416_pinf_I10_J,axiom,
% 5.25/5.49 ! [D: nat,S: nat] :
% 5.25/5.49 ? [Z2: nat] :
% 5.25/5.49 ! [X: nat] :
% 5.25/5.49 ( ( ord_less_nat @ Z2 @ X )
% 5.25/5.49 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) )
% 5.25/5.49 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % pinf(10)
% 5.25/5.49 thf(fact_3417_pinf_I10_J,axiom,
% 5.25/5.49 ! [D: int,S: int] :
% 5.25/5.49 ? [Z2: int] :
% 5.25/5.49 ! [X: int] :
% 5.25/5.49 ( ( ord_less_int @ Z2 @ X )
% 5.25/5.49 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) )
% 5.25/5.49 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % pinf(10)
% 5.25/5.49 thf(fact_3418_pinf_I9_J,axiom,
% 5.25/5.49 ! [D: code_integer,S: code_integer] :
% 5.25/5.49 ? [Z2: code_integer] :
% 5.25/5.49 ! [X: code_integer] :
% 5.25/5.49 ( ( ord_le6747313008572928689nteger @ Z2 @ X )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S ) )
% 5.25/5.49 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % pinf(9)
% 5.25/5.49 thf(fact_3419_pinf_I9_J,axiom,
% 5.25/5.49 ! [D: real,S: real] :
% 5.25/5.49 ? [Z2: real] :
% 5.25/5.49 ! [X: real] :
% 5.25/5.49 ( ( ord_less_real @ Z2 @ X )
% 5.25/5.49 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) )
% 5.25/5.49 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % pinf(9)
% 5.25/5.49 thf(fact_3420_pinf_I9_J,axiom,
% 5.25/5.49 ! [D: rat,S: rat] :
% 5.25/5.49 ? [Z2: rat] :
% 5.25/5.49 ! [X: rat] :
% 5.25/5.49 ( ( ord_less_rat @ Z2 @ X )
% 5.25/5.49 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) )
% 5.25/5.49 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % pinf(9)
% 5.25/5.49 thf(fact_3421_pinf_I9_J,axiom,
% 5.25/5.49 ! [D: nat,S: nat] :
% 5.25/5.49 ? [Z2: nat] :
% 5.25/5.49 ! [X: nat] :
% 5.25/5.49 ( ( ord_less_nat @ Z2 @ X )
% 5.25/5.49 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) )
% 5.25/5.49 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % pinf(9)
% 5.25/5.49 thf(fact_3422_pinf_I9_J,axiom,
% 5.25/5.49 ! [D: int,S: int] :
% 5.25/5.49 ? [Z2: int] :
% 5.25/5.49 ! [X: int] :
% 5.25/5.49 ( ( ord_less_int @ Z2 @ X )
% 5.25/5.49 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) )
% 5.25/5.49 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % pinf(9)
% 5.25/5.49 thf(fact_3423_dvd__div__eq__0__iff,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.49 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.25/5.49 = zero_z3403309356797280102nteger )
% 5.25/5.49 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_0_iff
% 5.25/5.49 thf(fact_3424_dvd__div__eq__0__iff,axiom,
% 5.25/5.49 ! [B: complex,A: complex] :
% 5.25/5.49 ( ( dvd_dvd_complex @ B @ A )
% 5.25/5.49 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.25/5.49 = zero_zero_complex )
% 5.25/5.49 = ( A = zero_zero_complex ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_0_iff
% 5.25/5.49 thf(fact_3425_dvd__div__eq__0__iff,axiom,
% 5.25/5.49 ! [B: real,A: real] :
% 5.25/5.49 ( ( dvd_dvd_real @ B @ A )
% 5.25/5.49 => ( ( ( divide_divide_real @ A @ B )
% 5.25/5.49 = zero_zero_real )
% 5.25/5.49 = ( A = zero_zero_real ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_0_iff
% 5.25/5.49 thf(fact_3426_dvd__div__eq__0__iff,axiom,
% 5.25/5.49 ! [B: rat,A: rat] :
% 5.25/5.49 ( ( dvd_dvd_rat @ B @ A )
% 5.25/5.49 => ( ( ( divide_divide_rat @ A @ B )
% 5.25/5.49 = zero_zero_rat )
% 5.25/5.49 = ( A = zero_zero_rat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_0_iff
% 5.25/5.49 thf(fact_3427_dvd__div__eq__0__iff,axiom,
% 5.25/5.49 ! [B: nat,A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.49 => ( ( ( divide_divide_nat @ A @ B )
% 5.25/5.49 = zero_zero_nat )
% 5.25/5.49 = ( A = zero_zero_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_0_iff
% 5.25/5.49 thf(fact_3428_dvd__div__eq__0__iff,axiom,
% 5.25/5.49 ! [B: int,A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ A )
% 5.25/5.49 => ( ( ( divide_divide_int @ A @ B )
% 5.25/5.49 = zero_zero_int )
% 5.25/5.49 = ( A = zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_0_iff
% 5.25/5.49 thf(fact_3429_unit__mult__right__cancel,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.49 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.25/5.49 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.25/5.49 = ( B = C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_mult_right_cancel
% 5.25/5.49 thf(fact_3430_unit__mult__right__cancel,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.49 => ( ( ( times_times_nat @ B @ A )
% 5.25/5.49 = ( times_times_nat @ C @ A ) )
% 5.25/5.49 = ( B = C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_mult_right_cancel
% 5.25/5.49 thf(fact_3431_unit__mult__right__cancel,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.49 => ( ( ( times_times_int @ B @ A )
% 5.25/5.49 = ( times_times_int @ C @ A ) )
% 5.25/5.49 = ( B = C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_mult_right_cancel
% 5.25/5.49 thf(fact_3432_unit__mult__left__cancel,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.49 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.25/5.49 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.25/5.49 = ( B = C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_mult_left_cancel
% 5.25/5.49 thf(fact_3433_unit__mult__left__cancel,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.49 => ( ( ( times_times_nat @ A @ B )
% 5.25/5.49 = ( times_times_nat @ A @ C ) )
% 5.25/5.49 = ( B = C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_mult_left_cancel
% 5.25/5.49 thf(fact_3434_unit__mult__left__cancel,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.49 => ( ( ( times_times_int @ A @ B )
% 5.25/5.49 = ( times_times_int @ A @ C ) )
% 5.25/5.49 = ( B = C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_mult_left_cancel
% 5.25/5.49 thf(fact_3435_mult__unit__dvd__iff_H,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.25/5.49 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_unit_dvd_iff'
% 5.25/5.49 thf(fact_3436_mult__unit__dvd__iff_H,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.49 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.49 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_unit_dvd_iff'
% 5.25/5.49 thf(fact_3437_mult__unit__dvd__iff_H,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.49 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_unit_dvd_iff'
% 5.25/5.49 thf(fact_3438_dvd__mult__unit__iff_H,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_unit_iff'
% 5.25/5.49 thf(fact_3439_dvd__mult__unit__iff_H,axiom,
% 5.25/5.49 ! [B: nat,A: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.49 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_unit_iff'
% 5.25/5.49 thf(fact_3440_dvd__mult__unit__iff_H,axiom,
% 5.25/5.49 ! [B: int,A: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_unit_iff'
% 5.25/5.49 thf(fact_3441_mult__unit__dvd__iff,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.25/5.49 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_unit_dvd_iff
% 5.25/5.49 thf(fact_3442_mult__unit__dvd__iff,axiom,
% 5.25/5.49 ! [B: nat,A: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.49 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.49 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_unit_dvd_iff
% 5.25/5.49 thf(fact_3443_mult__unit__dvd__iff,axiom,
% 5.25/5.49 ! [B: int,A: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.49 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_unit_dvd_iff
% 5.25/5.49 thf(fact_3444_dvd__mult__unit__iff,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.25/5.49 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_unit_iff
% 5.25/5.49 thf(fact_3445_dvd__mult__unit__iff,axiom,
% 5.25/5.49 ! [B: nat,A: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.49 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.25/5.49 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_unit_iff
% 5.25/5.49 thf(fact_3446_dvd__mult__unit__iff,axiom,
% 5.25/5.49 ! [B: int,A: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.25/5.49 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_unit_iff
% 5.25/5.49 thf(fact_3447_is__unit__mult__iff,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.25/5.49 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.49 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % is_unit_mult_iff
% 5.25/5.49 thf(fact_3448_is__unit__mult__iff,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.25/5.49 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.49 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % is_unit_mult_iff
% 5.25/5.49 thf(fact_3449_is__unit__mult__iff,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.25/5.49 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.49 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % is_unit_mult_iff
% 5.25/5.49 thf(fact_3450_diff__le__eq,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.25/5.49 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_le_eq
% 5.25/5.49 thf(fact_3451_diff__le__eq,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.25/5.49 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_le_eq
% 5.25/5.49 thf(fact_3452_diff__le__eq,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.25/5.49 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_le_eq
% 5.25/5.49 thf(fact_3453_le__diff__eq,axiom,
% 5.25/5.49 ! [A: real,C: real,B: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.25/5.49 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_diff_eq
% 5.25/5.49 thf(fact_3454_le__diff__eq,axiom,
% 5.25/5.49 ! [A: rat,C: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.25/5.49 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_diff_eq
% 5.25/5.49 thf(fact_3455_le__diff__eq,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.25/5.49 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_diff_eq
% 5.25/5.49 thf(fact_3456_add__le__imp__le__diff,axiom,
% 5.25/5.49 ! [I2: real,K: real,N: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 5.25/5.49 => ( ord_less_eq_real @ I2 @ ( minus_minus_real @ N @ K ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_le_imp_le_diff
% 5.25/5.49 thf(fact_3457_add__le__imp__le__diff,axiom,
% 5.25/5.49 ! [I2: rat,K: rat,N: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 5.25/5.49 => ( ord_less_eq_rat @ I2 @ ( minus_minus_rat @ N @ K ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_le_imp_le_diff
% 5.25/5.49 thf(fact_3458_add__le__imp__le__diff,axiom,
% 5.25/5.49 ! [I2: nat,K: nat,N: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 5.25/5.49 => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N @ K ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_le_imp_le_diff
% 5.25/5.49 thf(fact_3459_add__le__imp__le__diff,axiom,
% 5.25/5.49 ! [I2: int,K: int,N: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 5.25/5.49 => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N @ K ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_le_imp_le_diff
% 5.25/5.49 thf(fact_3460_diff__add,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.49 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.25/5.49 = B ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_add
% 5.25/5.49 thf(fact_3461_add__le__add__imp__diff__le,axiom,
% 5.25/5.49 ! [I2: real,K: real,N: real,J2: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 5.25/5.49 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J2 @ K ) )
% 5.25/5.49 => ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 5.25/5.49 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J2 @ K ) )
% 5.25/5.49 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J2 ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_le_add_imp_diff_le
% 5.25/5.49 thf(fact_3462_add__le__add__imp__diff__le,axiom,
% 5.25/5.49 ! [I2: rat,K: rat,N: rat,J2: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 5.25/5.49 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J2 @ K ) )
% 5.25/5.49 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 5.25/5.49 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J2 @ K ) )
% 5.25/5.49 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J2 ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_le_add_imp_diff_le
% 5.25/5.49 thf(fact_3463_add__le__add__imp__diff__le,axiom,
% 5.25/5.49 ! [I2: nat,K: nat,N: nat,J2: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 5.25/5.49 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J2 @ K ) )
% 5.25/5.49 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 5.25/5.49 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J2 @ K ) )
% 5.25/5.49 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J2 ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_le_add_imp_diff_le
% 5.25/5.49 thf(fact_3464_add__le__add__imp__diff__le,axiom,
% 5.25/5.49 ! [I2: int,K: int,N: int,J2: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 5.25/5.49 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J2 @ K ) )
% 5.25/5.49 => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 5.25/5.49 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J2 @ K ) )
% 5.25/5.49 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J2 ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_le_add_imp_diff_le
% 5.25/5.49 thf(fact_3465_le__add__diff,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.49 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_add_diff
% 5.25/5.49 thf(fact_3466_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.25/5.49 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.25/5.49 thf(fact_3467_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.49 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.25/5.49 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.25/5.49 thf(fact_3468_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.49 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 5.25/5.49 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.25/5.49 thf(fact_3469_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.49 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 5.25/5.49 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.25/5.49 thf(fact_3470_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.49 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 5.25/5.49 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.25/5.49 thf(fact_3471_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.49 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.25/5.49 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.25/5.49 thf(fact_3472_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.49 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.25/5.49 = B ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.25/5.49 thf(fact_3473_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.49 => ( ( ( minus_minus_nat @ B @ A )
% 5.25/5.49 = C )
% 5.25/5.49 = ( B
% 5.25/5.49 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.25/5.49 thf(fact_3474_diff__less__eq,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.25/5.49 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_less_eq
% 5.25/5.49 thf(fact_3475_diff__less__eq,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.25/5.49 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_less_eq
% 5.25/5.49 thf(fact_3476_diff__less__eq,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.25/5.49 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % diff_less_eq
% 5.25/5.49 thf(fact_3477_less__diff__eq,axiom,
% 5.25/5.49 ! [A: real,C: real,B: real] :
% 5.25/5.49 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.25/5.49 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % less_diff_eq
% 5.25/5.49 thf(fact_3478_less__diff__eq,axiom,
% 5.25/5.49 ! [A: rat,C: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.25/5.49 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % less_diff_eq
% 5.25/5.49 thf(fact_3479_less__diff__eq,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int] :
% 5.25/5.49 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.25/5.49 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % less_diff_eq
% 5.25/5.49 thf(fact_3480_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ~ ( ord_less_real @ A @ B )
% 5.25/5.49 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.25/5.49 = A ) ) ).
% 5.25/5.49
% 5.25/5.49 % linordered_semidom_class.add_diff_inverse
% 5.25/5.49 thf(fact_3481_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ~ ( ord_less_rat @ A @ B )
% 5.25/5.49 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.25/5.49 = A ) ) ).
% 5.25/5.49
% 5.25/5.49 % linordered_semidom_class.add_diff_inverse
% 5.25/5.49 thf(fact_3482_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ~ ( ord_less_nat @ A @ B )
% 5.25/5.49 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.25/5.49 = A ) ) ).
% 5.25/5.49
% 5.25/5.49 % linordered_semidom_class.add_diff_inverse
% 5.25/5.49 thf(fact_3483_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ~ ( ord_less_int @ A @ B )
% 5.25/5.49 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.25/5.49 = A ) ) ).
% 5.25/5.49
% 5.25/5.49 % linordered_semidom_class.add_diff_inverse
% 5.25/5.49 thf(fact_3484_dvd__div__mult,axiom,
% 5.25/5.49 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.49 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.25/5.49 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_mult
% 5.25/5.49 thf(fact_3485_dvd__div__mult,axiom,
% 5.25/5.49 ! [C: nat,B: nat,A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.49 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.25/5.49 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_mult
% 5.25/5.49 thf(fact_3486_dvd__div__mult,axiom,
% 5.25/5.49 ! [C: int,B: int,A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ C @ B )
% 5.25/5.49 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.25/5.49 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_mult
% 5.25/5.49 thf(fact_3487_div__mult__swap,axiom,
% 5.25/5.49 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.49 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.25/5.49 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_mult_swap
% 5.25/5.49 thf(fact_3488_div__mult__swap,axiom,
% 5.25/5.49 ! [C: nat,B: nat,A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.49 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.25/5.49 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_mult_swap
% 5.25/5.49 thf(fact_3489_div__mult__swap,axiom,
% 5.25/5.49 ! [C: int,B: int,A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ C @ B )
% 5.25/5.49 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.25/5.49 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_mult_swap
% 5.25/5.49 thf(fact_3490_div__div__eq__right,axiom,
% 5.25/5.49 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.49 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.25/5.49 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_div_eq_right
% 5.25/5.49 thf(fact_3491_div__div__eq__right,axiom,
% 5.25/5.49 ! [C: nat,B: nat,A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.49 => ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.49 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.25/5.49 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_div_eq_right
% 5.25/5.49 thf(fact_3492_div__div__eq__right,axiom,
% 5.25/5.49 ! [C: int,B: int,A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ C @ B )
% 5.25/5.49 => ( ( dvd_dvd_int @ B @ A )
% 5.25/5.49 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.25/5.49 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_div_eq_right
% 5.25/5.49 thf(fact_3493_dvd__div__mult2__eq,axiom,
% 5.25/5.49 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.25/5.49 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.25/5.49 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_mult2_eq
% 5.25/5.49 thf(fact_3494_dvd__div__mult2__eq,axiom,
% 5.25/5.49 ! [B: nat,C: nat,A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.25/5.49 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.25/5.49 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_mult2_eq
% 5.25/5.49 thf(fact_3495_dvd__div__mult2__eq,axiom,
% 5.25/5.49 ! [B: int,C: int,A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.25/5.49 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.25/5.49 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_mult2_eq
% 5.25/5.49 thf(fact_3496_dvd__mult__imp__div,axiom,
% 5.25/5.49 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_imp_div
% 5.25/5.49 thf(fact_3497_dvd__mult__imp__div,axiom,
% 5.25/5.49 ! [A: nat,C: nat,B: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.25/5.49 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_imp_div
% 5.25/5.49 thf(fact_3498_dvd__mult__imp__div,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.25/5.49 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_imp_div
% 5.25/5.49 thf(fact_3499_div__mult__div__if__dvd,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ D @ C )
% 5.25/5.49 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 5.25/5.49 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_mult_div_if_dvd
% 5.25/5.49 thf(fact_3500_div__mult__div__if__dvd,axiom,
% 5.25/5.49 ! [B: nat,A: nat,D: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.49 => ( ( dvd_dvd_nat @ D @ C )
% 5.25/5.49 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 5.25/5.49 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_mult_div_if_dvd
% 5.25/5.49 thf(fact_3501_div__mult__div__if__dvd,axiom,
% 5.25/5.49 ! [B: int,A: int,D: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ A )
% 5.25/5.49 => ( ( dvd_dvd_int @ D @ C )
% 5.25/5.49 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 5.25/5.49 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_mult_div_if_dvd
% 5.25/5.49 thf(fact_3502_unit__div__cancel,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.49 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.25/5.49 = ( divide6298287555418463151nteger @ C @ A ) )
% 5.25/5.49 = ( B = C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_div_cancel
% 5.25/5.49 thf(fact_3503_unit__div__cancel,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.49 => ( ( ( divide_divide_nat @ B @ A )
% 5.25/5.49 = ( divide_divide_nat @ C @ A ) )
% 5.25/5.49 = ( B = C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_div_cancel
% 5.25/5.49 thf(fact_3504_unit__div__cancel,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.49 => ( ( ( divide_divide_int @ B @ A )
% 5.25/5.49 = ( divide_divide_int @ C @ A ) )
% 5.25/5.49 = ( B = C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_div_cancel
% 5.25/5.49 thf(fact_3505_div__unit__dvd__iff,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.25/5.49 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_unit_dvd_iff
% 5.25/5.49 thf(fact_3506_div__unit__dvd__iff,axiom,
% 5.25/5.49 ! [B: nat,A: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.49 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.25/5.49 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_unit_dvd_iff
% 5.25/5.49 thf(fact_3507_div__unit__dvd__iff,axiom,
% 5.25/5.49 ! [B: int,A: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.25/5.49 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_unit_dvd_iff
% 5.25/5.49 thf(fact_3508_dvd__div__unit__iff,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 5.25/5.49 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_unit_iff
% 5.25/5.49 thf(fact_3509_dvd__div__unit__iff,axiom,
% 5.25/5.49 ! [B: nat,A: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.49 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 5.25/5.49 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_unit_iff
% 5.25/5.49 thf(fact_3510_dvd__div__unit__iff,axiom,
% 5.25/5.49 ! [B: int,A: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 5.25/5.49 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_unit_iff
% 5.25/5.49 thf(fact_3511_div__plus__div__distrib__dvd__right,axiom,
% 5.25/5.49 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.49 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.25/5.49 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_plus_div_distrib_dvd_right
% 5.25/5.49 thf(fact_3512_div__plus__div__distrib__dvd__right,axiom,
% 5.25/5.49 ! [C: nat,B: nat,A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.49 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_plus_div_distrib_dvd_right
% 5.25/5.49 thf(fact_3513_div__plus__div__distrib__dvd__right,axiom,
% 5.25/5.49 ! [C: int,B: int,A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ C @ B )
% 5.25/5.49 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_plus_div_distrib_dvd_right
% 5.25/5.49 thf(fact_3514_div__plus__div__distrib__dvd__left,axiom,
% 5.25/5.49 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.25/5.49 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.25/5.49 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_plus_div_distrib_dvd_left
% 5.25/5.49 thf(fact_3515_div__plus__div__distrib__dvd__left,axiom,
% 5.25/5.49 ! [C: nat,A: nat,B: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ C @ A )
% 5.25/5.49 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_plus_div_distrib_dvd_left
% 5.25/5.49 thf(fact_3516_div__plus__div__distrib__dvd__left,axiom,
% 5.25/5.49 ! [C: int,A: int,B: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ C @ A )
% 5.25/5.49 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_plus_div_distrib_dvd_left
% 5.25/5.49 thf(fact_3517_eq__add__iff1,axiom,
% 5.25/5.49 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.25/5.49 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.25/5.49 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.25/5.49 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 5.25/5.49 = D ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_add_iff1
% 5.25/5.49 thf(fact_3518_eq__add__iff1,axiom,
% 5.25/5.49 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.25/5.49 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.25/5.49 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.25/5.49 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 5.25/5.49 = D ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_add_iff1
% 5.25/5.49 thf(fact_3519_eq__add__iff1,axiom,
% 5.25/5.49 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.25/5.49 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.25/5.49 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 5.25/5.49 = D ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_add_iff1
% 5.25/5.49 thf(fact_3520_eq__add__iff2,axiom,
% 5.25/5.49 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.25/5.49 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.25/5.49 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.25/5.49 = ( C
% 5.25/5.49 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_add_iff2
% 5.25/5.49 thf(fact_3521_eq__add__iff2,axiom,
% 5.25/5.49 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.25/5.49 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.25/5.49 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.25/5.49 = ( C
% 5.25/5.49 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_add_iff2
% 5.25/5.49 thf(fact_3522_eq__add__iff2,axiom,
% 5.25/5.49 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.25/5.49 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.25/5.49 = ( C
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_add_iff2
% 5.25/5.49 thf(fact_3523_square__diff__square__factored,axiom,
% 5.25/5.49 ! [X3: real,Y: real] :
% 5.25/5.49 ( ( minus_minus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) )
% 5.25/5.49 = ( times_times_real @ ( plus_plus_real @ X3 @ Y ) @ ( minus_minus_real @ X3 @ Y ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % square_diff_square_factored
% 5.25/5.49 thf(fact_3524_square__diff__square__factored,axiom,
% 5.25/5.49 ! [X3: rat,Y: rat] :
% 5.25/5.49 ( ( minus_minus_rat @ ( times_times_rat @ X3 @ X3 ) @ ( times_times_rat @ Y @ Y ) )
% 5.25/5.49 = ( times_times_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( minus_minus_rat @ X3 @ Y ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % square_diff_square_factored
% 5.25/5.49 thf(fact_3525_square__diff__square__factored,axiom,
% 5.25/5.49 ! [X3: int,Y: int] :
% 5.25/5.49 ( ( minus_minus_int @ ( times_times_int @ X3 @ X3 ) @ ( times_times_int @ Y @ Y ) )
% 5.25/5.49 = ( times_times_int @ ( plus_plus_int @ X3 @ Y ) @ ( minus_minus_int @ X3 @ Y ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % square_diff_square_factored
% 5.25/5.49 thf(fact_3526_mult__diff__mult,axiom,
% 5.25/5.49 ! [X3: real,Y: real,A: real,B: real] :
% 5.25/5.49 ( ( minus_minus_real @ ( times_times_real @ X3 @ Y ) @ ( times_times_real @ A @ B ) )
% 5.25/5.49 = ( plus_plus_real @ ( times_times_real @ X3 @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X3 @ A ) @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_diff_mult
% 5.25/5.49 thf(fact_3527_mult__diff__mult,axiom,
% 5.25/5.49 ! [X3: rat,Y: rat,A: rat,B: rat] :
% 5.25/5.49 ( ( minus_minus_rat @ ( times_times_rat @ X3 @ Y ) @ ( times_times_rat @ A @ B ) )
% 5.25/5.49 = ( plus_plus_rat @ ( times_times_rat @ X3 @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X3 @ A ) @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_diff_mult
% 5.25/5.49 thf(fact_3528_mult__diff__mult,axiom,
% 5.25/5.49 ! [X3: int,Y: int,A: int,B: int] :
% 5.25/5.49 ( ( minus_minus_int @ ( times_times_int @ X3 @ Y ) @ ( times_times_int @ A @ B ) )
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ X3 @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X3 @ A ) @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_diff_mult
% 5.25/5.49 thf(fact_3529_num_Oexhaust,axiom,
% 5.25/5.49 ! [Y: num] :
% 5.25/5.49 ( ( Y != one )
% 5.25/5.49 => ( ! [X23: num] :
% 5.25/5.49 ( Y
% 5.25/5.49 != ( bit0 @ X23 ) )
% 5.25/5.49 => ~ ! [X33: num] :
% 5.25/5.49 ( Y
% 5.25/5.49 != ( bit1 @ X33 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % num.exhaust
% 5.25/5.49 thf(fact_3530_xor__num_Ocases,axiom,
% 5.25/5.49 ! [X3: product_prod_num_num] :
% 5.25/5.49 ( ( X3
% 5.25/5.49 != ( product_Pair_num_num @ one @ one ) )
% 5.25/5.49 => ( ! [N3: num] :
% 5.25/5.49 ( X3
% 5.25/5.49 != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 5.25/5.49 => ( ! [N3: num] :
% 5.25/5.49 ( X3
% 5.25/5.49 != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 5.25/5.49 => ( ! [M5: num] :
% 5.25/5.49 ( X3
% 5.25/5.49 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) )
% 5.25/5.49 => ( ! [M5: num,N3: num] :
% 5.25/5.49 ( X3
% 5.25/5.49 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) )
% 5.25/5.49 => ( ! [M5: num,N3: num] :
% 5.25/5.49 ( X3
% 5.25/5.49 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) )
% 5.25/5.49 => ( ! [M5: num] :
% 5.25/5.49 ( X3
% 5.25/5.49 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) )
% 5.25/5.49 => ( ! [M5: num,N3: num] :
% 5.25/5.49 ( X3
% 5.25/5.49 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) )
% 5.25/5.49 => ~ ! [M5: num,N3: num] :
% 5.25/5.49 ( X3
% 5.25/5.49 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % xor_num.cases
% 5.25/5.49 thf(fact_3531_div__power,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer,N: nat] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.49 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 5.25/5.49 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_power
% 5.25/5.49 thf(fact_3532_div__power,axiom,
% 5.25/5.49 ! [B: nat,A: nat,N: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.49 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 5.25/5.49 = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_power
% 5.25/5.49 thf(fact_3533_div__power,axiom,
% 5.25/5.49 ! [B: int,A: int,N: nat] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ A )
% 5.25/5.49 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 5.25/5.49 = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_power
% 5.25/5.49 thf(fact_3534_mod__0__imp__dvd,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ( modulo_modulo_nat @ A @ B )
% 5.25/5.49 = zero_zero_nat )
% 5.25/5.49 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_0_imp_dvd
% 5.25/5.49 thf(fact_3535_mod__0__imp__dvd,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ( modulo_modulo_int @ A @ B )
% 5.25/5.49 = zero_zero_int )
% 5.25/5.49 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_0_imp_dvd
% 5.25/5.49 thf(fact_3536_mod__0__imp__dvd,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer] :
% 5.25/5.49 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.25/5.49 = zero_z3403309356797280102nteger )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_0_imp_dvd
% 5.25/5.49 thf(fact_3537_dvd__eq__mod__eq__0,axiom,
% 5.25/5.49 ( dvd_dvd_nat
% 5.25/5.49 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.49 ( ( modulo_modulo_nat @ B2 @ A3 )
% 5.25/5.49 = zero_zero_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_eq_mod_eq_0
% 5.25/5.49 thf(fact_3538_dvd__eq__mod__eq__0,axiom,
% 5.25/5.49 ( dvd_dvd_int
% 5.25/5.49 = ( ^ [A3: int,B2: int] :
% 5.25/5.49 ( ( modulo_modulo_int @ B2 @ A3 )
% 5.25/5.49 = zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_eq_mod_eq_0
% 5.25/5.49 thf(fact_3539_dvd__eq__mod__eq__0,axiom,
% 5.25/5.49 ( dvd_dvd_Code_integer
% 5.25/5.49 = ( ^ [A3: code_integer,B2: code_integer] :
% 5.25/5.49 ( ( modulo364778990260209775nteger @ B2 @ A3 )
% 5.25/5.49 = zero_z3403309356797280102nteger ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_eq_mod_eq_0
% 5.25/5.49 thf(fact_3540_mod__eq__0__iff__dvd,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ( modulo_modulo_nat @ A @ B )
% 5.25/5.49 = zero_zero_nat )
% 5.25/5.49 = ( dvd_dvd_nat @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_eq_0_iff_dvd
% 5.25/5.49 thf(fact_3541_mod__eq__0__iff__dvd,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ( modulo_modulo_int @ A @ B )
% 5.25/5.49 = zero_zero_int )
% 5.25/5.49 = ( dvd_dvd_int @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_eq_0_iff_dvd
% 5.25/5.49 thf(fact_3542_mod__eq__0__iff__dvd,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer] :
% 5.25/5.49 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.25/5.49 = zero_z3403309356797280102nteger )
% 5.25/5.49 = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_eq_0_iff_dvd
% 5.25/5.49 thf(fact_3543_le__imp__power__dvd,axiom,
% 5.25/5.49 ! [M: nat,N: nat,A: code_integer] :
% 5.25/5.49 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_imp_power_dvd
% 5.25/5.49 thf(fact_3544_le__imp__power__dvd,axiom,
% 5.25/5.49 ! [M: nat,N: nat,A: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.49 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_imp_power_dvd
% 5.25/5.49 thf(fact_3545_le__imp__power__dvd,axiom,
% 5.25/5.49 ! [M: nat,N: nat,A: real] :
% 5.25/5.49 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.49 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_imp_power_dvd
% 5.25/5.49 thf(fact_3546_le__imp__power__dvd,axiom,
% 5.25/5.49 ! [M: nat,N: nat,A: int] :
% 5.25/5.49 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.49 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_imp_power_dvd
% 5.25/5.49 thf(fact_3547_le__imp__power__dvd,axiom,
% 5.25/5.49 ! [M: nat,N: nat,A: complex] :
% 5.25/5.49 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.49 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_imp_power_dvd
% 5.25/5.49 thf(fact_3548_power__le__dvd,axiom,
% 5.25/5.49 ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_le_dvd
% 5.25/5.49 thf(fact_3549_power__le__dvd,axiom,
% 5.25/5.49 ! [A: nat,N: nat,B: nat,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.49 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_le_dvd
% 5.25/5.49 thf(fact_3550_power__le__dvd,axiom,
% 5.25/5.49 ! [A: real,N: nat,B: real,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.49 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_le_dvd
% 5.25/5.49 thf(fact_3551_power__le__dvd,axiom,
% 5.25/5.49 ! [A: int,N: nat,B: int,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.49 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_le_dvd
% 5.25/5.49 thf(fact_3552_power__le__dvd,axiom,
% 5.25/5.49 ! [A: complex,N: nat,B: complex,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.49 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_le_dvd
% 5.25/5.49 thf(fact_3553_dvd__power__le,axiom,
% 5.25/5.49 ! [X3: code_integer,Y: code_integer,N: nat,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ X3 @ Y )
% 5.25/5.49 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X3 @ N ) @ ( power_8256067586552552935nteger @ Y @ M ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_le
% 5.25/5.49 thf(fact_3554_dvd__power__le,axiom,
% 5.25/5.49 ! [X3: nat,Y: nat,N: nat,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ X3 @ Y )
% 5.25/5.49 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.49 => ( dvd_dvd_nat @ ( power_power_nat @ X3 @ N ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_le
% 5.25/5.49 thf(fact_3555_dvd__power__le,axiom,
% 5.25/5.49 ! [X3: real,Y: real,N: nat,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_real @ X3 @ Y )
% 5.25/5.49 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.49 => ( dvd_dvd_real @ ( power_power_real @ X3 @ N ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_le
% 5.25/5.49 thf(fact_3556_dvd__power__le,axiom,
% 5.25/5.49 ! [X3: int,Y: int,N: nat,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_int @ X3 @ Y )
% 5.25/5.49 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.49 => ( dvd_dvd_int @ ( power_power_int @ X3 @ N ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_le
% 5.25/5.49 thf(fact_3557_dvd__power__le,axiom,
% 5.25/5.49 ! [X3: complex,Y: complex,N: nat,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_complex @ X3 @ Y )
% 5.25/5.49 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.49 => ( dvd_dvd_complex @ ( power_power_complex @ X3 @ N ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_le
% 5.25/5.49 thf(fact_3558_nat__dvd__not__less,axiom,
% 5.25/5.49 ! [M: nat,N: nat] :
% 5.25/5.49 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.49 => ( ( ord_less_nat @ M @ N )
% 5.25/5.49 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % nat_dvd_not_less
% 5.25/5.49 thf(fact_3559_dvd__pos__nat,axiom,
% 5.25/5.49 ! [N: nat,M: nat] :
% 5.25/5.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.49 => ( ( dvd_dvd_nat @ M @ N )
% 5.25/5.49 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_pos_nat
% 5.25/5.49 thf(fact_3560_zdvd__antisym__nonneg,axiom,
% 5.25/5.49 ! [M: int,N: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.25/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.25/5.49 => ( ( dvd_dvd_int @ M @ N )
% 5.25/5.49 => ( ( dvd_dvd_int @ N @ M )
% 5.25/5.49 => ( M = N ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zdvd_antisym_nonneg
% 5.25/5.49 thf(fact_3561_zdvd__mono,axiom,
% 5.25/5.49 ! [K: int,M: int,T: int] :
% 5.25/5.49 ( ( K != zero_zero_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ M @ T )
% 5.25/5.49 = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zdvd_mono
% 5.25/5.49 thf(fact_3562_zdvd__mult__cancel,axiom,
% 5.25/5.49 ! [K: int,M: int,N: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 5.25/5.49 => ( ( K != zero_zero_int )
% 5.25/5.49 => ( dvd_dvd_int @ M @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zdvd_mult_cancel
% 5.25/5.49 thf(fact_3563_bezout__add__nat,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ? [D3: nat,X5: nat,Y3: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ D3 @ A )
% 5.25/5.49 & ( dvd_dvd_nat @ D3 @ B )
% 5.25/5.49 & ( ( ( times_times_nat @ A @ X5 )
% 5.25/5.49 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 5.25/5.49 | ( ( times_times_nat @ B @ X5 )
% 5.25/5.49 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % bezout_add_nat
% 5.25/5.49 thf(fact_3564_bezout__lemma__nat,axiom,
% 5.25/5.49 ! [D: nat,A: nat,B: nat,X3: nat,Y: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ D @ A )
% 5.25/5.49 => ( ( dvd_dvd_nat @ D @ B )
% 5.25/5.49 => ( ( ( ( times_times_nat @ A @ X3 )
% 5.25/5.49 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 5.25/5.49 | ( ( times_times_nat @ B @ X3 )
% 5.25/5.49 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 5.25/5.49 => ? [X5: nat,Y3: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ D @ A )
% 5.25/5.49 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 5.25/5.49 & ( ( ( times_times_nat @ A @ X5 )
% 5.25/5.49 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D ) )
% 5.25/5.49 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X5 )
% 5.25/5.49 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % bezout_lemma_nat
% 5.25/5.49 thf(fact_3565_int__le__induct,axiom,
% 5.25/5.49 ! [I2: int,K: int,P: int > $o] :
% 5.25/5.49 ( ( ord_less_eq_int @ I2 @ K )
% 5.25/5.49 => ( ( P @ K )
% 5.25/5.49 => ( ! [I4: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ I4 @ K )
% 5.25/5.49 => ( ( P @ I4 )
% 5.25/5.49 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 5.25/5.49 => ( P @ I2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % int_le_induct
% 5.25/5.49 thf(fact_3566_int__less__induct,axiom,
% 5.25/5.49 ! [I2: int,K: int,P: int > $o] :
% 5.25/5.49 ( ( ord_less_int @ I2 @ K )
% 5.25/5.49 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.25/5.49 => ( ! [I4: int] :
% 5.25/5.49 ( ( ord_less_int @ I4 @ K )
% 5.25/5.49 => ( ( P @ I4 )
% 5.25/5.49 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 5.25/5.49 => ( P @ I2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % int_less_induct
% 5.25/5.49 thf(fact_3567_zdvd__reduce,axiom,
% 5.25/5.49 ! [K: int,N: int,M: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 5.25/5.49 = ( dvd_dvd_int @ K @ N ) ) ).
% 5.25/5.49
% 5.25/5.49 % zdvd_reduce
% 5.25/5.49 thf(fact_3568_zdvd__period,axiom,
% 5.25/5.49 ! [A: int,D: int,X3: int,T: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ D )
% 5.25/5.49 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X3 @ T ) )
% 5.25/5.49 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X3 @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zdvd_period
% 5.25/5.49 thf(fact_3569_unit__dvdE,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.49 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.49 => ! [C3: code_integer] :
% 5.25/5.49 ( B
% 5.25/5.49 != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_dvdE
% 5.25/5.49 thf(fact_3570_unit__dvdE,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.49 => ~ ( ( A != zero_zero_nat )
% 5.25/5.49 => ! [C3: nat] :
% 5.25/5.49 ( B
% 5.25/5.49 != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_dvdE
% 5.25/5.49 thf(fact_3571_unit__dvdE,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.49 => ~ ( ( A != zero_zero_int )
% 5.25/5.49 => ! [C3: int] :
% 5.25/5.49 ( B
% 5.25/5.49 != ( times_times_int @ A @ C3 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_dvdE
% 5.25/5.49 thf(fact_3572_unity__coeff__ex,axiom,
% 5.25/5.49 ! [P: code_integer > $o,L2: code_integer] :
% 5.25/5.49 ( ( ? [X2: code_integer] : ( P @ ( times_3573771949741848930nteger @ L2 @ X2 ) ) )
% 5.25/5.49 = ( ? [X2: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ L2 @ ( plus_p5714425477246183910nteger @ X2 @ zero_z3403309356797280102nteger ) )
% 5.25/5.49 & ( P @ X2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unity_coeff_ex
% 5.25/5.49 thf(fact_3573_unity__coeff__ex,axiom,
% 5.25/5.49 ! [P: complex > $o,L2: complex] :
% 5.25/5.49 ( ( ? [X2: complex] : ( P @ ( times_times_complex @ L2 @ X2 ) ) )
% 5.25/5.49 = ( ? [X2: complex] :
% 5.25/5.49 ( ( dvd_dvd_complex @ L2 @ ( plus_plus_complex @ X2 @ zero_zero_complex ) )
% 5.25/5.49 & ( P @ X2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unity_coeff_ex
% 5.25/5.49 thf(fact_3574_unity__coeff__ex,axiom,
% 5.25/5.49 ! [P: real > $o,L2: real] :
% 5.25/5.49 ( ( ? [X2: real] : ( P @ ( times_times_real @ L2 @ X2 ) ) )
% 5.25/5.49 = ( ? [X2: real] :
% 5.25/5.49 ( ( dvd_dvd_real @ L2 @ ( plus_plus_real @ X2 @ zero_zero_real ) )
% 5.25/5.49 & ( P @ X2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unity_coeff_ex
% 5.25/5.49 thf(fact_3575_unity__coeff__ex,axiom,
% 5.25/5.49 ! [P: rat > $o,L2: rat] :
% 5.25/5.49 ( ( ? [X2: rat] : ( P @ ( times_times_rat @ L2 @ X2 ) ) )
% 5.25/5.49 = ( ? [X2: rat] :
% 5.25/5.49 ( ( dvd_dvd_rat @ L2 @ ( plus_plus_rat @ X2 @ zero_zero_rat ) )
% 5.25/5.49 & ( P @ X2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unity_coeff_ex
% 5.25/5.49 thf(fact_3576_unity__coeff__ex,axiom,
% 5.25/5.49 ! [P: nat > $o,L2: nat] :
% 5.25/5.49 ( ( ? [X2: nat] : ( P @ ( times_times_nat @ L2 @ X2 ) ) )
% 5.25/5.49 = ( ? [X2: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ L2 @ ( plus_plus_nat @ X2 @ zero_zero_nat ) )
% 5.25/5.49 & ( P @ X2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unity_coeff_ex
% 5.25/5.49 thf(fact_3577_unity__coeff__ex,axiom,
% 5.25/5.49 ! [P: int > $o,L2: int] :
% 5.25/5.49 ( ( ? [X2: int] : ( P @ ( times_times_int @ L2 @ X2 ) ) )
% 5.25/5.49 = ( ? [X2: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ L2 @ ( plus_plus_int @ X2 @ zero_zero_int ) )
% 5.25/5.49 & ( P @ X2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unity_coeff_ex
% 5.25/5.49 thf(fact_3578_dvd__div__eq__mult,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.49 ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.49 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.25/5.49 = C )
% 5.25/5.49 = ( B
% 5.25/5.49 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_mult
% 5.25/5.49 thf(fact_3579_dvd__div__eq__mult,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( A != zero_zero_nat )
% 5.25/5.49 => ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.49 => ( ( ( divide_divide_nat @ B @ A )
% 5.25/5.49 = C )
% 5.25/5.49 = ( B
% 5.25/5.49 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_mult
% 5.25/5.49 thf(fact_3580_dvd__div__eq__mult,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( A != zero_zero_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ A @ B )
% 5.25/5.49 => ( ( ( divide_divide_int @ B @ A )
% 5.25/5.49 = C )
% 5.25/5.49 = ( B
% 5.25/5.49 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_eq_mult
% 5.25/5.49 thf(fact_3581_div__dvd__iff__mult,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.49 ( ( B != zero_z3403309356797280102nteger )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.25/5.49 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_dvd_iff_mult
% 5.25/5.49 thf(fact_3582_div__dvd__iff__mult,axiom,
% 5.25/5.49 ! [B: nat,A: nat,C: nat] :
% 5.25/5.49 ( ( B != zero_zero_nat )
% 5.25/5.49 => ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.49 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.25/5.49 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_dvd_iff_mult
% 5.25/5.49 thf(fact_3583_div__dvd__iff__mult,axiom,
% 5.25/5.49 ! [B: int,A: int,C: int] :
% 5.25/5.49 ( ( B != zero_zero_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ B @ A )
% 5.25/5.49 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.25/5.49 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_dvd_iff_mult
% 5.25/5.49 thf(fact_3584_dvd__div__iff__mult,axiom,
% 5.25/5.49 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.49 ( ( C != zero_z3403309356797280102nteger )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_iff_mult
% 5.25/5.49 thf(fact_3585_dvd__div__iff__mult,axiom,
% 5.25/5.49 ! [C: nat,B: nat,A: nat] :
% 5.25/5.49 ( ( C != zero_zero_nat )
% 5.25/5.49 => ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.49 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_iff_mult
% 5.25/5.49 thf(fact_3586_dvd__div__iff__mult,axiom,
% 5.25/5.49 ! [C: int,B: int,A: int] :
% 5.25/5.49 ( ( C != zero_zero_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ C @ B )
% 5.25/5.49 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.25/5.49 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_iff_mult
% 5.25/5.49 thf(fact_3587_dvd__div__div__eq__mult,axiom,
% 5.25/5.49 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.25/5.49 ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.49 => ( ( C != zero_z3403309356797280102nteger )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.25/5.49 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.25/5.49 = ( divide6298287555418463151nteger @ D @ C ) )
% 5.25/5.49 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.25/5.49 = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_div_eq_mult
% 5.25/5.49 thf(fact_3588_dvd__div__div__eq__mult,axiom,
% 5.25/5.49 ! [A: nat,C: nat,B: nat,D: nat] :
% 5.25/5.49 ( ( A != zero_zero_nat )
% 5.25/5.49 => ( ( C != zero_zero_nat )
% 5.25/5.49 => ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_nat @ C @ D )
% 5.25/5.49 => ( ( ( divide_divide_nat @ B @ A )
% 5.25/5.49 = ( divide_divide_nat @ D @ C ) )
% 5.25/5.49 = ( ( times_times_nat @ B @ C )
% 5.25/5.49 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_div_eq_mult
% 5.25/5.49 thf(fact_3589_dvd__div__div__eq__mult,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int,D: int] :
% 5.25/5.49 ( ( A != zero_zero_int )
% 5.25/5.49 => ( ( C != zero_zero_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ A @ B )
% 5.25/5.49 => ( ( dvd_dvd_int @ C @ D )
% 5.25/5.49 => ( ( ( divide_divide_int @ B @ A )
% 5.25/5.49 = ( divide_divide_int @ D @ C ) )
% 5.25/5.49 = ( ( times_times_int @ B @ C )
% 5.25/5.49 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_div_div_eq_mult
% 5.25/5.49 thf(fact_3590_unit__div__eq__0__iff,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.49 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.25/5.49 = zero_z3403309356797280102nteger )
% 5.25/5.49 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_div_eq_0_iff
% 5.25/5.49 thf(fact_3591_unit__div__eq__0__iff,axiom,
% 5.25/5.49 ! [B: nat,A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.49 => ( ( ( divide_divide_nat @ A @ B )
% 5.25/5.49 = zero_zero_nat )
% 5.25/5.49 = ( A = zero_zero_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_div_eq_0_iff
% 5.25/5.49 thf(fact_3592_unit__div__eq__0__iff,axiom,
% 5.25/5.49 ! [B: int,A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.49 => ( ( ( divide_divide_int @ A @ B )
% 5.25/5.49 = zero_zero_int )
% 5.25/5.49 = ( A = zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_div_eq_0_iff
% 5.25/5.49 thf(fact_3593_even__numeral,axiom,
% 5.25/5.49 ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % even_numeral
% 5.25/5.49 thf(fact_3594_even__numeral,axiom,
% 5.25/5.49 ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % even_numeral
% 5.25/5.49 thf(fact_3595_even__numeral,axiom,
% 5.25/5.49 ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % even_numeral
% 5.25/5.49 thf(fact_3596_ordered__ring__class_Ole__add__iff1,axiom,
% 5.25/5.49 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.25/5.49 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_ring_class.le_add_iff1
% 5.25/5.49 thf(fact_3597_ordered__ring__class_Ole__add__iff1,axiom,
% 5.25/5.49 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.25/5.49 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_ring_class.le_add_iff1
% 5.25/5.49 thf(fact_3598_ordered__ring__class_Ole__add__iff1,axiom,
% 5.25/5.49 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.25/5.49 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_ring_class.le_add_iff1
% 5.25/5.49 thf(fact_3599_ordered__ring__class_Ole__add__iff2,axiom,
% 5.25/5.49 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.25/5.49 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_ring_class.le_add_iff2
% 5.25/5.49 thf(fact_3600_ordered__ring__class_Ole__add__iff2,axiom,
% 5.25/5.49 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.25/5.49 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_ring_class.le_add_iff2
% 5.25/5.49 thf(fact_3601_ordered__ring__class_Ole__add__iff2,axiom,
% 5.25/5.49 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.25/5.49 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_ring_class.le_add_iff2
% 5.25/5.49 thf(fact_3602_unit__eq__div1,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.49 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.25/5.49 = C )
% 5.25/5.49 = ( A
% 5.25/5.49 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_eq_div1
% 5.25/5.49 thf(fact_3603_unit__eq__div1,axiom,
% 5.25/5.49 ! [B: nat,A: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.49 => ( ( ( divide_divide_nat @ A @ B )
% 5.25/5.49 = C )
% 5.25/5.49 = ( A
% 5.25/5.49 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_eq_div1
% 5.25/5.49 thf(fact_3604_unit__eq__div1,axiom,
% 5.25/5.49 ! [B: int,A: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.49 => ( ( ( divide_divide_int @ A @ B )
% 5.25/5.49 = C )
% 5.25/5.49 = ( A
% 5.25/5.49 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_eq_div1
% 5.25/5.49 thf(fact_3605_unit__eq__div2,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.49 => ( ( A
% 5.25/5.49 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.25/5.49 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.25/5.49 = C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_eq_div2
% 5.25/5.49 thf(fact_3606_unit__eq__div2,axiom,
% 5.25/5.49 ! [B: nat,A: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.49 => ( ( A
% 5.25/5.49 = ( divide_divide_nat @ C @ B ) )
% 5.25/5.49 = ( ( times_times_nat @ A @ B )
% 5.25/5.49 = C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_eq_div2
% 5.25/5.49 thf(fact_3607_unit__eq__div2,axiom,
% 5.25/5.49 ! [B: int,A: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.49 => ( ( A
% 5.25/5.49 = ( divide_divide_int @ C @ B ) )
% 5.25/5.49 = ( ( times_times_int @ A @ B )
% 5.25/5.49 = C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_eq_div2
% 5.25/5.49 thf(fact_3608_div__mult__unit2,axiom,
% 5.25/5.49 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.49 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.25/5.49 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_mult_unit2
% 5.25/5.49 thf(fact_3609_div__mult__unit2,axiom,
% 5.25/5.49 ! [C: nat,B: nat,A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.25/5.49 => ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.49 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.25/5.49 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_mult_unit2
% 5.25/5.49 thf(fact_3610_div__mult__unit2,axiom,
% 5.25/5.49 ! [C: int,B: int,A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ B @ A )
% 5.25/5.49 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.25/5.49 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_mult_unit2
% 5.25/5.49 thf(fact_3611_unit__div__commute,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.49 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.25/5.49 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_div_commute
% 5.25/5.49 thf(fact_3612_unit__div__commute,axiom,
% 5.25/5.49 ! [B: nat,A: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.49 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.25/5.49 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_div_commute
% 5.25/5.49 thf(fact_3613_unit__div__commute,axiom,
% 5.25/5.49 ! [B: int,A: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.49 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.25/5.49 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % unit_div_commute
% 5.25/5.49 thf(fact_3614_unit__div__mult__swap,axiom,
% 5.25/5.49 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.25/5.50 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.25/5.50 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % unit_div_mult_swap
% 5.25/5.50 thf(fact_3615_unit__div__mult__swap,axiom,
% 5.25/5.50 ! [C: nat,A: nat,B: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.25/5.50 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.25/5.50 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % unit_div_mult_swap
% 5.25/5.50 thf(fact_3616_unit__div__mult__swap,axiom,
% 5.25/5.50 ! [C: int,A: int,B: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.25/5.50 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.25/5.50 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % unit_div_mult_swap
% 5.25/5.50 thf(fact_3617_is__unit__div__mult2__eq,axiom,
% 5.25/5.50 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.50 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.25/5.50 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.25/5.50 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_div_mult2_eq
% 5.25/5.50 thf(fact_3618_is__unit__div__mult2__eq,axiom,
% 5.25/5.50 ! [B: nat,C: nat,A: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.50 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.25/5.50 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.25/5.50 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_div_mult2_eq
% 5.25/5.50 thf(fact_3619_is__unit__div__mult2__eq,axiom,
% 5.25/5.50 ! [B: int,C: int,A: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.50 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.25/5.50 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.25/5.50 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_div_mult2_eq
% 5.25/5.50 thf(fact_3620_less__add__iff1,axiom,
% 5.25/5.50 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.25/5.50 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.25/5.50 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.25/5.50
% 5.25/5.50 % less_add_iff1
% 5.25/5.50 thf(fact_3621_less__add__iff1,axiom,
% 5.25/5.50 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.25/5.50 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.25/5.50 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.25/5.50
% 5.25/5.50 % less_add_iff1
% 5.25/5.50 thf(fact_3622_less__add__iff1,axiom,
% 5.25/5.50 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.25/5.50 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.25/5.50 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.25/5.50
% 5.25/5.50 % less_add_iff1
% 5.25/5.50 thf(fact_3623_less__add__iff2,axiom,
% 5.25/5.50 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.25/5.50 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.25/5.50 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % less_add_iff2
% 5.25/5.50 thf(fact_3624_less__add__iff2,axiom,
% 5.25/5.50 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.25/5.50 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.25/5.50 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % less_add_iff2
% 5.25/5.50 thf(fact_3625_less__add__iff2,axiom,
% 5.25/5.50 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.25/5.50 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.25/5.50 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % less_add_iff2
% 5.25/5.50 thf(fact_3626_add__divide__eq__if__simps_I4_J,axiom,
% 5.25/5.50 ! [Z: complex,A: complex,B: complex] :
% 5.25/5.50 ( ( ( Z = zero_zero_complex )
% 5.25/5.50 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.25/5.50 = A ) )
% 5.25/5.50 & ( ( Z != zero_zero_complex )
% 5.25/5.50 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.25/5.50 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_divide_eq_if_simps(4)
% 5.25/5.50 thf(fact_3627_add__divide__eq__if__simps_I4_J,axiom,
% 5.25/5.50 ! [Z: real,A: real,B: real] :
% 5.25/5.50 ( ( ( Z = zero_zero_real )
% 5.25/5.50 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.25/5.50 = A ) )
% 5.25/5.50 & ( ( Z != zero_zero_real )
% 5.25/5.50 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.25/5.50 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_divide_eq_if_simps(4)
% 5.25/5.50 thf(fact_3628_add__divide__eq__if__simps_I4_J,axiom,
% 5.25/5.50 ! [Z: rat,A: rat,B: rat] :
% 5.25/5.50 ( ( ( Z = zero_zero_rat )
% 5.25/5.50 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.25/5.50 = A ) )
% 5.25/5.50 & ( ( Z != zero_zero_rat )
% 5.25/5.50 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.25/5.50 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_divide_eq_if_simps(4)
% 5.25/5.50 thf(fact_3629_diff__frac__eq,axiom,
% 5.25/5.50 ! [Y: complex,Z: complex,X3: complex,W: complex] :
% 5.25/5.50 ( ( Y != zero_zero_complex )
% 5.25/5.50 => ( ( Z != zero_zero_complex )
% 5.25/5.50 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X3 @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.25/5.50 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X3 @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % diff_frac_eq
% 5.25/5.50 thf(fact_3630_diff__frac__eq,axiom,
% 5.25/5.50 ! [Y: real,Z: real,X3: real,W: real] :
% 5.25/5.50 ( ( Y != zero_zero_real )
% 5.25/5.50 => ( ( Z != zero_zero_real )
% 5.25/5.50 => ( ( minus_minus_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.25/5.50 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % diff_frac_eq
% 5.25/5.50 thf(fact_3631_diff__frac__eq,axiom,
% 5.25/5.50 ! [Y: rat,Z: rat,X3: rat,W: rat] :
% 5.25/5.50 ( ( Y != zero_zero_rat )
% 5.25/5.50 => ( ( Z != zero_zero_rat )
% 5.25/5.50 => ( ( minus_minus_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.25/5.50 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % diff_frac_eq
% 5.25/5.50 thf(fact_3632_diff__divide__eq__iff,axiom,
% 5.25/5.50 ! [Z: complex,X3: complex,Y: complex] :
% 5.25/5.50 ( ( Z != zero_zero_complex )
% 5.25/5.50 => ( ( minus_minus_complex @ X3 @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.25/5.50 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X3 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % diff_divide_eq_iff
% 5.25/5.50 thf(fact_3633_diff__divide__eq__iff,axiom,
% 5.25/5.50 ! [Z: real,X3: real,Y: real] :
% 5.25/5.50 ( ( Z != zero_zero_real )
% 5.25/5.50 => ( ( minus_minus_real @ X3 @ ( divide_divide_real @ Y @ Z ) )
% 5.25/5.50 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % diff_divide_eq_iff
% 5.25/5.50 thf(fact_3634_diff__divide__eq__iff,axiom,
% 5.25/5.50 ! [Z: rat,X3: rat,Y: rat] :
% 5.25/5.50 ( ( Z != zero_zero_rat )
% 5.25/5.50 => ( ( minus_minus_rat @ X3 @ ( divide_divide_rat @ Y @ Z ) )
% 5.25/5.50 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % diff_divide_eq_iff
% 5.25/5.50 thf(fact_3635_divide__diff__eq__iff,axiom,
% 5.25/5.50 ! [Z: complex,X3: complex,Y: complex] :
% 5.25/5.50 ( ( Z != zero_zero_complex )
% 5.25/5.50 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X3 @ Z ) @ Y )
% 5.25/5.50 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X3 @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_diff_eq_iff
% 5.25/5.50 thf(fact_3636_divide__diff__eq__iff,axiom,
% 5.25/5.50 ! [Z: real,X3: real,Y: real] :
% 5.25/5.50 ( ( Z != zero_zero_real )
% 5.25/5.50 => ( ( minus_minus_real @ ( divide_divide_real @ X3 @ Z ) @ Y )
% 5.25/5.50 = ( divide_divide_real @ ( minus_minus_real @ X3 @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_diff_eq_iff
% 5.25/5.50 thf(fact_3637_divide__diff__eq__iff,axiom,
% 5.25/5.50 ! [Z: rat,X3: rat,Y: rat] :
% 5.25/5.50 ( ( Z != zero_zero_rat )
% 5.25/5.50 => ( ( minus_minus_rat @ ( divide_divide_rat @ X3 @ Z ) @ Y )
% 5.25/5.50 = ( divide_divide_rat @ ( minus_minus_rat @ X3 @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_diff_eq_iff
% 5.25/5.50 thf(fact_3638_numeral__Bit1,axiom,
% 5.25/5.50 ! [N: num] :
% 5.25/5.50 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.25/5.50 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.25/5.50
% 5.25/5.50 % numeral_Bit1
% 5.25/5.50 thf(fact_3639_numeral__Bit1,axiom,
% 5.25/5.50 ! [N: num] :
% 5.25/5.50 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.25/5.50 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.25/5.50
% 5.25/5.50 % numeral_Bit1
% 5.25/5.50 thf(fact_3640_numeral__Bit1,axiom,
% 5.25/5.50 ! [N: num] :
% 5.25/5.50 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.25/5.50 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.25/5.50
% 5.25/5.50 % numeral_Bit1
% 5.25/5.50 thf(fact_3641_numeral__Bit1,axiom,
% 5.25/5.50 ! [N: num] :
% 5.25/5.50 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.25/5.50 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.25/5.50
% 5.25/5.50 % numeral_Bit1
% 5.25/5.50 thf(fact_3642_numeral__Bit1,axiom,
% 5.25/5.50 ! [N: num] :
% 5.25/5.50 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.25/5.50 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % numeral_Bit1
% 5.25/5.50 thf(fact_3643_square__diff__one__factored,axiom,
% 5.25/5.50 ! [X3: complex] :
% 5.25/5.50 ( ( minus_minus_complex @ ( times_times_complex @ X3 @ X3 ) @ one_one_complex )
% 5.25/5.50 = ( times_times_complex @ ( plus_plus_complex @ X3 @ one_one_complex ) @ ( minus_minus_complex @ X3 @ one_one_complex ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % square_diff_one_factored
% 5.25/5.50 thf(fact_3644_square__diff__one__factored,axiom,
% 5.25/5.50 ! [X3: real] :
% 5.25/5.50 ( ( minus_minus_real @ ( times_times_real @ X3 @ X3 ) @ one_one_real )
% 5.25/5.50 = ( times_times_real @ ( plus_plus_real @ X3 @ one_one_real ) @ ( minus_minus_real @ X3 @ one_one_real ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % square_diff_one_factored
% 5.25/5.50 thf(fact_3645_square__diff__one__factored,axiom,
% 5.25/5.50 ! [X3: rat] :
% 5.25/5.50 ( ( minus_minus_rat @ ( times_times_rat @ X3 @ X3 ) @ one_one_rat )
% 5.25/5.50 = ( times_times_rat @ ( plus_plus_rat @ X3 @ one_one_rat ) @ ( minus_minus_rat @ X3 @ one_one_rat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % square_diff_one_factored
% 5.25/5.50 thf(fact_3646_square__diff__one__factored,axiom,
% 5.25/5.50 ! [X3: int] :
% 5.25/5.50 ( ( minus_minus_int @ ( times_times_int @ X3 @ X3 ) @ one_one_int )
% 5.25/5.50 = ( times_times_int @ ( plus_plus_int @ X3 @ one_one_int ) @ ( minus_minus_int @ X3 @ one_one_int ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % square_diff_one_factored
% 5.25/5.50 thf(fact_3647_unit__imp__mod__eq__0,axiom,
% 5.25/5.50 ! [B: nat,A: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.50 => ( ( modulo_modulo_nat @ A @ B )
% 5.25/5.50 = zero_zero_nat ) ) ).
% 5.25/5.50
% 5.25/5.50 % unit_imp_mod_eq_0
% 5.25/5.50 thf(fact_3648_unit__imp__mod__eq__0,axiom,
% 5.25/5.50 ! [B: int,A: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.50 => ( ( modulo_modulo_int @ A @ B )
% 5.25/5.50 = zero_zero_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % unit_imp_mod_eq_0
% 5.25/5.50 thf(fact_3649_unit__imp__mod__eq__0,axiom,
% 5.25/5.50 ! [B: code_integer,A: code_integer] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.50 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.25/5.50 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.50
% 5.25/5.50 % unit_imp_mod_eq_0
% 5.25/5.50 thf(fact_3650_is__unit__power__iff,axiom,
% 5.25/5.50 ! [A: code_integer,N: nat] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 5.25/5.50 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.50 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_power_iff
% 5.25/5.50 thf(fact_3651_is__unit__power__iff,axiom,
% 5.25/5.50 ! [A: nat,N: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 5.25/5.50 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.50 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_power_iff
% 5.25/5.50 thf(fact_3652_is__unit__power__iff,axiom,
% 5.25/5.50 ! [A: int,N: nat] :
% 5.25/5.50 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 5.25/5.50 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.50 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_power_iff
% 5.25/5.50 thf(fact_3653_eval__nat__numeral_I3_J,axiom,
% 5.25/5.50 ! [N: num] :
% 5.25/5.50 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.25/5.50 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % eval_nat_numeral(3)
% 5.25/5.50 thf(fact_3654_cong__exp__iff__simps_I10_J,axiom,
% 5.25/5.50 ! [M: num,Q2: num,N: num] :
% 5.25/5.50 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(10)
% 5.25/5.50 thf(fact_3655_cong__exp__iff__simps_I10_J,axiom,
% 5.25/5.50 ! [M: num,Q2: num,N: num] :
% 5.25/5.50 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(10)
% 5.25/5.50 thf(fact_3656_cong__exp__iff__simps_I10_J,axiom,
% 5.25/5.50 ! [M: num,Q2: num,N: num] :
% 5.25/5.50 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(10)
% 5.25/5.50 thf(fact_3657_cong__exp__iff__simps_I12_J,axiom,
% 5.25/5.50 ! [M: num,Q2: num,N: num] :
% 5.25/5.50 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(12)
% 5.25/5.50 thf(fact_3658_cong__exp__iff__simps_I12_J,axiom,
% 5.25/5.50 ! [M: num,Q2: num,N: num] :
% 5.25/5.50 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(12)
% 5.25/5.50 thf(fact_3659_cong__exp__iff__simps_I12_J,axiom,
% 5.25/5.50 ! [M: num,Q2: num,N: num] :
% 5.25/5.50 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(12)
% 5.25/5.50 thf(fact_3660_cong__exp__iff__simps_I13_J,axiom,
% 5.25/5.50 ! [M: num,Q2: num,N: num] :
% 5.25/5.50 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.25/5.50 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.25/5.50 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(13)
% 5.25/5.50 thf(fact_3661_cong__exp__iff__simps_I13_J,axiom,
% 5.25/5.50 ! [M: num,Q2: num,N: num] :
% 5.25/5.50 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.25/5.50 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.25/5.50 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(13)
% 5.25/5.50 thf(fact_3662_cong__exp__iff__simps_I13_J,axiom,
% 5.25/5.50 ! [M: num,Q2: num,N: num] :
% 5.25/5.50 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.25/5.50 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.25/5.50 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(13)
% 5.25/5.50 thf(fact_3663_minus__div__mult__eq__mod,axiom,
% 5.25/5.50 ! [A: nat,B: nat] :
% 5.25/5.50 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.25/5.50 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_div_mult_eq_mod
% 5.25/5.50 thf(fact_3664_minus__div__mult__eq__mod,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.25/5.50 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_div_mult_eq_mod
% 5.25/5.50 thf(fact_3665_minus__div__mult__eq__mod,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.25/5.50 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_div_mult_eq_mod
% 5.25/5.50 thf(fact_3666_minus__mod__eq__div__mult,axiom,
% 5.25/5.50 ! [A: nat,B: nat] :
% 5.25/5.50 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.25/5.50 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_mod_eq_div_mult
% 5.25/5.50 thf(fact_3667_minus__mod__eq__div__mult,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.25/5.50 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_mod_eq_div_mult
% 5.25/5.50 thf(fact_3668_minus__mod__eq__div__mult,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.25/5.50 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_mod_eq_div_mult
% 5.25/5.50 thf(fact_3669_minus__mod__eq__mult__div,axiom,
% 5.25/5.50 ! [A: nat,B: nat] :
% 5.25/5.50 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.25/5.50 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_mod_eq_mult_div
% 5.25/5.50 thf(fact_3670_minus__mod__eq__mult__div,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.25/5.50 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_mod_eq_mult_div
% 5.25/5.50 thf(fact_3671_minus__mod__eq__mult__div,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.25/5.50 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_mod_eq_mult_div
% 5.25/5.50 thf(fact_3672_minus__mult__div__eq__mod,axiom,
% 5.25/5.50 ! [A: nat,B: nat] :
% 5.25/5.50 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.25/5.50 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_mult_div_eq_mod
% 5.25/5.50 thf(fact_3673_minus__mult__div__eq__mod,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.25/5.50 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_mult_div_eq_mod
% 5.25/5.50 thf(fact_3674_minus__mult__div__eq__mod,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.25/5.50 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_mult_div_eq_mod
% 5.25/5.50 thf(fact_3675_dvd__imp__le,axiom,
% 5.25/5.50 ! [K: nat,N: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ K @ N )
% 5.25/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.50 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_imp_le
% 5.25/5.50 thf(fact_3676_nat__mult__dvd__cancel1,axiom,
% 5.25/5.50 ! [K: nat,M: nat,N: nat] :
% 5.25/5.50 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.50 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.25/5.50 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % nat_mult_dvd_cancel1
% 5.25/5.50 thf(fact_3677_dvd__mult__cancel,axiom,
% 5.25/5.50 ! [K: nat,M: nat,N: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.25/5.50 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.50 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_mult_cancel
% 5.25/5.50 thf(fact_3678_bezout__add__strong__nat,axiom,
% 5.25/5.50 ! [A: nat,B: nat] :
% 5.25/5.50 ( ( A != zero_zero_nat )
% 5.25/5.50 => ? [D3: nat,X5: nat,Y3: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ D3 @ A )
% 5.25/5.50 & ( dvd_dvd_nat @ D3 @ B )
% 5.25/5.50 & ( ( times_times_nat @ A @ X5 )
% 5.25/5.50 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % bezout_add_strong_nat
% 5.25/5.50 thf(fact_3679_zdvd__imp__le,axiom,
% 5.25/5.50 ! [Z: int,N: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ Z @ N )
% 5.25/5.50 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.25/5.50 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % zdvd_imp_le
% 5.25/5.50 thf(fact_3680_mod__greater__zero__iff__not__dvd,axiom,
% 5.25/5.50 ! [M: nat,N: nat] :
% 5.25/5.50 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.25/5.50 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_greater_zero_iff_not_dvd
% 5.25/5.50 thf(fact_3681_minusinfinity,axiom,
% 5.25/5.50 ! [D: int,P1: int > $o,P: int > $o] :
% 5.25/5.50 ( ( ord_less_int @ zero_zero_int @ D )
% 5.25/5.50 => ( ! [X5: int,K2: int] :
% 5.25/5.50 ( ( P1 @ X5 )
% 5.25/5.50 = ( P1 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.25/5.50 => ( ? [Z4: int] :
% 5.25/5.50 ! [X5: int] :
% 5.25/5.50 ( ( ord_less_int @ X5 @ Z4 )
% 5.25/5.50 => ( ( P @ X5 )
% 5.25/5.50 = ( P1 @ X5 ) ) )
% 5.25/5.50 => ( ? [X_1: int] : ( P1 @ X_1 )
% 5.25/5.50 => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % minusinfinity
% 5.25/5.50 thf(fact_3682_plusinfinity,axiom,
% 5.25/5.50 ! [D: int,P3: int > $o,P: int > $o] :
% 5.25/5.50 ( ( ord_less_int @ zero_zero_int @ D )
% 5.25/5.50 => ( ! [X5: int,K2: int] :
% 5.25/5.50 ( ( P3 @ X5 )
% 5.25/5.50 = ( P3 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.25/5.50 => ( ? [Z4: int] :
% 5.25/5.50 ! [X5: int] :
% 5.25/5.50 ( ( ord_less_int @ Z4 @ X5 )
% 5.25/5.50 => ( ( P @ X5 )
% 5.25/5.50 = ( P3 @ X5 ) ) )
% 5.25/5.50 => ( ? [X_1: int] : ( P3 @ X_1 )
% 5.25/5.50 => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % plusinfinity
% 5.25/5.50 thf(fact_3683_int__induct,axiom,
% 5.25/5.50 ! [P: int > $o,K: int,I2: int] :
% 5.25/5.50 ( ( P @ K )
% 5.25/5.50 => ( ! [I4: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ K @ I4 )
% 5.25/5.50 => ( ( P @ I4 )
% 5.25/5.50 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 5.25/5.50 => ( ! [I4: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ I4 @ K )
% 5.25/5.50 => ( ( P @ I4 )
% 5.25/5.50 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 5.25/5.50 => ( P @ I2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % int_induct
% 5.25/5.50 thf(fact_3684_even__mask__div__iff_H,axiom,
% 5.25/5.50 ! [M: nat,N: nat] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.50 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_mask_div_iff'
% 5.25/5.50 thf(fact_3685_even__mask__div__iff_H,axiom,
% 5.25/5.50 ! [M: nat,N: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.50 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_mask_div_iff'
% 5.25/5.50 thf(fact_3686_even__mask__div__iff_H,axiom,
% 5.25/5.50 ! [M: nat,N: nat] :
% 5.25/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.50 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_mask_div_iff'
% 5.25/5.50 thf(fact_3687_even__mask__div__iff,axiom,
% 5.25/5.50 ! [M: nat,N: nat] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.50 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 = zero_z3403309356797280102nteger )
% 5.25/5.50 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_mask_div_iff
% 5.25/5.50 thf(fact_3688_even__mask__div__iff,axiom,
% 5.25/5.50 ! [M: nat,N: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.50 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 = zero_zero_nat )
% 5.25/5.50 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_mask_div_iff
% 5.25/5.50 thf(fact_3689_even__mask__div__iff,axiom,
% 5.25/5.50 ! [M: nat,N: nat] :
% 5.25/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.50 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 = zero_zero_int )
% 5.25/5.50 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_mask_div_iff
% 5.25/5.50 thf(fact_3690_even__zero,axiom,
% 5.25/5.50 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.25/5.50
% 5.25/5.50 % even_zero
% 5.25/5.50 thf(fact_3691_even__zero,axiom,
% 5.25/5.50 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.25/5.50
% 5.25/5.50 % even_zero
% 5.25/5.50 thf(fact_3692_even__zero,axiom,
% 5.25/5.50 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.25/5.50
% 5.25/5.50 % even_zero
% 5.25/5.50 thf(fact_3693_is__unitE,axiom,
% 5.25/5.50 ! [A: code_integer,C: code_integer] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.50 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.50 => ! [B5: code_integer] :
% 5.25/5.50 ( ( B5 != zero_z3403309356797280102nteger )
% 5.25/5.50 => ( ( dvd_dvd_Code_integer @ B5 @ one_one_Code_integer )
% 5.25/5.50 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.25/5.50 = B5 )
% 5.25/5.50 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B5 )
% 5.25/5.50 = A )
% 5.25/5.50 => ( ( ( times_3573771949741848930nteger @ A @ B5 )
% 5.25/5.50 = one_one_Code_integer )
% 5.25/5.50 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.25/5.50 != ( times_3573771949741848930nteger @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unitE
% 5.25/5.50 thf(fact_3694_is__unitE,axiom,
% 5.25/5.50 ! [A: nat,C: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.50 => ~ ( ( A != zero_zero_nat )
% 5.25/5.50 => ! [B5: nat] :
% 5.25/5.50 ( ( B5 != zero_zero_nat )
% 5.25/5.50 => ( ( dvd_dvd_nat @ B5 @ one_one_nat )
% 5.25/5.50 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.25/5.50 = B5 )
% 5.25/5.50 => ( ( ( divide_divide_nat @ one_one_nat @ B5 )
% 5.25/5.50 = A )
% 5.25/5.50 => ( ( ( times_times_nat @ A @ B5 )
% 5.25/5.50 = one_one_nat )
% 5.25/5.50 => ( ( divide_divide_nat @ C @ A )
% 5.25/5.50 != ( times_times_nat @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unitE
% 5.25/5.50 thf(fact_3695_is__unitE,axiom,
% 5.25/5.50 ! [A: int,C: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.50 => ~ ( ( A != zero_zero_int )
% 5.25/5.50 => ! [B5: int] :
% 5.25/5.50 ( ( B5 != zero_zero_int )
% 5.25/5.50 => ( ( dvd_dvd_int @ B5 @ one_one_int )
% 5.25/5.50 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.25/5.50 = B5 )
% 5.25/5.50 => ( ( ( divide_divide_int @ one_one_int @ B5 )
% 5.25/5.50 = A )
% 5.25/5.50 => ( ( ( times_times_int @ A @ B5 )
% 5.25/5.50 = one_one_int )
% 5.25/5.50 => ( ( divide_divide_int @ C @ A )
% 5.25/5.50 != ( times_times_int @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unitE
% 5.25/5.50 thf(fact_3696_is__unit__div__mult__cancel__left,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.50 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.50 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.25/5.50 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_div_mult_cancel_left
% 5.25/5.50 thf(fact_3697_is__unit__div__mult__cancel__left,axiom,
% 5.25/5.50 ! [A: nat,B: nat] :
% 5.25/5.50 ( ( A != zero_zero_nat )
% 5.25/5.50 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.50 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.25/5.50 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_div_mult_cancel_left
% 5.25/5.50 thf(fact_3698_is__unit__div__mult__cancel__left,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( A != zero_zero_int )
% 5.25/5.50 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.50 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.25/5.50 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_div_mult_cancel_left
% 5.25/5.50 thf(fact_3699_is__unit__div__mult__cancel__right,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.50 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.50 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.25/5.50 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_div_mult_cancel_right
% 5.25/5.50 thf(fact_3700_is__unit__div__mult__cancel__right,axiom,
% 5.25/5.50 ! [A: nat,B: nat] :
% 5.25/5.50 ( ( A != zero_zero_nat )
% 5.25/5.50 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.50 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.25/5.50 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_div_mult_cancel_right
% 5.25/5.50 thf(fact_3701_is__unit__div__mult__cancel__right,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( A != zero_zero_int )
% 5.25/5.50 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.50 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.25/5.50 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_div_mult_cancel_right
% 5.25/5.50 thf(fact_3702_evenE,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ~ ! [B5: code_integer] :
% 5.25/5.50 ( A
% 5.25/5.50 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % evenE
% 5.25/5.50 thf(fact_3703_evenE,axiom,
% 5.25/5.50 ! [A: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ~ ! [B5: nat] :
% 5.25/5.50 ( A
% 5.25/5.50 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % evenE
% 5.25/5.50 thf(fact_3704_evenE,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ~ ! [B5: int] :
% 5.25/5.50 ( A
% 5.25/5.50 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % evenE
% 5.25/5.50 thf(fact_3705_odd__one,axiom,
% 5.25/5.50 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.25/5.50
% 5.25/5.50 % odd_one
% 5.25/5.50 thf(fact_3706_odd__one,axiom,
% 5.25/5.50 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.25/5.50
% 5.25/5.50 % odd_one
% 5.25/5.50 thf(fact_3707_odd__one,axiom,
% 5.25/5.50 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.25/5.50
% 5.25/5.50 % odd_one
% 5.25/5.50 thf(fact_3708_odd__even__add,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 5.25/5.50 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % odd_even_add
% 5.25/5.50 thf(fact_3709_odd__even__add,axiom,
% 5.25/5.50 ! [A: nat,B: nat] :
% 5.25/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.25/5.50 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % odd_even_add
% 5.25/5.50 thf(fact_3710_odd__even__add,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 5.25/5.50 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % odd_even_add
% 5.25/5.50 thf(fact_3711_frac__le__eq,axiom,
% 5.25/5.50 ! [Y: real,Z: real,X3: real,W: real] :
% 5.25/5.50 ( ( Y != zero_zero_real )
% 5.25/5.50 => ( ( Z != zero_zero_real )
% 5.25/5.50 => ( ( ord_less_eq_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.25/5.50 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % frac_le_eq
% 5.25/5.50 thf(fact_3712_frac__le__eq,axiom,
% 5.25/5.50 ! [Y: rat,Z: rat,X3: rat,W: rat] :
% 5.25/5.50 ( ( Y != zero_zero_rat )
% 5.25/5.50 => ( ( Z != zero_zero_rat )
% 5.25/5.50 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.25/5.50 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % frac_le_eq
% 5.25/5.50 thf(fact_3713_bit__eq__rec,axiom,
% 5.25/5.50 ( ( ^ [Y5: code_integer,Z3: code_integer] : ( Y5 = Z3 ) )
% 5.25/5.50 = ( ^ [A3: code_integer,B2: code_integer] :
% 5.25/5.50 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 )
% 5.25/5.50 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) )
% 5.25/5.50 & ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.50 = ( divide6298287555418463151nteger @ B2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % bit_eq_rec
% 5.25/5.50 thf(fact_3714_bit__eq__rec,axiom,
% 5.25/5.50 ( ( ^ [Y5: nat,Z3: nat] : ( Y5 = Z3 ) )
% 5.25/5.50 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.50 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 )
% 5.25/5.50 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) )
% 5.25/5.50 & ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = ( divide_divide_nat @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % bit_eq_rec
% 5.25/5.50 thf(fact_3715_bit__eq__rec,axiom,
% 5.25/5.50 ( ( ^ [Y5: int,Z3: int] : ( Y5 = Z3 ) )
% 5.25/5.50 = ( ^ [A3: int,B2: int] :
% 5.25/5.50 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 )
% 5.25/5.50 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) )
% 5.25/5.50 & ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.50 = ( divide_divide_int @ B2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % bit_eq_rec
% 5.25/5.50 thf(fact_3716_frac__less__eq,axiom,
% 5.25/5.50 ! [Y: real,Z: real,X3: real,W: real] :
% 5.25/5.50 ( ( Y != zero_zero_real )
% 5.25/5.50 => ( ( Z != zero_zero_real )
% 5.25/5.50 => ( ( ord_less_real @ ( divide_divide_real @ X3 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.25/5.50 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X3 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % frac_less_eq
% 5.25/5.50 thf(fact_3717_frac__less__eq,axiom,
% 5.25/5.50 ! [Y: rat,Z: rat,X3: rat,W: rat] :
% 5.25/5.50 ( ( Y != zero_zero_rat )
% 5.25/5.50 => ( ( Z != zero_zero_rat )
% 5.25/5.50 => ( ( ord_less_rat @ ( divide_divide_rat @ X3 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.25/5.50 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X3 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % frac_less_eq
% 5.25/5.50 thf(fact_3718_dvd__power__iff,axiom,
% 5.25/5.50 ! [X3: code_integer,M: nat,N: nat] :
% 5.25/5.50 ( ( X3 != zero_z3403309356797280102nteger )
% 5.25/5.50 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X3 @ M ) @ ( power_8256067586552552935nteger @ X3 @ N ) )
% 5.25/5.50 = ( ( dvd_dvd_Code_integer @ X3 @ one_one_Code_integer )
% 5.25/5.50 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power_iff
% 5.25/5.50 thf(fact_3719_dvd__power__iff,axiom,
% 5.25/5.50 ! [X3: nat,M: nat,N: nat] :
% 5.25/5.50 ( ( X3 != zero_zero_nat )
% 5.25/5.50 => ( ( dvd_dvd_nat @ ( power_power_nat @ X3 @ M ) @ ( power_power_nat @ X3 @ N ) )
% 5.25/5.50 = ( ( dvd_dvd_nat @ X3 @ one_one_nat )
% 5.25/5.50 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power_iff
% 5.25/5.50 thf(fact_3720_dvd__power__iff,axiom,
% 5.25/5.50 ! [X3: int,M: nat,N: nat] :
% 5.25/5.50 ( ( X3 != zero_zero_int )
% 5.25/5.50 => ( ( dvd_dvd_int @ ( power_power_int @ X3 @ M ) @ ( power_power_int @ X3 @ N ) )
% 5.25/5.50 = ( ( dvd_dvd_int @ X3 @ one_one_int )
% 5.25/5.50 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power_iff
% 5.25/5.50 thf(fact_3721_numeral__Bit1__div__2,axiom,
% 5.25/5.50 ! [N: num] :
% 5.25/5.50 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = ( numeral_numeral_nat @ N ) ) ).
% 5.25/5.50
% 5.25/5.50 % numeral_Bit1_div_2
% 5.25/5.50 thf(fact_3722_numeral__Bit1__div__2,axiom,
% 5.25/5.50 ! [N: num] :
% 5.25/5.50 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.50 = ( numeral_numeral_int @ N ) ) ).
% 5.25/5.50
% 5.25/5.50 % numeral_Bit1_div_2
% 5.25/5.50 thf(fact_3723_cong__exp__iff__simps_I3_J,axiom,
% 5.25/5.50 ! [N: num,Q2: num] :
% 5.25/5.50 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 != zero_zero_nat ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(3)
% 5.25/5.50 thf(fact_3724_cong__exp__iff__simps_I3_J,axiom,
% 5.25/5.50 ! [N: num,Q2: num] :
% 5.25/5.50 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 != zero_zero_int ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(3)
% 5.25/5.50 thf(fact_3725_cong__exp__iff__simps_I3_J,axiom,
% 5.25/5.50 ! [N: num,Q2: num] :
% 5.25/5.50 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 != zero_z3403309356797280102nteger ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(3)
% 5.25/5.50 thf(fact_3726_dvd__power,axiom,
% 5.25/5.50 ! [N: nat,X3: code_integer] :
% 5.25/5.50 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.50 | ( X3 = one_one_Code_integer ) )
% 5.25/5.50 => ( dvd_dvd_Code_integer @ X3 @ ( power_8256067586552552935nteger @ X3 @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power
% 5.25/5.50 thf(fact_3727_dvd__power,axiom,
% 5.25/5.50 ! [N: nat,X3: rat] :
% 5.25/5.50 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.50 | ( X3 = one_one_rat ) )
% 5.25/5.50 => ( dvd_dvd_rat @ X3 @ ( power_power_rat @ X3 @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power
% 5.25/5.50 thf(fact_3728_dvd__power,axiom,
% 5.25/5.50 ! [N: nat,X3: nat] :
% 5.25/5.50 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.50 | ( X3 = one_one_nat ) )
% 5.25/5.50 => ( dvd_dvd_nat @ X3 @ ( power_power_nat @ X3 @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power
% 5.25/5.50 thf(fact_3729_dvd__power,axiom,
% 5.25/5.50 ! [N: nat,X3: real] :
% 5.25/5.50 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.50 | ( X3 = one_one_real ) )
% 5.25/5.50 => ( dvd_dvd_real @ X3 @ ( power_power_real @ X3 @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power
% 5.25/5.50 thf(fact_3730_dvd__power,axiom,
% 5.25/5.50 ! [N: nat,X3: int] :
% 5.25/5.50 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.50 | ( X3 = one_one_int ) )
% 5.25/5.50 => ( dvd_dvd_int @ X3 @ ( power_power_int @ X3 @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power
% 5.25/5.50 thf(fact_3731_dvd__power,axiom,
% 5.25/5.50 ! [N: nat,X3: complex] :
% 5.25/5.50 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.50 | ( X3 = one_one_complex ) )
% 5.25/5.50 => ( dvd_dvd_complex @ X3 @ ( power_power_complex @ X3 @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power
% 5.25/5.50 thf(fact_3732_power3__eq__cube,axiom,
% 5.25/5.50 ! [A: complex] :
% 5.25/5.50 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.25/5.50 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % power3_eq_cube
% 5.25/5.50 thf(fact_3733_power3__eq__cube,axiom,
% 5.25/5.50 ! [A: real] :
% 5.25/5.50 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.25/5.50 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % power3_eq_cube
% 5.25/5.50 thf(fact_3734_power3__eq__cube,axiom,
% 5.25/5.50 ! [A: rat] :
% 5.25/5.50 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.25/5.50 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % power3_eq_cube
% 5.25/5.50 thf(fact_3735_power3__eq__cube,axiom,
% 5.25/5.50 ! [A: nat] :
% 5.25/5.50 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.25/5.50 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % power3_eq_cube
% 5.25/5.50 thf(fact_3736_power3__eq__cube,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.25/5.50 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % power3_eq_cube
% 5.25/5.50 thf(fact_3737_power2__commute,axiom,
% 5.25/5.50 ! [X3: complex,Y: complex] :
% 5.25/5.50 ( ( power_power_complex @ ( minus_minus_complex @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = ( power_power_complex @ ( minus_minus_complex @ Y @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power2_commute
% 5.25/5.50 thf(fact_3738_power2__commute,axiom,
% 5.25/5.50 ! [X3: real,Y: real] :
% 5.25/5.50 ( ( power_power_real @ ( minus_minus_real @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = ( power_power_real @ ( minus_minus_real @ Y @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power2_commute
% 5.25/5.50 thf(fact_3739_power2__commute,axiom,
% 5.25/5.50 ! [X3: rat,Y: rat] :
% 5.25/5.50 ( ( power_power_rat @ ( minus_minus_rat @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = ( power_power_rat @ ( minus_minus_rat @ Y @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power2_commute
% 5.25/5.50 thf(fact_3740_power2__commute,axiom,
% 5.25/5.50 ! [X3: int,Y: int] :
% 5.25/5.50 ( ( power_power_int @ ( minus_minus_int @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = ( power_power_int @ ( minus_minus_int @ Y @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power2_commute
% 5.25/5.50 thf(fact_3741_numeral__3__eq__3,axiom,
% 5.25/5.50 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.25/5.50 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % numeral_3_eq_3
% 5.25/5.50 thf(fact_3742_Suc3__eq__add__3,axiom,
% 5.25/5.50 ! [N: nat] :
% 5.25/5.50 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 5.25/5.50 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 5.25/5.50
% 5.25/5.50 % Suc3_eq_add_3
% 5.25/5.50 thf(fact_3743_even__signed__take__bit__iff,axiom,
% 5.25/5.50 ! [M: nat,A: code_integer] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 5.25/5.50 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_signed_take_bit_iff
% 5.25/5.50 thf(fact_3744_even__signed__take__bit__iff,axiom,
% 5.25/5.50 ! [M: nat,A: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 5.25/5.50 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_signed_take_bit_iff
% 5.25/5.50 thf(fact_3745_even__even__mod__4__iff,axiom,
% 5.25/5.50 ! [N: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_even_mod_4_iff
% 5.25/5.50 thf(fact_3746_dvd__mult__cancel2,axiom,
% 5.25/5.50 ! [M: nat,N: nat] :
% 5.25/5.50 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.50 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 5.25/5.50 = ( N = one_one_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_mult_cancel2
% 5.25/5.50 thf(fact_3747_dvd__mult__cancel1,axiom,
% 5.25/5.50 ! [M: nat,N: nat] :
% 5.25/5.50 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.50 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 5.25/5.50 = ( N = one_one_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_mult_cancel1
% 5.25/5.50 thf(fact_3748_power__dvd__imp__le,axiom,
% 5.25/5.50 ! [I2: nat,M: nat,N: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
% 5.25/5.50 => ( ( ord_less_nat @ one_one_nat @ I2 )
% 5.25/5.50 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_dvd_imp_le
% 5.25/5.50 thf(fact_3749_decr__mult__lemma,axiom,
% 5.25/5.50 ! [D: int,P: int > $o,K: int] :
% 5.25/5.50 ( ( ord_less_int @ zero_zero_int @ D )
% 5.25/5.50 => ( ! [X5: int] :
% 5.25/5.50 ( ( P @ X5 )
% 5.25/5.50 => ( P @ ( minus_minus_int @ X5 @ D ) ) )
% 5.25/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.50 => ! [X: int] :
% 5.25/5.50 ( ( P @ X )
% 5.25/5.50 => ( P @ ( minus_minus_int @ X @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % decr_mult_lemma
% 5.25/5.50 thf(fact_3750_mod__int__pos__iff,axiom,
% 5.25/5.50 ! [K: int,L2: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) )
% 5.25/5.50 = ( ( dvd_dvd_int @ L2 @ K )
% 5.25/5.50 | ( ( L2 = zero_zero_int )
% 5.25/5.50 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.25/5.50 | ( ord_less_int @ zero_zero_int @ L2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_int_pos_iff
% 5.25/5.50 thf(fact_3751_mod__pos__geq,axiom,
% 5.25/5.50 ! [L2: int,K: int] :
% 5.25/5.50 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.25/5.50 => ( ( ord_less_eq_int @ L2 @ K )
% 5.25/5.50 => ( ( modulo_modulo_int @ K @ L2 )
% 5.25/5.50 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_pos_geq
% 5.25/5.50 thf(fact_3752_num_Osize_I6_J,axiom,
% 5.25/5.50 ! [X32: num] :
% 5.25/5.50 ( ( size_size_num @ ( bit1 @ X32 ) )
% 5.25/5.50 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % num.size(6)
% 5.25/5.50 thf(fact_3753_even__two__times__div__two,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.25/5.50 = A ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_two_times_div_two
% 5.25/5.50 thf(fact_3754_even__two__times__div__two,axiom,
% 5.25/5.50 ! [A: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.50 = A ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_two_times_div_two
% 5.25/5.50 thf(fact_3755_even__two__times__div__two,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.25/5.50 = A ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_two_times_div_two
% 5.25/5.50 thf(fact_3756_scaling__mono,axiom,
% 5.25/5.50 ! [U: real,V: real,R2: real,S: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ U @ V )
% 5.25/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.25/5.50 => ( ( ord_less_eq_real @ R2 @ S )
% 5.25/5.50 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % scaling_mono
% 5.25/5.50 thf(fact_3757_scaling__mono,axiom,
% 5.25/5.50 ! [U: rat,V: rat,R2: rat,S: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ U @ V )
% 5.25/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 5.25/5.50 => ( ( ord_less_eq_rat @ R2 @ S )
% 5.25/5.50 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % scaling_mono
% 5.25/5.50 thf(fact_3758_even__iff__mod__2__eq__zero,axiom,
% 5.25/5.50 ! [A: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = zero_zero_nat ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_iff_mod_2_eq_zero
% 5.25/5.50 thf(fact_3759_even__iff__mod__2__eq__zero,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.50 = zero_zero_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_iff_mod_2_eq_zero
% 5.25/5.50 thf(fact_3760_even__iff__mod__2__eq__zero,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.50 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_iff_mod_2_eq_zero
% 5.25/5.50 thf(fact_3761_odd__iff__mod__2__eq__one,axiom,
% 5.25/5.50 ! [A: nat] :
% 5.25/5.50 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.50 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = one_one_nat ) ) ).
% 5.25/5.50
% 5.25/5.50 % odd_iff_mod_2_eq_one
% 5.25/5.50 thf(fact_3762_odd__iff__mod__2__eq__one,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.50 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.50 = one_one_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % odd_iff_mod_2_eq_one
% 5.25/5.50 thf(fact_3763_odd__iff__mod__2__eq__one,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.50 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.50 = one_one_Code_integer ) ) ).
% 5.25/5.50
% 5.25/5.50 % odd_iff_mod_2_eq_one
% 5.25/5.50 thf(fact_3764_cong__exp__iff__simps_I7_J,axiom,
% 5.25/5.50 ! [Q2: num,N: num] :
% 5.25/5.50 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.25/5.50 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.25/5.50 = zero_zero_nat ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(7)
% 5.25/5.50 thf(fact_3765_cong__exp__iff__simps_I7_J,axiom,
% 5.25/5.50 ! [Q2: num,N: num] :
% 5.25/5.50 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.25/5.50 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.25/5.50 = zero_zero_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(7)
% 5.25/5.50 thf(fact_3766_cong__exp__iff__simps_I7_J,axiom,
% 5.25/5.50 ! [Q2: num,N: num] :
% 5.25/5.50 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.25/5.50 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.25/5.50 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(7)
% 5.25/5.50 thf(fact_3767_cong__exp__iff__simps_I11_J,axiom,
% 5.25/5.50 ! [M: num,Q2: num] :
% 5.25/5.50 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.25/5.50 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.25/5.50 = zero_zero_nat ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(11)
% 5.25/5.50 thf(fact_3768_cong__exp__iff__simps_I11_J,axiom,
% 5.25/5.50 ! [M: num,Q2: num] :
% 5.25/5.50 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.25/5.50 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.25/5.50 = zero_zero_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(11)
% 5.25/5.50 thf(fact_3769_cong__exp__iff__simps_I11_J,axiom,
% 5.25/5.50 ! [M: num,Q2: num] :
% 5.25/5.50 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.25/5.50 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.25/5.50 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.25/5.50 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.50
% 5.25/5.50 % cong_exp_iff_simps(11)
% 5.25/5.50 thf(fact_3770_power__mono__odd,axiom,
% 5.25/5.50 ! [N: nat,A: real,B: real] :
% 5.25/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 => ( ( ord_less_eq_real @ A @ B )
% 5.25/5.50 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_mono_odd
% 5.25/5.50 thf(fact_3771_power__mono__odd,axiom,
% 5.25/5.50 ! [N: nat,A: rat,B: rat] :
% 5.25/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 => ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.50 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_mono_odd
% 5.25/5.50 thf(fact_3772_power__mono__odd,axiom,
% 5.25/5.50 ! [N: nat,A: int,B: int] :
% 5.25/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 => ( ( ord_less_eq_int @ A @ B )
% 5.25/5.50 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_mono_odd
% 5.25/5.50 thf(fact_3773_odd__pos,axiom,
% 5.25/5.50 ! [N: nat] :
% 5.25/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.25/5.50
% 5.25/5.50 % odd_pos
% 5.25/5.50 thf(fact_3774_Suc__div__eq__add3__div,axiom,
% 5.25/5.50 ! [M: nat,N: nat] :
% 5.25/5.50 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.25/5.50 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.25/5.50
% 5.25/5.50 % Suc_div_eq_add3_div
% 5.25/5.50 thf(fact_3775_dvd__power__iff__le,axiom,
% 5.25/5.50 ! [K: nat,M: nat,N: nat] :
% 5.25/5.50 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.25/5.50 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 5.25/5.50 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power_iff_le
% 5.25/5.50 thf(fact_3776_Suc__mod__eq__add3__mod,axiom,
% 5.25/5.50 ! [M: nat,N: nat] :
% 5.25/5.50 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.25/5.50 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.25/5.50
% 5.25/5.50 % Suc_mod_eq_add3_mod
% 5.25/5.50 thf(fact_3777_even__unset__bit__iff,axiom,
% 5.25/5.50 ! [M: nat,A: code_integer] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.25/5.50 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 | ( M = zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_unset_bit_iff
% 5.25/5.50 thf(fact_3778_even__unset__bit__iff,axiom,
% 5.25/5.50 ! [M: nat,A: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.25/5.50 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 | ( M = zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_unset_bit_iff
% 5.25/5.50 thf(fact_3779_even__unset__bit__iff,axiom,
% 5.25/5.50 ! [M: nat,A: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.25/5.50 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 | ( M = zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_unset_bit_iff
% 5.25/5.50 thf(fact_3780_even__set__bit__iff,axiom,
% 5.25/5.50 ! [M: nat,A: code_integer] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.25/5.50 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 & ( M != zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_set_bit_iff
% 5.25/5.50 thf(fact_3781_even__set__bit__iff,axiom,
% 5.25/5.50 ! [M: nat,A: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.25/5.50 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 & ( M != zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_set_bit_iff
% 5.25/5.50 thf(fact_3782_even__set__bit__iff,axiom,
% 5.25/5.50 ! [M: nat,A: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.25/5.50 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 & ( M != zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_set_bit_iff
% 5.25/5.50 thf(fact_3783_even__flip__bit__iff,axiom,
% 5.25/5.50 ! [M: nat,A: code_integer] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.25/5.50 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 != ( M = zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_flip_bit_iff
% 5.25/5.50 thf(fact_3784_even__flip__bit__iff,axiom,
% 5.25/5.50 ! [M: nat,A: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.25/5.50 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 != ( M = zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_flip_bit_iff
% 5.25/5.50 thf(fact_3785_even__flip__bit__iff,axiom,
% 5.25/5.50 ! [M: nat,A: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.25/5.50 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 != ( M = zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_flip_bit_iff
% 5.25/5.50 thf(fact_3786_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.25/5.50 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.25/5.50 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ X3 )
% 5.25/5.50 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.25/5.50 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % VEBT_internal.naive_member.simps(3)
% 5.25/5.50 thf(fact_3787_oddE,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ~ ! [B5: code_integer] :
% 5.25/5.50 ( A
% 5.25/5.50 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) @ one_one_Code_integer ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % oddE
% 5.25/5.50 thf(fact_3788_oddE,axiom,
% 5.25/5.50 ! [A: nat] :
% 5.25/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ~ ! [B5: nat] :
% 5.25/5.50 ( A
% 5.25/5.50 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) @ one_one_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % oddE
% 5.25/5.50 thf(fact_3789_oddE,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ~ ! [B5: int] :
% 5.25/5.50 ( A
% 5.25/5.50 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) @ one_one_int ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % oddE
% 5.25/5.50 thf(fact_3790_parity__cases,axiom,
% 5.25/5.50 ! [A: nat] :
% 5.25/5.50 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 != zero_zero_nat ) )
% 5.25/5.50 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 != one_one_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % parity_cases
% 5.25/5.50 thf(fact_3791_parity__cases,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.50 != zero_zero_int ) )
% 5.25/5.50 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.50 != one_one_int ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % parity_cases
% 5.25/5.50 thf(fact_3792_parity__cases,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.50 != zero_z3403309356797280102nteger ) )
% 5.25/5.50 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.50 != one_one_Code_integer ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % parity_cases
% 5.25/5.50 thf(fact_3793_mod2__eq__if,axiom,
% 5.25/5.50 ! [A: nat] :
% 5.25/5.50 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = zero_zero_nat ) )
% 5.25/5.50 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = one_one_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod2_eq_if
% 5.25/5.50 thf(fact_3794_mod2__eq__if,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.50 = zero_zero_int ) )
% 5.25/5.50 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.50 = one_one_int ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod2_eq_if
% 5.25/5.50 thf(fact_3795_mod2__eq__if,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.50 = zero_z3403309356797280102nteger ) )
% 5.25/5.50 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.50 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.50 = one_one_Code_integer ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod2_eq_if
% 5.25/5.50 thf(fact_3796_zero__le__even__power,axiom,
% 5.25/5.50 ! [N: nat,A: real] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % zero_le_even_power
% 5.25/5.50 thf(fact_3797_zero__le__even__power,axiom,
% 5.25/5.50 ! [N: nat,A: rat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % zero_le_even_power
% 5.25/5.50 thf(fact_3798_zero__le__even__power,axiom,
% 5.25/5.50 ! [N: nat,A: int] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % zero_le_even_power
% 5.25/5.50 thf(fact_3799_zero__le__odd__power,axiom,
% 5.25/5.50 ! [N: nat,A: real] :
% 5.25/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.25/5.50 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % zero_le_odd_power
% 5.25/5.50 thf(fact_3800_zero__le__odd__power,axiom,
% 5.25/5.50 ! [N: nat,A: rat] :
% 5.25/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.25/5.50 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % zero_le_odd_power
% 5.25/5.50 thf(fact_3801_zero__le__odd__power,axiom,
% 5.25/5.50 ! [N: nat,A: int] :
% 5.25/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.25/5.50 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % zero_le_odd_power
% 5.25/5.50 thf(fact_3802_zero__le__power__eq,axiom,
% 5.25/5.50 ! [A: real,N: nat] :
% 5.25/5.50 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.25/5.50 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % zero_le_power_eq
% 5.25/5.50 thf(fact_3803_zero__le__power__eq,axiom,
% 5.25/5.50 ! [A: rat,N: nat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.25/5.50 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % zero_le_power_eq
% 5.25/5.50 thf(fact_3804_zero__le__power__eq,axiom,
% 5.25/5.50 ! [A: int,N: nat] :
% 5.25/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.25/5.50 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % zero_le_power_eq
% 5.25/5.50 thf(fact_3805_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.25/5.50 ! [V: nat,TreeList: list_VEBT_VEBT,Vd2: vEBT_VEBT,X3: nat] :
% 5.25/5.50 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd2 ) @ X3 )
% 5.25/5.50 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.25/5.50 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % VEBT_internal.membermima.simps(5)
% 5.25/5.50 thf(fact_3806_div__pos__geq,axiom,
% 5.25/5.50 ! [L2: int,K: int] :
% 5.25/5.50 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.25/5.50 => ( ( ord_less_eq_int @ L2 @ K )
% 5.25/5.50 => ( ( divide_divide_int @ K @ L2 )
% 5.25/5.50 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) @ one_one_int ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % div_pos_geq
% 5.25/5.50 thf(fact_3807_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.25/5.50 ! [Mi: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 5.25/5.50 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc ) @ X3 )
% 5.25/5.50 = ( ( X3 = Mi )
% 5.25/5.50 | ( X3 = Ma )
% 5.25/5.50 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.25/5.50 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % VEBT_internal.membermima.simps(4)
% 5.25/5.50 thf(fact_3808_vebt__member_Osimps_I5_J,axiom,
% 5.25/5.50 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 5.25/5.50 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X3 )
% 5.25/5.50 = ( ( X3 != Mi )
% 5.25/5.50 => ( ( X3 != Ma )
% 5.25/5.50 => ( ~ ( ord_less_nat @ X3 @ Mi )
% 5.25/5.50 & ( ~ ( ord_less_nat @ X3 @ Mi )
% 5.25/5.50 => ( ~ ( ord_less_nat @ Ma @ X3 )
% 5.25/5.50 & ( ~ ( ord_less_nat @ Ma @ X3 )
% 5.25/5.50 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.25/5.50 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % vebt_member.simps(5)
% 5.25/5.50 thf(fact_3809_add__0__iff,axiom,
% 5.25/5.50 ! [B: complex,A: complex] :
% 5.25/5.50 ( ( B
% 5.25/5.50 = ( plus_plus_complex @ B @ A ) )
% 5.25/5.50 = ( A = zero_zero_complex ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_0_iff
% 5.25/5.50 thf(fact_3810_add__0__iff,axiom,
% 5.25/5.50 ! [B: real,A: real] :
% 5.25/5.50 ( ( B
% 5.25/5.50 = ( plus_plus_real @ B @ A ) )
% 5.25/5.50 = ( A = zero_zero_real ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_0_iff
% 5.25/5.50 thf(fact_3811_add__0__iff,axiom,
% 5.25/5.50 ! [B: rat,A: rat] :
% 5.25/5.50 ( ( B
% 5.25/5.50 = ( plus_plus_rat @ B @ A ) )
% 5.25/5.50 = ( A = zero_zero_rat ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_0_iff
% 5.25/5.50 thf(fact_3812_add__0__iff,axiom,
% 5.25/5.50 ! [B: nat,A: nat] :
% 5.25/5.50 ( ( B
% 5.25/5.50 = ( plus_plus_nat @ B @ A ) )
% 5.25/5.50 = ( A = zero_zero_nat ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_0_iff
% 5.25/5.50 thf(fact_3813_add__0__iff,axiom,
% 5.25/5.50 ! [B: int,A: int] :
% 5.25/5.50 ( ( B
% 5.25/5.50 = ( plus_plus_int @ B @ A ) )
% 5.25/5.50 = ( A = zero_zero_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_0_iff
% 5.25/5.50 thf(fact_3814_crossproduct__noteq,axiom,
% 5.25/5.50 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.50 ( ( ( A != B )
% 5.25/5.50 & ( C != D ) )
% 5.25/5.50 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 5.25/5.50 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % crossproduct_noteq
% 5.25/5.50 thf(fact_3815_crossproduct__noteq,axiom,
% 5.25/5.50 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.50 ( ( ( A != B )
% 5.25/5.50 & ( C != D ) )
% 5.25/5.50 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 5.25/5.50 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % crossproduct_noteq
% 5.25/5.50 thf(fact_3816_crossproduct__noteq,axiom,
% 5.25/5.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.50 ( ( ( A != B )
% 5.25/5.50 & ( C != D ) )
% 5.25/5.50 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 5.25/5.50 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % crossproduct_noteq
% 5.25/5.50 thf(fact_3817_crossproduct__noteq,axiom,
% 5.25/5.50 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.50 ( ( ( A != B )
% 5.25/5.50 & ( C != D ) )
% 5.25/5.50 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 5.25/5.50 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % crossproduct_noteq
% 5.25/5.50 thf(fact_3818_crossproduct__eq,axiom,
% 5.25/5.50 ! [W: real,Y: real,X3: real,Z: real] :
% 5.25/5.50 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y ) @ ( times_times_real @ X3 @ Z ) )
% 5.25/5.50 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X3 @ Y ) ) )
% 5.25/5.50 = ( ( W = X3 )
% 5.25/5.50 | ( Y = Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % crossproduct_eq
% 5.25/5.50 thf(fact_3819_crossproduct__eq,axiom,
% 5.25/5.50 ! [W: rat,Y: rat,X3: rat,Z: rat] :
% 5.25/5.50 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X3 @ Z ) )
% 5.25/5.50 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X3 @ Y ) ) )
% 5.25/5.50 = ( ( W = X3 )
% 5.25/5.50 | ( Y = Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % crossproduct_eq
% 5.25/5.50 thf(fact_3820_crossproduct__eq,axiom,
% 5.25/5.50 ! [W: nat,Y: nat,X3: nat,Z: nat] :
% 5.25/5.50 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X3 @ Z ) )
% 5.25/5.50 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X3 @ Y ) ) )
% 5.25/5.50 = ( ( W = X3 )
% 5.25/5.50 | ( Y = Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % crossproduct_eq
% 5.25/5.50 thf(fact_3821_crossproduct__eq,axiom,
% 5.25/5.50 ! [W: int,Y: int,X3: int,Z: int] :
% 5.25/5.50 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X3 @ Z ) )
% 5.25/5.50 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X3 @ Y ) ) )
% 5.25/5.50 = ( ( W = X3 )
% 5.25/5.50 | ( Y = Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % crossproduct_eq
% 5.25/5.50 thf(fact_3822_power2__diff,axiom,
% 5.25/5.50 ! [X3: complex,Y: complex] :
% 5.25/5.50 ( ( power_power_complex @ ( minus_minus_complex @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power2_diff
% 5.25/5.50 thf(fact_3823_power2__diff,axiom,
% 5.25/5.50 ! [X3: real,Y: real] :
% 5.25/5.50 ( ( power_power_real @ ( minus_minus_real @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( 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 ) ) @ X3 ) @ Y ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power2_diff
% 5.25/5.50 thf(fact_3824_power2__diff,axiom,
% 5.25/5.50 ! [X3: rat,Y: rat] :
% 5.25/5.50 ( ( power_power_rat @ ( minus_minus_rat @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X3 ) @ Y ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power2_diff
% 5.25/5.50 thf(fact_3825_power2__diff,axiom,
% 5.25/5.50 ! [X3: int,Y: int] :
% 5.25/5.50 ( ( power_power_int @ ( minus_minus_int @ X3 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X3 @ ( 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 ) ) @ X3 ) @ Y ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power2_diff
% 5.25/5.50 thf(fact_3826_zero__less__power__eq,axiom,
% 5.25/5.50 ! [A: real,N: nat] :
% 5.25/5.50 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.25/5.50 = ( ( N = zero_zero_nat )
% 5.25/5.50 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( A != zero_zero_real ) )
% 5.25/5.50 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % zero_less_power_eq
% 5.25/5.50 thf(fact_3827_zero__less__power__eq,axiom,
% 5.25/5.50 ! [A: rat,N: nat] :
% 5.25/5.50 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.25/5.50 = ( ( N = zero_zero_nat )
% 5.25/5.50 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( A != zero_zero_rat ) )
% 5.25/5.50 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % zero_less_power_eq
% 5.25/5.50 thf(fact_3828_zero__less__power__eq,axiom,
% 5.25/5.50 ! [A: int,N: nat] :
% 5.25/5.50 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.25/5.50 = ( ( N = zero_zero_nat )
% 5.25/5.50 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( A != zero_zero_int ) )
% 5.25/5.50 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % zero_less_power_eq
% 5.25/5.50 thf(fact_3829_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.25/5.50 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.50 ( ~ ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 5.25/5.50 => ( ! [A5: $o,B5: $o] :
% 5.25/5.50 ( ( X3
% 5.25/5.50 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.50 => ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.50 => A5 )
% 5.25/5.50 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.50 => ( ( ( Xa2 = one_one_nat )
% 5.25/5.50 => B5 )
% 5.25/5.50 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.25/5.50 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 != ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 5.25/5.50 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.25/5.50 ( ? [S2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.25/5.50 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.50 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % VEBT_internal.naive_member.elims(3)
% 5.25/5.50 thf(fact_3830_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.25/5.50 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.50 ( ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 5.25/5.50 => ( ! [A5: $o,B5: $o] :
% 5.25/5.50 ( ( X3
% 5.25/5.50 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.50 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.50 => A5 )
% 5.25/5.50 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.50 => ( ( ( Xa2 = one_one_nat )
% 5.25/5.50 => B5 )
% 5.25/5.50 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.25/5.50 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.25/5.50 ( ? [S2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.25/5.50 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.50 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % VEBT_internal.naive_member.elims(2)
% 5.25/5.50 thf(fact_3831_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.25/5.50 ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.25/5.50 ( ( ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 5.25/5.50 = Y )
% 5.25/5.50 => ( ! [A5: $o,B5: $o] :
% 5.25/5.50 ( ( X3
% 5.25/5.50 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.50 => ( Y
% 5.25/5.50 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.50 => A5 )
% 5.25/5.50 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.50 => ( ( ( Xa2 = one_one_nat )
% 5.25/5.50 => B5 )
% 5.25/5.50 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.25/5.50 => ( ( ? [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 5.25/5.50 => Y )
% 5.25/5.50 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.25/5.50 ( ? [S2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.25/5.50 => ( Y
% 5.25/5.50 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.50 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % VEBT_internal.naive_member.elims(1)
% 5.25/5.50 thf(fact_3832_signed__take__bit__int__less__eq,axiom,
% 5.25/5.50 ! [N: nat,K: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.25/5.50 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % signed_take_bit_int_less_eq
% 5.25/5.50 thf(fact_3833_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.25/5.50 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.50 ( ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 5.25/5.50 => ( ! [Mi2: nat,Ma2: nat] :
% 5.25/5.50 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.25/5.50 => ~ ( ( Xa2 = Mi2 )
% 5.25/5.50 | ( Xa2 = Ma2 ) ) )
% 5.25/5.50 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.25/5.50 ( ? [Vc2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.25/5.50 => ~ ( ( Xa2 = Mi2 )
% 5.25/5.50 | ( Xa2 = Ma2 )
% 5.25/5.50 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.50 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.25/5.50 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.25/5.50 ( ? [Vd: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.25/5.50 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.50 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % VEBT_internal.membermima.elims(2)
% 5.25/5.50 thf(fact_3834_divmod__digit__1_I2_J,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.50 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.25/5.50 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.25/5.50 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.25/5.50 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divmod_digit_1(2)
% 5.25/5.50 thf(fact_3835_divmod__digit__1_I2_J,axiom,
% 5.25/5.50 ! [A: nat,B: nat] :
% 5.25/5.50 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.50 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.50 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.25/5.50 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.25/5.50 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divmod_digit_1(2)
% 5.25/5.50 thf(fact_3836_divmod__digit__1_I2_J,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.50 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.50 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.25/5.50 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.25/5.50 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divmod_digit_1(2)
% 5.25/5.50 thf(fact_3837_power__le__zero__eq,axiom,
% 5.25/5.50 ! [A: real,N: nat] :
% 5.25/5.50 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.25/5.50 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.50 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.25/5.50 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_le_zero_eq
% 5.25/5.50 thf(fact_3838_power__le__zero__eq,axiom,
% 5.25/5.50 ! [A: rat,N: nat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.25/5.50 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.50 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.25/5.50 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_le_zero_eq
% 5.25/5.50 thf(fact_3839_power__le__zero__eq,axiom,
% 5.25/5.50 ! [A: int,N: nat] :
% 5.25/5.50 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.25/5.50 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.50 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.25/5.50 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.50 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_le_zero_eq
% 5.25/5.50 thf(fact_3840_vebt__member_Oelims_I2_J,axiom,
% 5.25/5.50 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.50 ( ( vEBT_vebt_member @ X3 @ Xa2 )
% 5.25/5.50 => ( ! [A5: $o,B5: $o] :
% 5.25/5.50 ( ( X3
% 5.25/5.50 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.50 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.50 => A5 )
% 5.25/5.50 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.50 => ( ( ( Xa2 = one_one_nat )
% 5.25/5.50 => B5 )
% 5.25/5.50 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.25/5.50 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 5.25/5.50 ( ? [Summary2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.25/5.50 => ~ ( ( Xa2 != Mi2 )
% 5.25/5.50 => ( ( Xa2 != Ma2 )
% 5.25/5.50 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.25/5.50 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.25/5.50 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.25/5.50 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.25/5.50 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.50 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % vebt_member.elims(2)
% 5.25/5.50 thf(fact_3841_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.25/5.50 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.50 ( ~ ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 5.25/5.50 => ( ! [Uu: $o,Uv: $o] :
% 5.25/5.50 ( X3
% 5.25/5.50 != ( vEBT_Leaf @ Uu @ Uv ) )
% 5.25/5.50 => ( ! [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) )
% 5.25/5.50 => ( ! [Mi2: nat,Ma2: nat] :
% 5.25/5.50 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.25/5.50 => ( ( Xa2 = Mi2 )
% 5.25/5.50 | ( Xa2 = Ma2 ) ) )
% 5.25/5.50 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.25/5.50 ( ? [Vc2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.25/5.50 => ( ( Xa2 = Mi2 )
% 5.25/5.50 | ( Xa2 = Ma2 )
% 5.25/5.50 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.50 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.25/5.50 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.25/5.50 ( ? [Vd: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.25/5.50 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.50 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % VEBT_internal.membermima.elims(3)
% 5.25/5.50 thf(fact_3842_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.25/5.50 ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.25/5.50 ( ( ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 5.25/5.50 = Y )
% 5.25/5.50 => ( ( ? [Uu: $o,Uv: $o] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.25/5.50 => Y )
% 5.25/5.50 => ( ( ? [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) )
% 5.25/5.50 => Y )
% 5.25/5.50 => ( ! [Mi2: nat,Ma2: nat] :
% 5.25/5.50 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.25/5.50 => ( Y
% 5.25/5.50 = ( ~ ( ( Xa2 = Mi2 )
% 5.25/5.50 | ( Xa2 = Ma2 ) ) ) ) )
% 5.25/5.50 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.25/5.50 ( ? [Vc2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.25/5.50 => ( Y
% 5.25/5.50 = ( ~ ( ( Xa2 = Mi2 )
% 5.25/5.50 | ( Xa2 = Ma2 )
% 5.25/5.50 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.50 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 5.25/5.50 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.25/5.50 ( ? [Vd: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.25/5.50 => ( Y
% 5.25/5.50 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.50 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % VEBT_internal.membermima.elims(1)
% 5.25/5.50 thf(fact_3843_vebt__insert_Osimps_I5_J,axiom,
% 5.25/5.50 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X3: nat] :
% 5.25/5.50 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X3 )
% 5.25/5.50 = ( if_VEBT_VEBT
% 5.25/5.50 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.25/5.50 & ~ ( ( X3 = Mi )
% 5.25/5.50 | ( X3 = Ma ) ) )
% 5.25/5.50 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ X3 @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ Ma ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X3 @ Mi ) @ Mi @ X3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 5.25/5.50 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % vebt_insert.simps(5)
% 5.25/5.50 thf(fact_3844_vebt__member_Oelims_I1_J,axiom,
% 5.25/5.50 ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.25/5.50 ( ( ( vEBT_vebt_member @ X3 @ Xa2 )
% 5.25/5.50 = Y )
% 5.25/5.50 => ( ! [A5: $o,B5: $o] :
% 5.25/5.50 ( ( X3
% 5.25/5.50 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.50 => ( Y
% 5.25/5.50 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.50 => A5 )
% 5.25/5.50 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.50 => ( ( ( Xa2 = one_one_nat )
% 5.25/5.50 => B5 )
% 5.25/5.50 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.25/5.50 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.25/5.50 => Y )
% 5.25/5.50 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.25/5.50 => Y )
% 5.25/5.50 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.25/5.50 => Y )
% 5.25/5.50 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 5.25/5.50 ( ? [Summary2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.25/5.50 => ( Y
% 5.25/5.50 = ( ~ ( ( Xa2 != Mi2 )
% 5.25/5.50 => ( ( Xa2 != Ma2 )
% 5.25/5.50 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.25/5.50 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.25/5.50 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.25/5.50 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.25/5.50 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.50 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % vebt_member.elims(1)
% 5.25/5.50 thf(fact_3845_vebt__member_Oelims_I3_J,axiom,
% 5.25/5.50 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.50 ( ~ ( vEBT_vebt_member @ X3 @ Xa2 )
% 5.25/5.50 => ( ! [A5: $o,B5: $o] :
% 5.25/5.50 ( ( X3
% 5.25/5.50 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.50 => ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.50 => A5 )
% 5.25/5.50 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.50 => ( ( ( Xa2 = one_one_nat )
% 5.25/5.50 => B5 )
% 5.25/5.50 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.25/5.50 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.25/5.50 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.25/5.50 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.25/5.50 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 5.25/5.50 ( ? [Summary2: vEBT_VEBT] :
% 5.25/5.50 ( X3
% 5.25/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.25/5.50 => ( ( Xa2 != Mi2 )
% 5.25/5.50 => ( ( Xa2 != Ma2 )
% 5.25/5.50 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.25/5.50 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.25/5.50 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.25/5.50 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.25/5.50 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.50 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.50 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % vebt_member.elims(3)
% 5.25/5.50 thf(fact_3846_neg__zmod__mult__2,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.50 => ( ( 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 ) )
% 5.25/5.50 = ( 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 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_zmod_mult_2
% 5.25/5.50 thf(fact_3847_divmod__step__eq,axiom,
% 5.25/5.50 ! [L2: num,R2: nat,Q2: nat] :
% 5.25/5.50 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R2 )
% 5.25/5.50 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.25/5.50 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L2 ) ) ) ) )
% 5.25/5.50 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R2 )
% 5.25/5.50 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.25/5.50 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divmod_step_eq
% 5.25/5.50 thf(fact_3848_divmod__step__eq,axiom,
% 5.25/5.50 ! [L2: num,R2: int,Q2: int] :
% 5.25/5.50 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R2 )
% 5.25/5.50 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.25/5.50 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L2 ) ) ) ) )
% 5.25/5.50 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R2 )
% 5.25/5.50 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.25/5.50 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divmod_step_eq
% 5.25/5.50 thf(fact_3849_divmod__step__eq,axiom,
% 5.25/5.50 ! [L2: num,R2: code_integer,Q2: code_integer] :
% 5.25/5.50 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R2 )
% 5.25/5.50 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 5.25/5.50 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L2 ) ) ) ) )
% 5.25/5.50 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R2 )
% 5.25/5.50 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 5.25/5.50 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divmod_step_eq
% 5.25/5.50 thf(fact_3850_mod__exhaust__less__4,axiom,
% 5.25/5.50 ! [M: nat] :
% 5.25/5.50 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.25/5.50 = zero_zero_nat )
% 5.25/5.50 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.25/5.50 = one_one_nat )
% 5.25/5.50 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.25/5.50 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.25/5.50 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_exhaust_less_4
% 5.25/5.50 thf(fact_3851_vebt__insert_Opelims,axiom,
% 5.25/5.50 ! [X3: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.25/5.50 ( ( ( vEBT_vebt_insert @ X3 @ Xa2 )
% 5.25/5.50 = Y )
% 5.25/5.50 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 5.25/5.50 => ( ! [A5: $o,B5: $o] :
% 5.25/5.50 ( ( X3
% 5.25/5.50 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.50 => ( ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.50 => ( Y
% 5.25/5.50 = ( vEBT_Leaf @ $true @ B5 ) ) )
% 5.25/5.50 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.50 => ( ( ( Xa2 = one_one_nat )
% 5.25/5.50 => ( Y
% 5.25/5.50 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 5.25/5.50 & ( ( Xa2 != one_one_nat )
% 5.25/5.50 => ( Y
% 5.25/5.50 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) )
% 5.25/5.50 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.25/5.50 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.25/5.50 ( ( X3
% 5.25/5.50 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.25/5.50 => ( ( Y
% 5.25/5.50 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.25/5.50 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 5.25/5.50 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.25/5.50 ( ( X3
% 5.25/5.50 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.25/5.50 => ( ( Y
% 5.25/5.50 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.25/5.50 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 5.25/5.50 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.25/5.50 ( ( X3
% 5.25/5.50 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.25/5.50 => ( ( Y
% 5.25/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.25/5.50 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 5.25/5.50 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.25/5.50 ( ( X3
% 5.25/5.50 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.25/5.50 => ( ( Y
% 5.25/5.50 = ( if_VEBT_VEBT
% 5.25/5.50 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.50 & ~ ( ( Xa2 = Mi2 )
% 5.25/5.50 | ( Xa2 = Ma2 ) ) )
% 5.25/5.50 @ ( 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 @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.25/5.50 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) )
% 5.25/5.50 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % vebt_insert.pelims
% 5.25/5.50 thf(fact_3852_div2__even__ext__nat,axiom,
% 5.25/5.50 ! [X3: nat,Y: nat] :
% 5.25/5.50 ( ( ( divide_divide_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.50 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X3 )
% 5.25/5.50 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 5.25/5.50 => ( X3 = Y ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % div2_even_ext_nat
% 5.25/5.50 thf(fact_3853_signed__take__bit__Suc__minus__bit1,axiom,
% 5.25/5.50 ! [N: nat,K: num] :
% 5.25/5.50 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.25/5.50 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % signed_take_bit_Suc_minus_bit1
% 5.25/5.50 thf(fact_3854_signed__take__bit__numeral__bit1,axiom,
% 5.25/5.50 ! [L2: num,K: num] :
% 5.25/5.50 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.25/5.50 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % signed_take_bit_numeral_bit1
% 5.25/5.50 thf(fact_3855_dbl__inc__simps_I3_J,axiom,
% 5.25/5.50 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.25/5.50 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dbl_inc_simps(3)
% 5.25/5.50 thf(fact_3856_dbl__inc__simps_I3_J,axiom,
% 5.25/5.50 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.25/5.50 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dbl_inc_simps(3)
% 5.25/5.50 thf(fact_3857_dbl__inc__simps_I3_J,axiom,
% 5.25/5.50 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.25/5.50 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dbl_inc_simps(3)
% 5.25/5.50 thf(fact_3858_dbl__inc__simps_I3_J,axiom,
% 5.25/5.50 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.25/5.50 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dbl_inc_simps(3)
% 5.25/5.50 thf(fact_3859_vebt__buildup_Oelims,axiom,
% 5.25/5.50 ! [X3: nat,Y: vEBT_VEBT] :
% 5.25/5.50 ( ( ( vEBT_vebt_buildup @ X3 )
% 5.25/5.50 = Y )
% 5.25/5.50 => ( ( ( X3 = zero_zero_nat )
% 5.25/5.50 => ( Y
% 5.25/5.50 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.25/5.50 => ( ( ( X3
% 5.25/5.50 = ( suc @ zero_zero_nat ) )
% 5.25/5.50 => ( Y
% 5.25/5.50 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.25/5.50 => ~ ! [Va: nat] :
% 5.25/5.50 ( ( X3
% 5.25/5.50 = ( suc @ ( suc @ Va ) ) )
% 5.25/5.50 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.25/5.50 => ( Y
% 5.25/5.50 = ( 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 ) ) ) ) ) ) )
% 5.25/5.50 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.25/5.50 => ( Y
% 5.25/5.50 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % vebt_buildup.elims
% 5.25/5.50 thf(fact_3860_intind,axiom,
% 5.25/5.50 ! [I2: nat,N: nat,P: nat > $o,X3: nat] :
% 5.25/5.50 ( ( ord_less_nat @ I2 @ N )
% 5.25/5.50 => ( ( P @ X3 )
% 5.25/5.50 => ( P @ ( nth_nat @ ( replicate_nat @ N @ X3 ) @ I2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % intind
% 5.25/5.50 thf(fact_3861_intind,axiom,
% 5.25/5.50 ! [I2: nat,N: nat,P: int > $o,X3: int] :
% 5.25/5.50 ( ( ord_less_nat @ I2 @ N )
% 5.25/5.50 => ( ( P @ X3 )
% 5.25/5.50 => ( P @ ( nth_int @ ( replicate_int @ N @ X3 ) @ I2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % intind
% 5.25/5.50 thf(fact_3862_intind,axiom,
% 5.25/5.50 ! [I2: nat,N: nat,P: vEBT_VEBT > $o,X3: vEBT_VEBT] :
% 5.25/5.50 ( ( ord_less_nat @ I2 @ N )
% 5.25/5.50 => ( ( P @ X3 )
% 5.25/5.50 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X3 ) @ I2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % intind
% 5.25/5.50 thf(fact_3863_neg__equal__iff__equal,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( ( uminus_uminus_int @ A )
% 5.25/5.50 = ( uminus_uminus_int @ B ) )
% 5.25/5.50 = ( A = B ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_equal_iff_equal
% 5.25/5.50 thf(fact_3864_neg__equal__iff__equal,axiom,
% 5.25/5.50 ! [A: real,B: real] :
% 5.25/5.50 ( ( ( uminus_uminus_real @ A )
% 5.25/5.50 = ( uminus_uminus_real @ B ) )
% 5.25/5.50 = ( A = B ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_equal_iff_equal
% 5.25/5.50 thf(fact_3865_neg__equal__iff__equal,axiom,
% 5.25/5.50 ! [A: complex,B: complex] :
% 5.25/5.50 ( ( ( uminus1482373934393186551omplex @ A )
% 5.25/5.50 = ( uminus1482373934393186551omplex @ B ) )
% 5.25/5.50 = ( A = B ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_equal_iff_equal
% 5.25/5.50 thf(fact_3866_neg__equal__iff__equal,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( ( uminus1351360451143612070nteger @ A )
% 5.25/5.50 = ( uminus1351360451143612070nteger @ B ) )
% 5.25/5.50 = ( A = B ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_equal_iff_equal
% 5.25/5.50 thf(fact_3867_neg__equal__iff__equal,axiom,
% 5.25/5.50 ! [A: rat,B: rat] :
% 5.25/5.50 ( ( ( uminus_uminus_rat @ A )
% 5.25/5.50 = ( uminus_uminus_rat @ B ) )
% 5.25/5.50 = ( A = B ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_equal_iff_equal
% 5.25/5.50 thf(fact_3868_add_Oinverse__inverse,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % add.inverse_inverse
% 5.25/5.50 thf(fact_3869_add_Oinverse__inverse,axiom,
% 5.25/5.50 ! [A: real] :
% 5.25/5.50 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % add.inverse_inverse
% 5.25/5.50 thf(fact_3870_add_Oinverse__inverse,axiom,
% 5.25/5.50 ! [A: complex] :
% 5.25/5.50 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % add.inverse_inverse
% 5.25/5.50 thf(fact_3871_add_Oinverse__inverse,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % add.inverse_inverse
% 5.25/5.50 thf(fact_3872_add_Oinverse__inverse,axiom,
% 5.25/5.50 ! [A: rat] :
% 5.25/5.50 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % add.inverse_inverse
% 5.25/5.50 thf(fact_3873_diff__Suc__Suc,axiom,
% 5.25/5.50 ! [M: nat,N: nat] :
% 5.25/5.50 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.25/5.50 = ( minus_minus_nat @ M @ N ) ) ).
% 5.25/5.50
% 5.25/5.50 % diff_Suc_Suc
% 5.25/5.50 thf(fact_3874_Suc__diff__diff,axiom,
% 5.25/5.50 ! [M: nat,N: nat,K: nat] :
% 5.25/5.50 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 5.25/5.50 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 5.25/5.50
% 5.25/5.50 % Suc_diff_diff
% 5.25/5.50 thf(fact_3875_diff__0__eq__0,axiom,
% 5.25/5.50 ! [N: nat] :
% 5.25/5.50 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 5.25/5.50 = zero_zero_nat ) ).
% 5.25/5.50
% 5.25/5.50 % diff_0_eq_0
% 5.25/5.50 thf(fact_3876_diff__self__eq__0,axiom,
% 5.25/5.50 ! [M: nat] :
% 5.25/5.50 ( ( minus_minus_nat @ M @ M )
% 5.25/5.50 = zero_zero_nat ) ).
% 5.25/5.50
% 5.25/5.50 % diff_self_eq_0
% 5.25/5.50 thf(fact_3877_diff__diff__cancel,axiom,
% 5.25/5.50 ! [I2: nat,N: nat] :
% 5.25/5.50 ( ( ord_less_eq_nat @ I2 @ N )
% 5.25/5.50 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
% 5.25/5.50 = I2 ) ) ).
% 5.25/5.50
% 5.25/5.50 % diff_diff_cancel
% 5.25/5.50 thf(fact_3878_diff__diff__left,axiom,
% 5.25/5.50 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.50 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J2 ) @ K )
% 5.25/5.50 = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J2 @ K ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % diff_diff_left
% 5.25/5.50 thf(fact_3879_idiff__0,axiom,
% 5.25/5.50 ! [N: extended_enat] :
% 5.25/5.50 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.25/5.50 = zero_z5237406670263579293d_enat ) ).
% 5.25/5.50
% 5.25/5.50 % idiff_0
% 5.25/5.50 thf(fact_3880_idiff__0__right,axiom,
% 5.25/5.50 ! [N: extended_enat] :
% 5.25/5.50 ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.25/5.50 = N ) ).
% 5.25/5.50
% 5.25/5.50 % idiff_0_right
% 5.25/5.50 thf(fact_3881_neg__le__iff__le,axiom,
% 5.25/5.50 ! [B: real,A: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.25/5.50 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_le_iff_le
% 5.25/5.50 thf(fact_3882_neg__le__iff__le,axiom,
% 5.25/5.50 ! [B: code_integer,A: code_integer] :
% 5.25/5.50 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.25/5.50 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_le_iff_le
% 5.25/5.50 thf(fact_3883_neg__le__iff__le,axiom,
% 5.25/5.50 ! [B: rat,A: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.25/5.50 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_le_iff_le
% 5.25/5.50 thf(fact_3884_neg__le__iff__le,axiom,
% 5.25/5.50 ! [B: int,A: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.25/5.50 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_le_iff_le
% 5.25/5.50 thf(fact_3885_neg__equal__zero,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( ( uminus_uminus_int @ A )
% 5.25/5.50 = A )
% 5.25/5.50 = ( A = zero_zero_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_equal_zero
% 5.25/5.50 thf(fact_3886_neg__equal__zero,axiom,
% 5.25/5.50 ! [A: real] :
% 5.25/5.50 ( ( ( uminus_uminus_real @ A )
% 5.25/5.50 = A )
% 5.25/5.50 = ( A = zero_zero_real ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_equal_zero
% 5.25/5.50 thf(fact_3887_neg__equal__zero,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( ( uminus1351360451143612070nteger @ A )
% 5.25/5.50 = A )
% 5.25/5.50 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_equal_zero
% 5.25/5.50 thf(fact_3888_neg__equal__zero,axiom,
% 5.25/5.50 ! [A: rat] :
% 5.25/5.50 ( ( ( uminus_uminus_rat @ A )
% 5.25/5.50 = A )
% 5.25/5.50 = ( A = zero_zero_rat ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_equal_zero
% 5.25/5.50 thf(fact_3889_equal__neg__zero,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( A
% 5.25/5.50 = ( uminus_uminus_int @ A ) )
% 5.25/5.50 = ( A = zero_zero_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % equal_neg_zero
% 5.25/5.50 thf(fact_3890_equal__neg__zero,axiom,
% 5.25/5.50 ! [A: real] :
% 5.25/5.50 ( ( A
% 5.25/5.50 = ( uminus_uminus_real @ A ) )
% 5.25/5.50 = ( A = zero_zero_real ) ) ).
% 5.25/5.50
% 5.25/5.50 % equal_neg_zero
% 5.25/5.50 thf(fact_3891_equal__neg__zero,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( A
% 5.25/5.50 = ( uminus1351360451143612070nteger @ A ) )
% 5.25/5.50 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.50
% 5.25/5.50 % equal_neg_zero
% 5.25/5.50 thf(fact_3892_equal__neg__zero,axiom,
% 5.25/5.50 ! [A: rat] :
% 5.25/5.50 ( ( A
% 5.25/5.50 = ( uminus_uminus_rat @ A ) )
% 5.25/5.50 = ( A = zero_zero_rat ) ) ).
% 5.25/5.50
% 5.25/5.50 % equal_neg_zero
% 5.25/5.50 thf(fact_3893_neg__equal__0__iff__equal,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( ( uminus_uminus_int @ A )
% 5.25/5.50 = zero_zero_int )
% 5.25/5.50 = ( A = zero_zero_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_equal_0_iff_equal
% 5.25/5.50 thf(fact_3894_neg__equal__0__iff__equal,axiom,
% 5.25/5.50 ! [A: real] :
% 5.25/5.50 ( ( ( uminus_uminus_real @ A )
% 5.25/5.50 = zero_zero_real )
% 5.25/5.50 = ( A = zero_zero_real ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_equal_0_iff_equal
% 5.25/5.50 thf(fact_3895_neg__equal__0__iff__equal,axiom,
% 5.25/5.50 ! [A: complex] :
% 5.25/5.50 ( ( ( uminus1482373934393186551omplex @ A )
% 5.25/5.50 = zero_zero_complex )
% 5.25/5.50 = ( A = zero_zero_complex ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_equal_0_iff_equal
% 5.25/5.50 thf(fact_3896_neg__equal__0__iff__equal,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( ( uminus1351360451143612070nteger @ A )
% 5.25/5.50 = zero_z3403309356797280102nteger )
% 5.25/5.50 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_equal_0_iff_equal
% 5.25/5.50 thf(fact_3897_neg__equal__0__iff__equal,axiom,
% 5.25/5.50 ! [A: rat] :
% 5.25/5.50 ( ( ( uminus_uminus_rat @ A )
% 5.25/5.50 = zero_zero_rat )
% 5.25/5.50 = ( A = zero_zero_rat ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_equal_0_iff_equal
% 5.25/5.50 thf(fact_3898_neg__0__equal__iff__equal,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( zero_zero_int
% 5.25/5.50 = ( uminus_uminus_int @ A ) )
% 5.25/5.50 = ( zero_zero_int = A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_0_equal_iff_equal
% 5.25/5.50 thf(fact_3899_neg__0__equal__iff__equal,axiom,
% 5.25/5.50 ! [A: real] :
% 5.25/5.50 ( ( zero_zero_real
% 5.25/5.50 = ( uminus_uminus_real @ A ) )
% 5.25/5.50 = ( zero_zero_real = A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_0_equal_iff_equal
% 5.25/5.50 thf(fact_3900_neg__0__equal__iff__equal,axiom,
% 5.25/5.50 ! [A: complex] :
% 5.25/5.50 ( ( zero_zero_complex
% 5.25/5.50 = ( uminus1482373934393186551omplex @ A ) )
% 5.25/5.50 = ( zero_zero_complex = A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_0_equal_iff_equal
% 5.25/5.50 thf(fact_3901_neg__0__equal__iff__equal,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( zero_z3403309356797280102nteger
% 5.25/5.50 = ( uminus1351360451143612070nteger @ A ) )
% 5.25/5.50 = ( zero_z3403309356797280102nteger = A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_0_equal_iff_equal
% 5.25/5.50 thf(fact_3902_neg__0__equal__iff__equal,axiom,
% 5.25/5.50 ! [A: rat] :
% 5.25/5.50 ( ( zero_zero_rat
% 5.25/5.50 = ( uminus_uminus_rat @ A ) )
% 5.25/5.50 = ( zero_zero_rat = A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_0_equal_iff_equal
% 5.25/5.50 thf(fact_3903_add_Oinverse__neutral,axiom,
% 5.25/5.50 ( ( uminus_uminus_int @ zero_zero_int )
% 5.25/5.50 = zero_zero_int ) ).
% 5.25/5.50
% 5.25/5.50 % add.inverse_neutral
% 5.25/5.50 thf(fact_3904_add_Oinverse__neutral,axiom,
% 5.25/5.50 ( ( uminus_uminus_real @ zero_zero_real )
% 5.25/5.50 = zero_zero_real ) ).
% 5.25/5.50
% 5.25/5.50 % add.inverse_neutral
% 5.25/5.50 thf(fact_3905_add_Oinverse__neutral,axiom,
% 5.25/5.50 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 5.25/5.50 = zero_zero_complex ) ).
% 5.25/5.50
% 5.25/5.50 % add.inverse_neutral
% 5.25/5.50 thf(fact_3906_add_Oinverse__neutral,axiom,
% 5.25/5.50 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.25/5.50 = zero_z3403309356797280102nteger ) ).
% 5.25/5.50
% 5.25/5.50 % add.inverse_neutral
% 5.25/5.50 thf(fact_3907_add_Oinverse__neutral,axiom,
% 5.25/5.50 ( ( uminus_uminus_rat @ zero_zero_rat )
% 5.25/5.50 = zero_zero_rat ) ).
% 5.25/5.50
% 5.25/5.50 % add.inverse_neutral
% 5.25/5.50 thf(fact_3908_neg__less__iff__less,axiom,
% 5.25/5.50 ! [B: int,A: int] :
% 5.25/5.50 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.25/5.50 = ( ord_less_int @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_less_iff_less
% 5.25/5.50 thf(fact_3909_neg__less__iff__less,axiom,
% 5.25/5.50 ! [B: real,A: real] :
% 5.25/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.25/5.50 = ( ord_less_real @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_less_iff_less
% 5.25/5.50 thf(fact_3910_neg__less__iff__less,axiom,
% 5.25/5.50 ! [B: code_integer,A: code_integer] :
% 5.25/5.50 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.25/5.50 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_less_iff_less
% 5.25/5.50 thf(fact_3911_neg__less__iff__less,axiom,
% 5.25/5.50 ! [B: rat,A: rat] :
% 5.25/5.50 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.25/5.50 = ( ord_less_rat @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_less_iff_less
% 5.25/5.50 thf(fact_3912_neg__numeral__eq__iff,axiom,
% 5.25/5.50 ! [M: num,N: num] :
% 5.25/5.50 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.25/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.50 = ( M = N ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_numeral_eq_iff
% 5.25/5.50 thf(fact_3913_neg__numeral__eq__iff,axiom,
% 5.25/5.50 ! [M: num,N: num] :
% 5.25/5.50 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.25/5.50 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.25/5.50 = ( M = N ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_numeral_eq_iff
% 5.25/5.50 thf(fact_3914_neg__numeral__eq__iff,axiom,
% 5.25/5.50 ! [M: num,N: num] :
% 5.25/5.50 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.25/5.50 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.25/5.50 = ( M = N ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_numeral_eq_iff
% 5.25/5.50 thf(fact_3915_neg__numeral__eq__iff,axiom,
% 5.25/5.50 ! [M: num,N: num] :
% 5.25/5.50 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.25/5.50 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.25/5.50 = ( M = N ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_numeral_eq_iff
% 5.25/5.50 thf(fact_3916_neg__numeral__eq__iff,axiom,
% 5.25/5.50 ! [M: num,N: num] :
% 5.25/5.50 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.25/5.50 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.25/5.50 = ( M = N ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_numeral_eq_iff
% 5.25/5.50 thf(fact_3917_mult__minus__left,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.25/5.50 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_minus_left
% 5.25/5.50 thf(fact_3918_mult__minus__left,axiom,
% 5.25/5.50 ! [A: real,B: real] :
% 5.25/5.50 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.25/5.50 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_minus_left
% 5.25/5.50 thf(fact_3919_mult__minus__left,axiom,
% 5.25/5.50 ! [A: complex,B: complex] :
% 5.25/5.50 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.25/5.50 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_minus_left
% 5.25/5.50 thf(fact_3920_mult__minus__left,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.25/5.50 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_minus_left
% 5.25/5.50 thf(fact_3921_mult__minus__left,axiom,
% 5.25/5.50 ! [A: rat,B: rat] :
% 5.25/5.50 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.25/5.50 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_minus_left
% 5.25/5.50 thf(fact_3922_minus__mult__minus,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.25/5.50 = ( times_times_int @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_mult_minus
% 5.25/5.50 thf(fact_3923_minus__mult__minus,axiom,
% 5.25/5.50 ! [A: real,B: real] :
% 5.25/5.50 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.25/5.50 = ( times_times_real @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_mult_minus
% 5.25/5.50 thf(fact_3924_minus__mult__minus,axiom,
% 5.25/5.50 ! [A: complex,B: complex] :
% 5.25/5.50 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.25/5.50 = ( times_times_complex @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_mult_minus
% 5.25/5.50 thf(fact_3925_minus__mult__minus,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.25/5.50 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_mult_minus
% 5.25/5.50 thf(fact_3926_minus__mult__minus,axiom,
% 5.25/5.50 ! [A: rat,B: rat] :
% 5.25/5.50 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.25/5.50 = ( times_times_rat @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_mult_minus
% 5.25/5.50 thf(fact_3927_mult__minus__right,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.25/5.50 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_minus_right
% 5.25/5.50 thf(fact_3928_mult__minus__right,axiom,
% 5.25/5.50 ! [A: real,B: real] :
% 5.25/5.50 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.25/5.50 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_minus_right
% 5.25/5.50 thf(fact_3929_mult__minus__right,axiom,
% 5.25/5.50 ! [A: complex,B: complex] :
% 5.25/5.50 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.25/5.50 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_minus_right
% 5.25/5.50 thf(fact_3930_mult__minus__right,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.25/5.50 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_minus_right
% 5.25/5.50 thf(fact_3931_mult__minus__right,axiom,
% 5.25/5.50 ! [A: rat,B: rat] :
% 5.25/5.50 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.25/5.50 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_minus_right
% 5.25/5.50 thf(fact_3932_add__minus__cancel,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.25/5.50 = B ) ).
% 5.25/5.50
% 5.25/5.50 % add_minus_cancel
% 5.25/5.50 thf(fact_3933_add__minus__cancel,axiom,
% 5.25/5.50 ! [A: real,B: real] :
% 5.25/5.50 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.25/5.50 = B ) ).
% 5.25/5.50
% 5.25/5.50 % add_minus_cancel
% 5.25/5.50 thf(fact_3934_add__minus__cancel,axiom,
% 5.25/5.50 ! [A: complex,B: complex] :
% 5.25/5.50 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.25/5.50 = B ) ).
% 5.25/5.50
% 5.25/5.50 % add_minus_cancel
% 5.25/5.50 thf(fact_3935_add__minus__cancel,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.25/5.50 = B ) ).
% 5.25/5.50
% 5.25/5.50 % add_minus_cancel
% 5.25/5.50 thf(fact_3936_add__minus__cancel,axiom,
% 5.25/5.50 ! [A: rat,B: rat] :
% 5.25/5.50 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 5.25/5.50 = B ) ).
% 5.25/5.50
% 5.25/5.50 % add_minus_cancel
% 5.25/5.50 thf(fact_3937_minus__add__cancel,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.25/5.50 = B ) ).
% 5.25/5.50
% 5.25/5.50 % minus_add_cancel
% 5.25/5.50 thf(fact_3938_minus__add__cancel,axiom,
% 5.25/5.50 ! [A: real,B: real] :
% 5.25/5.50 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.25/5.50 = B ) ).
% 5.25/5.50
% 5.25/5.50 % minus_add_cancel
% 5.25/5.50 thf(fact_3939_minus__add__cancel,axiom,
% 5.25/5.50 ! [A: complex,B: complex] :
% 5.25/5.50 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.25/5.50 = B ) ).
% 5.25/5.50
% 5.25/5.50 % minus_add_cancel
% 5.25/5.50 thf(fact_3940_minus__add__cancel,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.25/5.50 = B ) ).
% 5.25/5.50
% 5.25/5.50 % minus_add_cancel
% 5.25/5.50 thf(fact_3941_minus__add__cancel,axiom,
% 5.25/5.50 ! [A: rat,B: rat] :
% 5.25/5.50 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 5.25/5.50 = B ) ).
% 5.25/5.50
% 5.25/5.50 % minus_add_cancel
% 5.25/5.50 thf(fact_3942_minus__add__distrib,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.25/5.50 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_add_distrib
% 5.25/5.50 thf(fact_3943_minus__add__distrib,axiom,
% 5.25/5.50 ! [A: real,B: real] :
% 5.25/5.50 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.25/5.50 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_add_distrib
% 5.25/5.50 thf(fact_3944_minus__add__distrib,axiom,
% 5.25/5.50 ! [A: complex,B: complex] :
% 5.25/5.50 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.25/5.50 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_add_distrib
% 5.25/5.50 thf(fact_3945_minus__add__distrib,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.25/5.50 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_add_distrib
% 5.25/5.50 thf(fact_3946_minus__add__distrib,axiom,
% 5.25/5.50 ! [A: rat,B: rat] :
% 5.25/5.50 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.25/5.50 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_add_distrib
% 5.25/5.50 thf(fact_3947_minus__diff__eq,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 5.25/5.50 = ( minus_minus_int @ B @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_diff_eq
% 5.25/5.50 thf(fact_3948_minus__diff__eq,axiom,
% 5.25/5.50 ! [A: real,B: real] :
% 5.25/5.50 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 5.25/5.50 = ( minus_minus_real @ B @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_diff_eq
% 5.25/5.50 thf(fact_3949_minus__diff__eq,axiom,
% 5.25/5.50 ! [A: complex,B: complex] :
% 5.25/5.50 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 5.25/5.50 = ( minus_minus_complex @ B @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_diff_eq
% 5.25/5.50 thf(fact_3950_minus__diff__eq,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.25/5.50 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_diff_eq
% 5.25/5.50 thf(fact_3951_minus__diff__eq,axiom,
% 5.25/5.50 ! [A: rat,B: rat] :
% 5.25/5.50 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 5.25/5.50 = ( minus_minus_rat @ B @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_diff_eq
% 5.25/5.50 thf(fact_3952_div__minus__minus,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.25/5.50 = ( divide_divide_int @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % div_minus_minus
% 5.25/5.50 thf(fact_3953_div__minus__minus,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.25/5.50 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 5.25/5.50
% 5.25/5.50 % div_minus_minus
% 5.25/5.50 thf(fact_3954_minus__dvd__iff,axiom,
% 5.25/5.50 ! [X3: int,Y: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X3 ) @ Y )
% 5.25/5.50 = ( dvd_dvd_int @ X3 @ Y ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_dvd_iff
% 5.25/5.50 thf(fact_3955_minus__dvd__iff,axiom,
% 5.25/5.50 ! [X3: real,Y: real] :
% 5.25/5.50 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X3 ) @ Y )
% 5.25/5.50 = ( dvd_dvd_real @ X3 @ Y ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_dvd_iff
% 5.25/5.50 thf(fact_3956_minus__dvd__iff,axiom,
% 5.25/5.50 ! [X3: complex,Y: complex] :
% 5.25/5.50 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X3 ) @ Y )
% 5.25/5.50 = ( dvd_dvd_complex @ X3 @ Y ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_dvd_iff
% 5.25/5.50 thf(fact_3957_minus__dvd__iff,axiom,
% 5.25/5.50 ! [X3: code_integer,Y: code_integer] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X3 ) @ Y )
% 5.25/5.50 = ( dvd_dvd_Code_integer @ X3 @ Y ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_dvd_iff
% 5.25/5.50 thf(fact_3958_minus__dvd__iff,axiom,
% 5.25/5.50 ! [X3: rat,Y: rat] :
% 5.25/5.50 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X3 ) @ Y )
% 5.25/5.50 = ( dvd_dvd_rat @ X3 @ Y ) ) ).
% 5.25/5.50
% 5.25/5.50 % minus_dvd_iff
% 5.25/5.50 thf(fact_3959_dvd__minus__iff,axiom,
% 5.25/5.50 ! [X3: int,Y: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ X3 @ ( uminus_uminus_int @ Y ) )
% 5.25/5.50 = ( dvd_dvd_int @ X3 @ Y ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_minus_iff
% 5.25/5.50 thf(fact_3960_dvd__minus__iff,axiom,
% 5.25/5.50 ! [X3: real,Y: real] :
% 5.25/5.50 ( ( dvd_dvd_real @ X3 @ ( uminus_uminus_real @ Y ) )
% 5.25/5.50 = ( dvd_dvd_real @ X3 @ Y ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_minus_iff
% 5.25/5.50 thf(fact_3961_dvd__minus__iff,axiom,
% 5.25/5.50 ! [X3: complex,Y: complex] :
% 5.25/5.50 ( ( dvd_dvd_complex @ X3 @ ( uminus1482373934393186551omplex @ Y ) )
% 5.25/5.50 = ( dvd_dvd_complex @ X3 @ Y ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_minus_iff
% 5.25/5.50 thf(fact_3962_dvd__minus__iff,axiom,
% 5.25/5.50 ! [X3: code_integer,Y: code_integer] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ X3 @ ( uminus1351360451143612070nteger @ Y ) )
% 5.25/5.50 = ( dvd_dvd_Code_integer @ X3 @ Y ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_minus_iff
% 5.25/5.50 thf(fact_3963_dvd__minus__iff,axiom,
% 5.25/5.50 ! [X3: rat,Y: rat] :
% 5.25/5.50 ( ( dvd_dvd_rat @ X3 @ ( uminus_uminus_rat @ Y ) )
% 5.25/5.50 = ( dvd_dvd_rat @ X3 @ Y ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_minus_iff
% 5.25/5.50 thf(fact_3964_zero__less__diff,axiom,
% 5.25/5.50 ! [N: nat,M: nat] :
% 5.25/5.50 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 5.25/5.50 = ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.50
% 5.25/5.50 % zero_less_diff
% 5.25/5.50 thf(fact_3965_diff__is__0__eq,axiom,
% 5.25/5.50 ! [M: nat,N: nat] :
% 5.25/5.50 ( ( ( minus_minus_nat @ M @ N )
% 5.25/5.50 = zero_zero_nat )
% 5.25/5.50 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.50
% 5.25/5.50 % diff_is_0_eq
% 5.25/5.50 thf(fact_3966_diff__is__0__eq_H,axiom,
% 5.25/5.50 ! [M: nat,N: nat] :
% 5.25/5.50 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.50 => ( ( minus_minus_nat @ M @ N )
% 5.25/5.50 = zero_zero_nat ) ) ).
% 5.25/5.50
% 5.25/5.50 % diff_is_0_eq'
% 5.25/5.50 thf(fact_3967_mod__minus__minus,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.25/5.50 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_minus_minus
% 5.25/5.50 thf(fact_3968_mod__minus__minus,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.25/5.50 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_minus_minus
% 5.25/5.50 thf(fact_3969_Nat_Odiff__diff__right,axiom,
% 5.25/5.50 ! [K: nat,J2: nat,I2: nat] :
% 5.25/5.50 ( ( ord_less_eq_nat @ K @ J2 )
% 5.25/5.50 => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J2 @ K ) )
% 5.25/5.50 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % Nat.diff_diff_right
% 5.25/5.50 thf(fact_3970_Nat_Oadd__diff__assoc2,axiom,
% 5.25/5.50 ! [K: nat,J2: nat,I2: nat] :
% 5.25/5.50 ( ( ord_less_eq_nat @ K @ J2 )
% 5.25/5.50 => ( ( plus_plus_nat @ ( minus_minus_nat @ J2 @ K ) @ I2 )
% 5.25/5.50 = ( minus_minus_nat @ ( plus_plus_nat @ J2 @ I2 ) @ K ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % Nat.add_diff_assoc2
% 5.25/5.50 thf(fact_3971_Nat_Oadd__diff__assoc,axiom,
% 5.25/5.50 ! [K: nat,J2: nat,I2: nat] :
% 5.25/5.50 ( ( ord_less_eq_nat @ K @ J2 )
% 5.25/5.50 => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J2 @ K ) )
% 5.25/5.50 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % Nat.add_diff_assoc
% 5.25/5.50 thf(fact_3972_diff__Suc__1,axiom,
% 5.25/5.50 ! [N: nat] :
% 5.25/5.50 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 5.25/5.50 = N ) ).
% 5.25/5.50
% 5.25/5.50 % diff_Suc_1
% 5.25/5.50 thf(fact_3973_replicate__eq__replicate,axiom,
% 5.25/5.50 ! [M: nat,X3: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 5.25/5.50 ( ( ( replicate_VEBT_VEBT @ M @ X3 )
% 5.25/5.50 = ( replicate_VEBT_VEBT @ N @ Y ) )
% 5.25/5.50 = ( ( M = N )
% 5.25/5.50 & ( ( M != zero_zero_nat )
% 5.25/5.50 => ( X3 = Y ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % replicate_eq_replicate
% 5.25/5.50 thf(fact_3974_length__replicate,axiom,
% 5.25/5.50 ! [N: nat,X3: vEBT_VEBT] :
% 5.25/5.50 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X3 ) )
% 5.25/5.50 = N ) ).
% 5.25/5.50
% 5.25/5.50 % length_replicate
% 5.25/5.50 thf(fact_3975_length__replicate,axiom,
% 5.25/5.50 ! [N: nat,X3: $o] :
% 5.25/5.50 ( ( size_size_list_o @ ( replicate_o @ N @ X3 ) )
% 5.25/5.50 = N ) ).
% 5.25/5.50
% 5.25/5.50 % length_replicate
% 5.25/5.50 thf(fact_3976_length__replicate,axiom,
% 5.25/5.50 ! [N: nat,X3: nat] :
% 5.25/5.50 ( ( size_size_list_nat @ ( replicate_nat @ N @ X3 ) )
% 5.25/5.50 = N ) ).
% 5.25/5.50
% 5.25/5.50 % length_replicate
% 5.25/5.50 thf(fact_3977_length__replicate,axiom,
% 5.25/5.50 ! [N: nat,X3: int] :
% 5.25/5.50 ( ( size_size_list_int @ ( replicate_int @ N @ X3 ) )
% 5.25/5.50 = N ) ).
% 5.25/5.50
% 5.25/5.50 % length_replicate
% 5.25/5.50 thf(fact_3978_neg__less__eq__nonneg,axiom,
% 5.25/5.50 ! [A: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.25/5.50 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_less_eq_nonneg
% 5.25/5.50 thf(fact_3979_neg__less__eq__nonneg,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.25/5.50 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_less_eq_nonneg
% 5.25/5.50 thf(fact_3980_neg__less__eq__nonneg,axiom,
% 5.25/5.50 ! [A: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.25/5.50 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_less_eq_nonneg
% 5.25/5.50 thf(fact_3981_neg__less__eq__nonneg,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.25/5.50 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_less_eq_nonneg
% 5.25/5.50 thf(fact_3982_less__eq__neg__nonpos,axiom,
% 5.25/5.50 ! [A: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.25/5.50 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.25/5.50
% 5.25/5.50 % less_eq_neg_nonpos
% 5.25/5.50 thf(fact_3983_less__eq__neg__nonpos,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.25/5.50 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.25/5.50
% 5.25/5.50 % less_eq_neg_nonpos
% 5.25/5.50 thf(fact_3984_less__eq__neg__nonpos,axiom,
% 5.25/5.50 ! [A: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.25/5.50 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.50
% 5.25/5.50 % less_eq_neg_nonpos
% 5.25/5.50 thf(fact_3985_less__eq__neg__nonpos,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.25/5.50 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % less_eq_neg_nonpos
% 5.25/5.50 thf(fact_3986_neg__le__0__iff__le,axiom,
% 5.25/5.50 ! [A: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.25/5.50 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_le_0_iff_le
% 5.25/5.50 thf(fact_3987_neg__le__0__iff__le,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.25/5.50 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_le_0_iff_le
% 5.25/5.50 thf(fact_3988_neg__le__0__iff__le,axiom,
% 5.25/5.50 ! [A: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.25/5.50 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_le_0_iff_le
% 5.25/5.50 thf(fact_3989_neg__le__0__iff__le,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.25/5.50 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_le_0_iff_le
% 5.25/5.50 thf(fact_3990_neg__0__le__iff__le,axiom,
% 5.25/5.50 ! [A: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.25/5.50 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_0_le_iff_le
% 5.25/5.50 thf(fact_3991_neg__0__le__iff__le,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.25/5.50 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_0_le_iff_le
% 5.25/5.50 thf(fact_3992_neg__0__le__iff__le,axiom,
% 5.25/5.50 ! [A: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.25/5.50 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_0_le_iff_le
% 5.25/5.50 thf(fact_3993_neg__0__le__iff__le,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.25/5.50 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_0_le_iff_le
% 5.25/5.50 thf(fact_3994_neg__less__0__iff__less,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.25/5.50 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_less_0_iff_less
% 5.25/5.50 thf(fact_3995_neg__less__0__iff__less,axiom,
% 5.25/5.50 ! [A: real] :
% 5.25/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.25/5.50 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_less_0_iff_less
% 5.25/5.50 thf(fact_3996_neg__less__0__iff__less,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.25/5.50 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_less_0_iff_less
% 5.25/5.50 thf(fact_3997_neg__less__0__iff__less,axiom,
% 5.25/5.50 ! [A: rat] :
% 5.25/5.50 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.25/5.50 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_less_0_iff_less
% 5.25/5.50 thf(fact_3998_neg__0__less__iff__less,axiom,
% 5.25/5.50 ! [A: int] :
% 5.25/5.50 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.25/5.50 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_0_less_iff_less
% 5.25/5.50 thf(fact_3999_neg__0__less__iff__less,axiom,
% 5.25/5.50 ! [A: real] :
% 5.25/5.50 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.25/5.50 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_0_less_iff_less
% 5.25/5.50 thf(fact_4000_neg__0__less__iff__less,axiom,
% 5.25/5.50 ! [A: code_integer] :
% 5.25/5.50 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.25/5.51 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_0_less_iff_less
% 5.25/5.51 thf(fact_4001_neg__0__less__iff__less,axiom,
% 5.25/5.51 ! [A: rat] :
% 5.25/5.51 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.25/5.51 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_0_less_iff_less
% 5.25/5.51 thf(fact_4002_neg__less__pos,axiom,
% 5.25/5.51 ! [A: int] :
% 5.25/5.51 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.25/5.51 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_less_pos
% 5.25/5.51 thf(fact_4003_neg__less__pos,axiom,
% 5.25/5.51 ! [A: real] :
% 5.25/5.51 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.25/5.51 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_less_pos
% 5.25/5.51 thf(fact_4004_neg__less__pos,axiom,
% 5.25/5.51 ! [A: code_integer] :
% 5.25/5.51 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.25/5.51 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_less_pos
% 5.25/5.51 thf(fact_4005_neg__less__pos,axiom,
% 5.25/5.51 ! [A: rat] :
% 5.25/5.51 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.25/5.51 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_less_pos
% 5.25/5.51 thf(fact_4006_less__neg__neg,axiom,
% 5.25/5.51 ! [A: int] :
% 5.25/5.51 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.25/5.51 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_neg_neg
% 5.25/5.51 thf(fact_4007_less__neg__neg,axiom,
% 5.25/5.51 ! [A: real] :
% 5.25/5.51 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.25/5.51 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_neg_neg
% 5.25/5.51 thf(fact_4008_less__neg__neg,axiom,
% 5.25/5.51 ! [A: code_integer] :
% 5.25/5.51 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.25/5.51 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_neg_neg
% 5.25/5.51 thf(fact_4009_less__neg__neg,axiom,
% 5.25/5.51 ! [A: rat] :
% 5.25/5.51 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.25/5.51 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_neg_neg
% 5.25/5.51 thf(fact_4010_add_Oright__inverse,axiom,
% 5.25/5.51 ! [A: int] :
% 5.25/5.51 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.25/5.51 = zero_zero_int ) ).
% 5.25/5.51
% 5.25/5.51 % add.right_inverse
% 5.25/5.51 thf(fact_4011_add_Oright__inverse,axiom,
% 5.25/5.51 ! [A: real] :
% 5.25/5.51 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.25/5.51 = zero_zero_real ) ).
% 5.25/5.51
% 5.25/5.51 % add.right_inverse
% 5.25/5.51 thf(fact_4012_add_Oright__inverse,axiom,
% 5.25/5.51 ! [A: complex] :
% 5.25/5.51 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.25/5.51 = zero_zero_complex ) ).
% 5.25/5.51
% 5.25/5.51 % add.right_inverse
% 5.25/5.51 thf(fact_4013_add_Oright__inverse,axiom,
% 5.25/5.51 ! [A: code_integer] :
% 5.25/5.51 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.25/5.51 = zero_z3403309356797280102nteger ) ).
% 5.25/5.51
% 5.25/5.51 % add.right_inverse
% 5.25/5.51 thf(fact_4014_add_Oright__inverse,axiom,
% 5.25/5.51 ! [A: rat] :
% 5.25/5.51 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.25/5.51 = zero_zero_rat ) ).
% 5.25/5.51
% 5.25/5.51 % add.right_inverse
% 5.25/5.51 thf(fact_4015_ab__left__minus,axiom,
% 5.25/5.51 ! [A: int] :
% 5.25/5.51 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.25/5.51 = zero_zero_int ) ).
% 5.25/5.51
% 5.25/5.51 % ab_left_minus
% 5.25/5.51 thf(fact_4016_ab__left__minus,axiom,
% 5.25/5.51 ! [A: real] :
% 5.25/5.51 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.25/5.51 = zero_zero_real ) ).
% 5.25/5.51
% 5.25/5.51 % ab_left_minus
% 5.25/5.51 thf(fact_4017_ab__left__minus,axiom,
% 5.25/5.51 ! [A: complex] :
% 5.25/5.51 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.25/5.51 = zero_zero_complex ) ).
% 5.25/5.51
% 5.25/5.51 % ab_left_minus
% 5.25/5.51 thf(fact_4018_ab__left__minus,axiom,
% 5.25/5.51 ! [A: code_integer] :
% 5.25/5.51 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.25/5.51 = zero_z3403309356797280102nteger ) ).
% 5.25/5.51
% 5.25/5.51 % ab_left_minus
% 5.25/5.51 thf(fact_4019_ab__left__minus,axiom,
% 5.25/5.51 ! [A: rat] :
% 5.25/5.51 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.25/5.51 = zero_zero_rat ) ).
% 5.25/5.51
% 5.25/5.51 % ab_left_minus
% 5.25/5.51 thf(fact_4020_diff__0,axiom,
% 5.25/5.51 ! [A: int] :
% 5.25/5.51 ( ( minus_minus_int @ zero_zero_int @ A )
% 5.25/5.51 = ( uminus_uminus_int @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_0
% 5.25/5.51 thf(fact_4021_diff__0,axiom,
% 5.25/5.51 ! [A: real] :
% 5.25/5.51 ( ( minus_minus_real @ zero_zero_real @ A )
% 5.25/5.51 = ( uminus_uminus_real @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_0
% 5.25/5.51 thf(fact_4022_diff__0,axiom,
% 5.25/5.51 ! [A: complex] :
% 5.25/5.51 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_0
% 5.25/5.51 thf(fact_4023_diff__0,axiom,
% 5.25/5.51 ! [A: code_integer] :
% 5.25/5.51 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_0
% 5.25/5.51 thf(fact_4024_diff__0,axiom,
% 5.25/5.51 ! [A: rat] :
% 5.25/5.51 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 5.25/5.51 = ( uminus_uminus_rat @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_0
% 5.25/5.51 thf(fact_4025_add__neg__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.51 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_simps(3)
% 5.25/5.51 thf(fact_4026_add__neg__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.25/5.51 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_simps(3)
% 5.25/5.51 thf(fact_4027_add__neg__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_simps(3)
% 5.25/5.51 thf(fact_4028_add__neg__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_simps(3)
% 5.25/5.51 thf(fact_4029_add__neg__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.25/5.51 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_simps(3)
% 5.25/5.51 thf(fact_4030_mult__minus1__right,axiom,
% 5.25/5.51 ! [Z: int] :
% 5.25/5.51 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.51 = ( uminus_uminus_int @ Z ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_minus1_right
% 5.25/5.51 thf(fact_4031_mult__minus1__right,axiom,
% 5.25/5.51 ! [Z: real] :
% 5.25/5.51 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.51 = ( uminus_uminus_real @ Z ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_minus1_right
% 5.25/5.51 thf(fact_4032_mult__minus1__right,axiom,
% 5.25/5.51 ! [Z: complex] :
% 5.25/5.51 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_minus1_right
% 5.25/5.51 thf(fact_4033_mult__minus1__right,axiom,
% 5.25/5.51 ! [Z: code_integer] :
% 5.25/5.51 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_minus1_right
% 5.25/5.51 thf(fact_4034_mult__minus1__right,axiom,
% 5.25/5.51 ! [Z: rat] :
% 5.25/5.51 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.51 = ( uminus_uminus_rat @ Z ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_minus1_right
% 5.25/5.51 thf(fact_4035_mult__minus1,axiom,
% 5.25/5.51 ! [Z: int] :
% 5.25/5.51 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 5.25/5.51 = ( uminus_uminus_int @ Z ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_minus1
% 5.25/5.51 thf(fact_4036_mult__minus1,axiom,
% 5.25/5.51 ! [Z: real] :
% 5.25/5.51 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 5.25/5.51 = ( uminus_uminus_real @ Z ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_minus1
% 5.25/5.51 thf(fact_4037_mult__minus1,axiom,
% 5.25/5.51 ! [Z: complex] :
% 5.25/5.51 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_minus1
% 5.25/5.51 thf(fact_4038_mult__minus1,axiom,
% 5.25/5.51 ! [Z: code_integer] :
% 5.25/5.51 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_minus1
% 5.25/5.51 thf(fact_4039_mult__minus1,axiom,
% 5.25/5.51 ! [Z: rat] :
% 5.25/5.51 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 5.25/5.51 = ( uminus_uminus_rat @ Z ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_minus1
% 5.25/5.51 thf(fact_4040_diff__minus__eq__add,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.25/5.51 = ( plus_plus_int @ A @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_minus_eq_add
% 5.25/5.51 thf(fact_4041_diff__minus__eq__add,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.25/5.51 = ( plus_plus_real @ A @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_minus_eq_add
% 5.25/5.51 thf(fact_4042_diff__minus__eq__add,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.25/5.51 = ( plus_plus_complex @ A @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_minus_eq_add
% 5.25/5.51 thf(fact_4043_diff__minus__eq__add,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.25/5.51 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_minus_eq_add
% 5.25/5.51 thf(fact_4044_diff__minus__eq__add,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.25/5.51 = ( plus_plus_rat @ A @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_minus_eq_add
% 5.25/5.51 thf(fact_4045_uminus__add__conv__diff,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.25/5.51 = ( minus_minus_int @ B @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % uminus_add_conv_diff
% 5.25/5.51 thf(fact_4046_uminus__add__conv__diff,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.25/5.51 = ( minus_minus_real @ B @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % uminus_add_conv_diff
% 5.25/5.51 thf(fact_4047_uminus__add__conv__diff,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.25/5.51 = ( minus_minus_complex @ B @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % uminus_add_conv_diff
% 5.25/5.51 thf(fact_4048_uminus__add__conv__diff,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.25/5.51 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % uminus_add_conv_diff
% 5.25/5.51 thf(fact_4049_uminus__add__conv__diff,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.25/5.51 = ( minus_minus_rat @ B @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % uminus_add_conv_diff
% 5.25/5.51 thf(fact_4050_div__minus1__right,axiom,
% 5.25/5.51 ! [A: int] :
% 5.25/5.51 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.51 = ( uminus_uminus_int @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % div_minus1_right
% 5.25/5.51 thf(fact_4051_div__minus1__right,axiom,
% 5.25/5.51 ! [A: code_integer] :
% 5.25/5.51 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % div_minus1_right
% 5.25/5.51 thf(fact_4052_divide__minus1,axiom,
% 5.25/5.51 ! [X3: real] :
% 5.25/5.51 ( ( divide_divide_real @ X3 @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.51 = ( uminus_uminus_real @ X3 ) ) ).
% 5.25/5.51
% 5.25/5.51 % divide_minus1
% 5.25/5.51 thf(fact_4053_divide__minus1,axiom,
% 5.25/5.51 ! [X3: complex] :
% 5.25/5.51 ( ( divide1717551699836669952omplex @ X3 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ X3 ) ) ).
% 5.25/5.51
% 5.25/5.51 % divide_minus1
% 5.25/5.51 thf(fact_4054_divide__minus1,axiom,
% 5.25/5.51 ! [X3: rat] :
% 5.25/5.51 ( ( divide_divide_rat @ X3 @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.51 = ( uminus_uminus_rat @ X3 ) ) ).
% 5.25/5.51
% 5.25/5.51 % divide_minus1
% 5.25/5.51 thf(fact_4055_Suc__pred,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.51 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.25/5.51 = N ) ) ).
% 5.25/5.51
% 5.25/5.51 % Suc_pred
% 5.25/5.51 thf(fact_4056_minus__mod__self1,axiom,
% 5.25/5.51 ! [B: int,A: int] :
% 5.25/5.51 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 5.25/5.51 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_mod_self1
% 5.25/5.51 thf(fact_4057_minus__mod__self1,axiom,
% 5.25/5.51 ! [B: code_integer,A: code_integer] :
% 5.25/5.51 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 5.25/5.51 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_mod_self1
% 5.25/5.51 thf(fact_4058_diff__Suc__diff__eq2,axiom,
% 5.25/5.51 ! [K: nat,J2: nat,I2: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ K @ J2 )
% 5.25/5.51 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J2 @ K ) ) @ I2 )
% 5.25/5.51 = ( minus_minus_nat @ ( suc @ J2 ) @ ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_Suc_diff_eq2
% 5.25/5.51 thf(fact_4059_diff__Suc__diff__eq1,axiom,
% 5.25/5.51 ! [K: nat,J2: nat,I2: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ K @ J2 )
% 5.25/5.51 => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J2 @ K ) ) )
% 5.25/5.51 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ ( suc @ J2 ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_Suc_diff_eq1
% 5.25/5.51 thf(fact_4060_signed__take__bit__of__minus__1,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.51
% 5.25/5.51 % signed_take_bit_of_minus_1
% 5.25/5.51 thf(fact_4061_signed__take__bit__of__minus__1,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.51 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.51
% 5.25/5.51 % signed_take_bit_of_minus_1
% 5.25/5.51 thf(fact_4062_in__set__replicate,axiom,
% 5.25/5.51 ! [X3: real,N: nat,Y: real] :
% 5.25/5.51 ( ( member_real @ X3 @ ( set_real2 @ ( replicate_real @ N @ Y ) ) )
% 5.25/5.51 = ( ( X3 = Y )
% 5.25/5.51 & ( N != zero_zero_nat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % in_set_replicate
% 5.25/5.51 thf(fact_4063_in__set__replicate,axiom,
% 5.25/5.51 ! [X3: complex,N: nat,Y: complex] :
% 5.25/5.51 ( ( member_complex @ X3 @ ( set_complex2 @ ( replicate_complex @ N @ Y ) ) )
% 5.25/5.51 = ( ( X3 = Y )
% 5.25/5.51 & ( N != zero_zero_nat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % in_set_replicate
% 5.25/5.51 thf(fact_4064_in__set__replicate,axiom,
% 5.25/5.51 ! [X3: product_prod_nat_nat,N: nat,Y: product_prod_nat_nat] :
% 5.25/5.51 ( ( member8440522571783428010at_nat @ X3 @ ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N @ Y ) ) )
% 5.25/5.51 = ( ( X3 = Y )
% 5.25/5.51 & ( N != zero_zero_nat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % in_set_replicate
% 5.25/5.51 thf(fact_4065_in__set__replicate,axiom,
% 5.25/5.51 ! [X3: int,N: nat,Y: int] :
% 5.25/5.51 ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N @ Y ) ) )
% 5.25/5.51 = ( ( X3 = Y )
% 5.25/5.51 & ( N != zero_zero_nat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % in_set_replicate
% 5.25/5.51 thf(fact_4066_in__set__replicate,axiom,
% 5.25/5.51 ! [X3: nat,N: nat,Y: nat] :
% 5.25/5.51 ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ Y ) ) )
% 5.25/5.51 = ( ( X3 = Y )
% 5.25/5.51 & ( N != zero_zero_nat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % in_set_replicate
% 5.25/5.51 thf(fact_4067_in__set__replicate,axiom,
% 5.25/5.51 ! [X3: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 5.25/5.51 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y ) ) )
% 5.25/5.51 = ( ( X3 = Y )
% 5.25/5.51 & ( N != zero_zero_nat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % in_set_replicate
% 5.25/5.51 thf(fact_4068_Bex__set__replicate,axiom,
% 5.25/5.51 ! [N: nat,A: int,P: int > $o] :
% 5.25/5.51 ( ( ? [X2: int] :
% 5.25/5.51 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.25/5.51 & ( P @ X2 ) ) )
% 5.25/5.51 = ( ( P @ A )
% 5.25/5.51 & ( N != zero_zero_nat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Bex_set_replicate
% 5.25/5.51 thf(fact_4069_Bex__set__replicate,axiom,
% 5.25/5.51 ! [N: nat,A: nat,P: nat > $o] :
% 5.25/5.51 ( ( ? [X2: nat] :
% 5.25/5.51 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.25/5.51 & ( P @ X2 ) ) )
% 5.25/5.51 = ( ( P @ A )
% 5.25/5.51 & ( N != zero_zero_nat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Bex_set_replicate
% 5.25/5.51 thf(fact_4070_Bex__set__replicate,axiom,
% 5.25/5.51 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.25/5.51 ( ( ? [X2: vEBT_VEBT] :
% 5.25/5.51 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.25/5.51 & ( P @ X2 ) ) )
% 5.25/5.51 = ( ( P @ A )
% 5.25/5.51 & ( N != zero_zero_nat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Bex_set_replicate
% 5.25/5.51 thf(fact_4071_Ball__set__replicate,axiom,
% 5.25/5.51 ! [N: nat,A: int,P: int > $o] :
% 5.25/5.51 ( ( ! [X2: int] :
% 5.25/5.51 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.25/5.51 => ( P @ X2 ) ) )
% 5.25/5.51 = ( ( P @ A )
% 5.25/5.51 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Ball_set_replicate
% 5.25/5.51 thf(fact_4072_Ball__set__replicate,axiom,
% 5.25/5.51 ! [N: nat,A: nat,P: nat > $o] :
% 5.25/5.51 ( ( ! [X2: nat] :
% 5.25/5.51 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.25/5.51 => ( P @ X2 ) ) )
% 5.25/5.51 = ( ( P @ A )
% 5.25/5.51 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Ball_set_replicate
% 5.25/5.51 thf(fact_4073_Ball__set__replicate,axiom,
% 5.25/5.51 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.25/5.51 ( ( ! [X2: vEBT_VEBT] :
% 5.25/5.51 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.25/5.51 => ( P @ X2 ) ) )
% 5.25/5.51 = ( ( P @ A )
% 5.25/5.51 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Ball_set_replicate
% 5.25/5.51 thf(fact_4074_pred__numeral__simps_I1_J,axiom,
% 5.25/5.51 ( ( pred_numeral @ one )
% 5.25/5.51 = zero_zero_nat ) ).
% 5.25/5.51
% 5.25/5.51 % pred_numeral_simps(1)
% 5.25/5.51 thf(fact_4075_diff__Suc__numeral,axiom,
% 5.25/5.51 ! [N: nat,K: num] :
% 5.25/5.51 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.25/5.51 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_Suc_numeral
% 5.25/5.51 thf(fact_4076_diff__numeral__Suc,axiom,
% 5.25/5.51 ! [K: num,N: nat] :
% 5.25/5.51 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.25/5.51 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_Suc
% 5.25/5.51 thf(fact_4077_eq__numeral__Suc,axiom,
% 5.25/5.51 ! [K: num,N: nat] :
% 5.25/5.51 ( ( ( numeral_numeral_nat @ K )
% 5.25/5.51 = ( suc @ N ) )
% 5.25/5.51 = ( ( pred_numeral @ K )
% 5.25/5.51 = N ) ) ).
% 5.25/5.51
% 5.25/5.51 % eq_numeral_Suc
% 5.25/5.51 thf(fact_4078_Suc__eq__numeral,axiom,
% 5.25/5.51 ! [N: nat,K: num] :
% 5.25/5.51 ( ( ( suc @ N )
% 5.25/5.51 = ( numeral_numeral_nat @ K ) )
% 5.25/5.51 = ( N
% 5.25/5.51 = ( pred_numeral @ K ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Suc_eq_numeral
% 5.25/5.51 thf(fact_4079_nth__replicate,axiom,
% 5.25/5.51 ! [I2: nat,N: nat,X3: nat] :
% 5.25/5.51 ( ( ord_less_nat @ I2 @ N )
% 5.25/5.51 => ( ( nth_nat @ ( replicate_nat @ N @ X3 ) @ I2 )
% 5.25/5.51 = X3 ) ) ).
% 5.25/5.51
% 5.25/5.51 % nth_replicate
% 5.25/5.51 thf(fact_4080_nth__replicate,axiom,
% 5.25/5.51 ! [I2: nat,N: nat,X3: int] :
% 5.25/5.51 ( ( ord_less_nat @ I2 @ N )
% 5.25/5.51 => ( ( nth_int @ ( replicate_int @ N @ X3 ) @ I2 )
% 5.25/5.51 = X3 ) ) ).
% 5.25/5.51
% 5.25/5.51 % nth_replicate
% 5.25/5.51 thf(fact_4081_nth__replicate,axiom,
% 5.25/5.51 ! [I2: nat,N: nat,X3: vEBT_VEBT] :
% 5.25/5.51 ( ( ord_less_nat @ I2 @ N )
% 5.25/5.51 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X3 ) @ I2 )
% 5.25/5.51 = X3 ) ) ).
% 5.25/5.51
% 5.25/5.51 % nth_replicate
% 5.25/5.51 thf(fact_4082_dbl__simps_I1_J,axiom,
% 5.25/5.51 ! [K: num] :
% 5.25/5.51 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.25/5.51 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_simps(1)
% 5.25/5.51 thf(fact_4083_dbl__simps_I1_J,axiom,
% 5.25/5.51 ! [K: num] :
% 5.25/5.51 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.25/5.51 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_simps(1)
% 5.25/5.51 thf(fact_4084_dbl__simps_I1_J,axiom,
% 5.25/5.51 ! [K: num] :
% 5.25/5.51 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_simps(1)
% 5.25/5.51 thf(fact_4085_dbl__simps_I1_J,axiom,
% 5.25/5.51 ! [K: num] :
% 5.25/5.51 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_simps(1)
% 5.25/5.51 thf(fact_4086_dbl__simps_I1_J,axiom,
% 5.25/5.51 ! [K: num] :
% 5.25/5.51 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.25/5.51 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_simps(1)
% 5.25/5.51 thf(fact_4087_dbl__inc__simps_I2_J,axiom,
% 5.25/5.51 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.25/5.51 = one_one_complex ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_inc_simps(2)
% 5.25/5.51 thf(fact_4088_dbl__inc__simps_I2_J,axiom,
% 5.25/5.51 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.25/5.51 = one_one_real ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_inc_simps(2)
% 5.25/5.51 thf(fact_4089_dbl__inc__simps_I2_J,axiom,
% 5.25/5.51 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.25/5.51 = one_one_rat ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_inc_simps(2)
% 5.25/5.51 thf(fact_4090_dbl__inc__simps_I2_J,axiom,
% 5.25/5.51 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.25/5.51 = one_one_int ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_inc_simps(2)
% 5.25/5.51 thf(fact_4091_dbl__inc__simps_I4_J,axiom,
% 5.25/5.51 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.51 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_inc_simps(4)
% 5.25/5.51 thf(fact_4092_dbl__inc__simps_I4_J,axiom,
% 5.25/5.51 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.51 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_inc_simps(4)
% 5.25/5.51 thf(fact_4093_dbl__inc__simps_I4_J,axiom,
% 5.25/5.51 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_inc_simps(4)
% 5.25/5.51 thf(fact_4094_dbl__inc__simps_I4_J,axiom,
% 5.25/5.51 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_inc_simps(4)
% 5.25/5.51 thf(fact_4095_dbl__inc__simps_I4_J,axiom,
% 5.25/5.51 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.51 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_inc_simps(4)
% 5.25/5.51 thf(fact_4096_dbl__inc__simps_I5_J,axiom,
% 5.25/5.51 ! [K: num] :
% 5.25/5.51 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.25/5.51 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_inc_simps(5)
% 5.25/5.51 thf(fact_4097_dbl__inc__simps_I5_J,axiom,
% 5.25/5.51 ! [K: num] :
% 5.25/5.51 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.25/5.51 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_inc_simps(5)
% 5.25/5.51 thf(fact_4098_dbl__inc__simps_I5_J,axiom,
% 5.25/5.51 ! [K: num] :
% 5.25/5.51 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 5.25/5.51 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_inc_simps(5)
% 5.25/5.51 thf(fact_4099_dbl__inc__simps_I5_J,axiom,
% 5.25/5.51 ! [K: num] :
% 5.25/5.51 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.25/5.51 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_inc_simps(5)
% 5.25/5.51 thf(fact_4100_add__neg__numeral__special_I7_J,axiom,
% 5.25/5.51 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.51 = zero_zero_int ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(7)
% 5.25/5.51 thf(fact_4101_add__neg__numeral__special_I7_J,axiom,
% 5.25/5.51 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.51 = zero_zero_real ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(7)
% 5.25/5.51 thf(fact_4102_add__neg__numeral__special_I7_J,axiom,
% 5.25/5.51 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.25/5.51 = zero_zero_complex ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(7)
% 5.25/5.51 thf(fact_4103_add__neg__numeral__special_I7_J,axiom,
% 5.25/5.51 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.51 = zero_z3403309356797280102nteger ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(7)
% 5.25/5.51 thf(fact_4104_add__neg__numeral__special_I7_J,axiom,
% 5.25/5.51 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.51 = zero_zero_rat ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(7)
% 5.25/5.51 thf(fact_4105_add__neg__numeral__special_I8_J,axiom,
% 5.25/5.51 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.25/5.51 = zero_zero_int ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(8)
% 5.25/5.51 thf(fact_4106_add__neg__numeral__special_I8_J,axiom,
% 5.25/5.51 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.25/5.51 = zero_zero_real ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(8)
% 5.25/5.51 thf(fact_4107_add__neg__numeral__special_I8_J,axiom,
% 5.25/5.51 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.25/5.51 = zero_zero_complex ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(8)
% 5.25/5.51 thf(fact_4108_add__neg__numeral__special_I8_J,axiom,
% 5.25/5.51 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.25/5.51 = zero_z3403309356797280102nteger ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(8)
% 5.25/5.51 thf(fact_4109_add__neg__numeral__special_I8_J,axiom,
% 5.25/5.51 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.25/5.51 = zero_zero_rat ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(8)
% 5.25/5.51 thf(fact_4110_diff__numeral__special_I12_J,axiom,
% 5.25/5.51 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.51 = zero_zero_int ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(12)
% 5.25/5.51 thf(fact_4111_diff__numeral__special_I12_J,axiom,
% 5.25/5.51 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.51 = zero_zero_real ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(12)
% 5.25/5.51 thf(fact_4112_diff__numeral__special_I12_J,axiom,
% 5.25/5.51 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.25/5.51 = zero_zero_complex ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(12)
% 5.25/5.51 thf(fact_4113_diff__numeral__special_I12_J,axiom,
% 5.25/5.51 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.51 = zero_z3403309356797280102nteger ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(12)
% 5.25/5.51 thf(fact_4114_diff__numeral__special_I12_J,axiom,
% 5.25/5.51 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.51 = zero_zero_rat ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(12)
% 5.25/5.51 thf(fact_4115_neg__one__eq__numeral__iff,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( ( uminus_uminus_int @ one_one_int )
% 5.25/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.51 = ( N = one ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_eq_numeral_iff
% 5.25/5.51 thf(fact_4116_neg__one__eq__numeral__iff,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( ( uminus_uminus_real @ one_one_real )
% 5.25/5.51 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.25/5.51 = ( N = one ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_eq_numeral_iff
% 5.25/5.51 thf(fact_4117_neg__one__eq__numeral__iff,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.25/5.51 = ( N = one ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_eq_numeral_iff
% 5.25/5.51 thf(fact_4118_neg__one__eq__numeral__iff,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.25/5.51 = ( N = one ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_eq_numeral_iff
% 5.25/5.51 thf(fact_4119_neg__one__eq__numeral__iff,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.25/5.51 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.25/5.51 = ( N = one ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_eq_numeral_iff
% 5.25/5.51 thf(fact_4120_numeral__eq__neg__one__iff,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 5.25/5.51 = ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.51 = ( N = one ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_eq_neg_one_iff
% 5.25/5.51 thf(fact_4121_numeral__eq__neg__one__iff,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 5.25/5.51 = ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.51 = ( N = one ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_eq_neg_one_iff
% 5.25/5.51 thf(fact_4122_numeral__eq__neg__one__iff,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.25/5.51 = ( N = one ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_eq_neg_one_iff
% 5.25/5.51 thf(fact_4123_numeral__eq__neg__one__iff,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.51 = ( N = one ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_eq_neg_one_iff
% 5.25/5.51 thf(fact_4124_numeral__eq__neg__one__iff,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 5.25/5.51 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.51 = ( N = one ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_eq_neg_one_iff
% 5.25/5.51 thf(fact_4125_minus__one__mult__self,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 5.25/5.51 = one_one_int ) ).
% 5.25/5.51
% 5.25/5.51 % minus_one_mult_self
% 5.25/5.51 thf(fact_4126_minus__one__mult__self,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 5.25/5.51 = one_one_real ) ).
% 5.25/5.51
% 5.25/5.51 % minus_one_mult_self
% 5.25/5.51 thf(fact_4127_minus__one__mult__self,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 5.25/5.51 = one_one_complex ) ).
% 5.25/5.51
% 5.25/5.51 % minus_one_mult_self
% 5.25/5.51 thf(fact_4128_minus__one__mult__self,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 5.25/5.51 = one_one_Code_integer ) ).
% 5.25/5.51
% 5.25/5.51 % minus_one_mult_self
% 5.25/5.51 thf(fact_4129_minus__one__mult__self,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 5.25/5.51 = one_one_rat ) ).
% 5.25/5.51
% 5.25/5.51 % minus_one_mult_self
% 5.25/5.51 thf(fact_4130_left__minus__one__mult__self,axiom,
% 5.25/5.51 ! [N: nat,A: int] :
% 5.25/5.51 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 5.25/5.51 = A ) ).
% 5.25/5.51
% 5.25/5.51 % left_minus_one_mult_self
% 5.25/5.51 thf(fact_4131_left__minus__one__mult__self,axiom,
% 5.25/5.51 ! [N: nat,A: real] :
% 5.25/5.51 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ A ) )
% 5.25/5.51 = A ) ).
% 5.25/5.51
% 5.25/5.51 % left_minus_one_mult_self
% 5.25/5.51 thf(fact_4132_left__minus__one__mult__self,axiom,
% 5.25/5.51 ! [N: nat,A: complex] :
% 5.25/5.51 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 5.25/5.51 = A ) ).
% 5.25/5.51
% 5.25/5.51 % left_minus_one_mult_self
% 5.25/5.51 thf(fact_4133_left__minus__one__mult__self,axiom,
% 5.25/5.51 ! [N: nat,A: code_integer] :
% 5.25/5.51 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 5.25/5.51 = A ) ).
% 5.25/5.51
% 5.25/5.51 % left_minus_one_mult_self
% 5.25/5.51 thf(fact_4134_left__minus__one__mult__self,axiom,
% 5.25/5.51 ! [N: nat,A: rat] :
% 5.25/5.51 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 5.25/5.51 = A ) ).
% 5.25/5.51
% 5.25/5.51 % left_minus_one_mult_self
% 5.25/5.51 thf(fact_4135_mod__minus1__right,axiom,
% 5.25/5.51 ! [A: int] :
% 5.25/5.51 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.51 = zero_zero_int ) ).
% 5.25/5.51
% 5.25/5.51 % mod_minus1_right
% 5.25/5.51 thf(fact_4136_mod__minus1__right,axiom,
% 5.25/5.51 ! [A: code_integer] :
% 5.25/5.51 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.51 = zero_z3403309356797280102nteger ) ).
% 5.25/5.51
% 5.25/5.51 % mod_minus1_right
% 5.25/5.51 thf(fact_4137_max__number__of_I4_J,axiom,
% 5.25/5.51 ! [U: num,V: num] :
% 5.25/5.51 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.25/5.51 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.25/5.51 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.25/5.51 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.25/5.51 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.25/5.51 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % max_number_of(4)
% 5.25/5.51 thf(fact_4138_max__number__of_I4_J,axiom,
% 5.25/5.51 ! [U: num,V: num] :
% 5.25/5.51 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.25/5.51 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.25/5.51 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.25/5.51 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % max_number_of(4)
% 5.25/5.51 thf(fact_4139_max__number__of_I4_J,axiom,
% 5.25/5.51 ! [U: num,V: num] :
% 5.25/5.51 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.25/5.51 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.25/5.51 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.25/5.51 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.25/5.51 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.25/5.51 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % max_number_of(4)
% 5.25/5.51 thf(fact_4140_max__number__of_I4_J,axiom,
% 5.25/5.51 ! [U: num,V: num] :
% 5.25/5.51 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.25/5.51 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.25/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.25/5.51 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.25/5.51 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.25/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % max_number_of(4)
% 5.25/5.51 thf(fact_4141_max__number__of_I3_J,axiom,
% 5.25/5.51 ! [U: num,V: num] :
% 5.25/5.51 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.25/5.51 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.25/5.51 = ( numeral_numeral_real @ V ) ) )
% 5.25/5.51 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.25/5.51 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.25/5.51 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % max_number_of(3)
% 5.25/5.51 thf(fact_4142_max__number__of_I3_J,axiom,
% 5.25/5.51 ! [U: num,V: num] :
% 5.25/5.51 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.25/5.51 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.25/5.51 = ( numera6620942414471956472nteger @ V ) ) )
% 5.25/5.51 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.25/5.51 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % max_number_of(3)
% 5.25/5.51 thf(fact_4143_max__number__of_I3_J,axiom,
% 5.25/5.51 ! [U: num,V: num] :
% 5.25/5.51 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.25/5.51 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.25/5.51 = ( numeral_numeral_rat @ V ) ) )
% 5.25/5.51 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.25/5.51 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.25/5.51 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % max_number_of(3)
% 5.25/5.51 thf(fact_4144_max__number__of_I3_J,axiom,
% 5.25/5.51 ! [U: num,V: num] :
% 5.25/5.51 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.25/5.51 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.25/5.51 = ( numeral_numeral_int @ V ) ) )
% 5.25/5.51 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.25/5.51 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.25/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % max_number_of(3)
% 5.25/5.51 thf(fact_4145_max__number__of_I2_J,axiom,
% 5.25/5.51 ! [U: num,V: num] :
% 5.25/5.51 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.25/5.51 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.25/5.51 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.25/5.51 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.25/5.51 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.25/5.51 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % max_number_of(2)
% 5.25/5.51 thf(fact_4146_max__number__of_I2_J,axiom,
% 5.25/5.51 ! [U: num,V: num] :
% 5.25/5.51 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.25/5.51 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.25/5.51 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.25/5.51 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.25/5.51 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % max_number_of(2)
% 5.25/5.51 thf(fact_4147_max__number__of_I2_J,axiom,
% 5.25/5.51 ! [U: num,V: num] :
% 5.25/5.51 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.25/5.51 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.25/5.51 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.25/5.51 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.25/5.51 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.25/5.51 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % max_number_of(2)
% 5.25/5.51 thf(fact_4148_max__number__of_I2_J,axiom,
% 5.25/5.51 ! [U: num,V: num] :
% 5.25/5.51 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.25/5.51 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.25/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.25/5.51 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.25/5.51 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.25/5.51 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % max_number_of(2)
% 5.25/5.51 thf(fact_4149_Suc__diff__1,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.51 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.25/5.51 = N ) ) ).
% 5.25/5.51
% 5.25/5.51 % Suc_diff_1
% 5.25/5.51 thf(fact_4150_semiring__norm_I168_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: int] :
% 5.25/5.51 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.25/5.51 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(168)
% 5.25/5.51 thf(fact_4151_semiring__norm_I168_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: real] :
% 5.25/5.51 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.25/5.51 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(168)
% 5.25/5.51 thf(fact_4152_semiring__norm_I168_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: complex] :
% 5.25/5.51 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.25/5.51 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(168)
% 5.25/5.51 thf(fact_4153_semiring__norm_I168_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: code_integer] :
% 5.25/5.51 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.25/5.51 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(168)
% 5.25/5.51 thf(fact_4154_semiring__norm_I168_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: rat] :
% 5.25/5.51 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.25/5.51 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(168)
% 5.25/5.51 thf(fact_4155_diff__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_simps(3)
% 5.25/5.51 thf(fact_4156_diff__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.25/5.51 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_simps(3)
% 5.25/5.51 thf(fact_4157_diff__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_simps(3)
% 5.25/5.51 thf(fact_4158_diff__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_simps(3)
% 5.25/5.51 thf(fact_4159_diff__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.25/5.51 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_simps(3)
% 5.25/5.51 thf(fact_4160_diff__numeral__simps_I2_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.51 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_simps(2)
% 5.25/5.51 thf(fact_4161_diff__numeral__simps_I2_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.25/5.51 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_simps(2)
% 5.25/5.51 thf(fact_4162_diff__numeral__simps_I2_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.25/5.51 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_simps(2)
% 5.25/5.51 thf(fact_4163_diff__numeral__simps_I2_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.25/5.51 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_simps(2)
% 5.25/5.51 thf(fact_4164_diff__numeral__simps_I2_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.25/5.51 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_simps(2)
% 5.25/5.51 thf(fact_4165_semiring__norm_I172_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: int] :
% 5.25/5.51 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.25/5.51 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(172)
% 5.25/5.51 thf(fact_4166_semiring__norm_I172_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: real] :
% 5.25/5.51 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.25/5.51 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(172)
% 5.25/5.51 thf(fact_4167_semiring__norm_I172_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: complex] :
% 5.25/5.51 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.25/5.51 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(172)
% 5.25/5.51 thf(fact_4168_semiring__norm_I172_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: code_integer] :
% 5.25/5.51 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.25/5.51 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(172)
% 5.25/5.51 thf(fact_4169_semiring__norm_I172_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: rat] :
% 5.25/5.51 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.25/5.51 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(172)
% 5.25/5.51 thf(fact_4170_semiring__norm_I171_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: int] :
% 5.25/5.51 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.25/5.51 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(171)
% 5.25/5.51 thf(fact_4171_semiring__norm_I171_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: real] :
% 5.25/5.51 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.25/5.51 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(171)
% 5.25/5.51 thf(fact_4172_semiring__norm_I171_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: complex] :
% 5.25/5.51 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.25/5.51 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(171)
% 5.25/5.51 thf(fact_4173_semiring__norm_I171_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: code_integer] :
% 5.25/5.51 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.25/5.51 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(171)
% 5.25/5.51 thf(fact_4174_semiring__norm_I171_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: rat] :
% 5.25/5.51 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.25/5.51 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(171)
% 5.25/5.51 thf(fact_4175_semiring__norm_I170_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: int] :
% 5.25/5.51 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 5.25/5.51 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(170)
% 5.25/5.51 thf(fact_4176_semiring__norm_I170_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: real] :
% 5.25/5.51 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y ) )
% 5.25/5.51 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(170)
% 5.25/5.51 thf(fact_4177_semiring__norm_I170_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: complex] :
% 5.25/5.51 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y ) )
% 5.25/5.51 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(170)
% 5.25/5.51 thf(fact_4178_semiring__norm_I170_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: code_integer] :
% 5.25/5.51 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 5.25/5.51 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(170)
% 5.25/5.51 thf(fact_4179_semiring__norm_I170_J,axiom,
% 5.25/5.51 ! [V: num,W: num,Y: rat] :
% 5.25/5.51 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 5.25/5.51 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.25/5.51
% 5.25/5.51 % semiring_norm(170)
% 5.25/5.51 thf(fact_4180_mult__neg__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(3)
% 5.25/5.51 thf(fact_4181_mult__neg__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.25/5.51 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(3)
% 5.25/5.51 thf(fact_4182_mult__neg__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(3)
% 5.25/5.51 thf(fact_4183_mult__neg__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(3)
% 5.25/5.51 thf(fact_4184_mult__neg__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.25/5.51 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(3)
% 5.25/5.51 thf(fact_4185_mult__neg__numeral__simps_I2_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(2)
% 5.25/5.51 thf(fact_4186_mult__neg__numeral__simps_I2_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.25/5.51 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(2)
% 5.25/5.51 thf(fact_4187_mult__neg__numeral__simps_I2_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(2)
% 5.25/5.51 thf(fact_4188_mult__neg__numeral__simps_I2_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(2)
% 5.25/5.51 thf(fact_4189_mult__neg__numeral__simps_I2_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.25/5.51 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(2)
% 5.25/5.51 thf(fact_4190_mult__neg__numeral__simps_I1_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.51 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(1)
% 5.25/5.51 thf(fact_4191_mult__neg__numeral__simps_I1_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.25/5.51 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(1)
% 5.25/5.51 thf(fact_4192_mult__neg__numeral__simps_I1_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.25/5.51 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(1)
% 5.25/5.51 thf(fact_4193_mult__neg__numeral__simps_I1_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.25/5.51 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(1)
% 5.25/5.51 thf(fact_4194_mult__neg__numeral__simps_I1_J,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.25/5.51 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mult_neg_numeral_simps(1)
% 5.25/5.51 thf(fact_4195_less__Suc__numeral,axiom,
% 5.25/5.51 ! [N: nat,K: num] :
% 5.25/5.51 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.25/5.51 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_Suc_numeral
% 5.25/5.51 thf(fact_4196_less__numeral__Suc,axiom,
% 5.25/5.51 ! [K: num,N: nat] :
% 5.25/5.51 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.25/5.51 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_numeral_Suc
% 5.25/5.51 thf(fact_4197_pred__numeral__simps_I3_J,axiom,
% 5.25/5.51 ! [K: num] :
% 5.25/5.51 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.25/5.51 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % pred_numeral_simps(3)
% 5.25/5.51 thf(fact_4198_le__Suc__numeral,axiom,
% 5.25/5.51 ! [N: nat,K: num] :
% 5.25/5.51 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.25/5.51 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_Suc_numeral
% 5.25/5.51 thf(fact_4199_le__numeral__Suc,axiom,
% 5.25/5.51 ! [K: num,N: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.25/5.51 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_numeral_Suc
% 5.25/5.51 thf(fact_4200_neg__numeral__le__iff,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.25/5.51 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_le_iff
% 5.25/5.51 thf(fact_4201_neg__numeral__le__iff,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.25/5.51 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_le_iff
% 5.25/5.51 thf(fact_4202_neg__numeral__le__iff,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.25/5.51 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_le_iff
% 5.25/5.51 thf(fact_4203_neg__numeral__le__iff,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.51 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_le_iff
% 5.25/5.51 thf(fact_4204_neg__numeral__less__iff,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.51 = ( ord_less_num @ N @ M ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_less_iff
% 5.25/5.51 thf(fact_4205_neg__numeral__less__iff,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.25/5.51 = ( ord_less_num @ N @ M ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_less_iff
% 5.25/5.51 thf(fact_4206_neg__numeral__less__iff,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.25/5.51 = ( ord_less_num @ N @ M ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_less_iff
% 5.25/5.51 thf(fact_4207_neg__numeral__less__iff,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.25/5.51 = ( ord_less_num @ N @ M ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_less_iff
% 5.25/5.51 thf(fact_4208_max__Suc__numeral,axiom,
% 5.25/5.51 ! [N: nat,K: num] :
% 5.25/5.51 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.25/5.51 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % max_Suc_numeral
% 5.25/5.51 thf(fact_4209_max__numeral__Suc,axiom,
% 5.25/5.51 ! [K: num,N: nat] :
% 5.25/5.51 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.25/5.51 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % max_numeral_Suc
% 5.25/5.51 thf(fact_4210_not__neg__one__le__neg__numeral__iff,axiom,
% 5.25/5.51 ! [M: num] :
% 5.25/5.51 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.25/5.51 = ( M != one ) ) ).
% 5.25/5.51
% 5.25/5.51 % not_neg_one_le_neg_numeral_iff
% 5.25/5.51 thf(fact_4211_not__neg__one__le__neg__numeral__iff,axiom,
% 5.25/5.51 ! [M: num] :
% 5.25/5.51 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.25/5.51 = ( M != one ) ) ).
% 5.25/5.51
% 5.25/5.51 % not_neg_one_le_neg_numeral_iff
% 5.25/5.51 thf(fact_4212_not__neg__one__le__neg__numeral__iff,axiom,
% 5.25/5.51 ! [M: num] :
% 5.25/5.51 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.25/5.51 = ( M != one ) ) ).
% 5.25/5.51
% 5.25/5.51 % not_neg_one_le_neg_numeral_iff
% 5.25/5.51 thf(fact_4213_not__neg__one__le__neg__numeral__iff,axiom,
% 5.25/5.51 ! [M: num] :
% 5.25/5.51 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.25/5.51 = ( M != one ) ) ).
% 5.25/5.51
% 5.25/5.51 % not_neg_one_le_neg_numeral_iff
% 5.25/5.51 thf(fact_4214_divide__le__eq__numeral1_I2_J,axiom,
% 5.25/5.51 ! [B: real,W: num,A: real] :
% 5.25/5.51 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.25/5.51 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % divide_le_eq_numeral1(2)
% 5.25/5.51 thf(fact_4215_divide__le__eq__numeral1_I2_J,axiom,
% 5.25/5.51 ! [B: rat,W: num,A: rat] :
% 5.25/5.51 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.25/5.51 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % divide_le_eq_numeral1(2)
% 5.25/5.51 thf(fact_4216_le__divide__eq__numeral1_I2_J,axiom,
% 5.25/5.51 ! [A: real,B: real,W: num] :
% 5.25/5.51 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.25/5.51 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_divide_eq_numeral1(2)
% 5.25/5.51 thf(fact_4217_le__divide__eq__numeral1_I2_J,axiom,
% 5.25/5.51 ! [A: rat,B: rat,W: num] :
% 5.25/5.51 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.25/5.51 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_divide_eq_numeral1(2)
% 5.25/5.51 thf(fact_4218_eq__divide__eq__numeral1_I2_J,axiom,
% 5.25/5.51 ! [A: real,B: real,W: num] :
% 5.25/5.51 ( ( A
% 5.25/5.51 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.25/5.51 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.25/5.51 != zero_zero_real )
% 5.25/5.51 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.51 = B ) )
% 5.25/5.51 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.25/5.51 = zero_zero_real )
% 5.25/5.51 => ( A = zero_zero_real ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % eq_divide_eq_numeral1(2)
% 5.25/5.51 thf(fact_4219_eq__divide__eq__numeral1_I2_J,axiom,
% 5.25/5.51 ! [A: complex,B: complex,W: num] :
% 5.25/5.51 ( ( A
% 5.25/5.51 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.25/5.51 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.25/5.51 != zero_zero_complex )
% 5.25/5.51 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.25/5.51 = B ) )
% 5.25/5.51 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.25/5.51 = zero_zero_complex )
% 5.25/5.51 => ( A = zero_zero_complex ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % eq_divide_eq_numeral1(2)
% 5.25/5.51 thf(fact_4220_eq__divide__eq__numeral1_I2_J,axiom,
% 5.25/5.51 ! [A: rat,B: rat,W: num] :
% 5.25/5.51 ( ( A
% 5.25/5.51 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.25/5.51 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.25/5.51 != zero_zero_rat )
% 5.25/5.51 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.25/5.51 = B ) )
% 5.25/5.51 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.25/5.51 = zero_zero_rat )
% 5.25/5.51 => ( A = zero_zero_rat ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % eq_divide_eq_numeral1(2)
% 5.25/5.51 thf(fact_4221_divide__eq__eq__numeral1_I2_J,axiom,
% 5.25/5.51 ! [B: real,W: num,A: real] :
% 5.25/5.51 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.51 = A )
% 5.25/5.51 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.25/5.51 != zero_zero_real )
% 5.25/5.51 => ( B
% 5.25/5.51 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.25/5.51 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.25/5.51 = zero_zero_real )
% 5.25/5.51 => ( A = zero_zero_real ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % divide_eq_eq_numeral1(2)
% 5.25/5.51 thf(fact_4222_divide__eq__eq__numeral1_I2_J,axiom,
% 5.25/5.51 ! [B: complex,W: num,A: complex] :
% 5.25/5.51 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.25/5.51 = A )
% 5.25/5.51 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.25/5.51 != zero_zero_complex )
% 5.25/5.51 => ( B
% 5.25/5.51 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.25/5.51 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.25/5.51 = zero_zero_complex )
% 5.25/5.51 => ( A = zero_zero_complex ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % divide_eq_eq_numeral1(2)
% 5.25/5.51 thf(fact_4223_divide__eq__eq__numeral1_I2_J,axiom,
% 5.25/5.51 ! [B: rat,W: num,A: rat] :
% 5.25/5.51 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.25/5.51 = A )
% 5.25/5.51 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.25/5.51 != zero_zero_rat )
% 5.25/5.51 => ( B
% 5.25/5.51 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 5.25/5.51 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.25/5.51 = zero_zero_rat )
% 5.25/5.51 => ( A = zero_zero_rat ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % divide_eq_eq_numeral1(2)
% 5.25/5.51 thf(fact_4224_neg__numeral__less__neg__one__iff,axiom,
% 5.25/5.51 ! [M: num] :
% 5.25/5.51 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.51 = ( M != one ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_less_neg_one_iff
% 5.25/5.51 thf(fact_4225_neg__numeral__less__neg__one__iff,axiom,
% 5.25/5.51 ! [M: num] :
% 5.25/5.51 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.51 = ( M != one ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_less_neg_one_iff
% 5.25/5.51 thf(fact_4226_neg__numeral__less__neg__one__iff,axiom,
% 5.25/5.51 ! [M: num] :
% 5.25/5.51 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.51 = ( M != one ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_less_neg_one_iff
% 5.25/5.51 thf(fact_4227_neg__numeral__less__neg__one__iff,axiom,
% 5.25/5.51 ! [M: num] :
% 5.25/5.51 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.51 = ( M != one ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_less_neg_one_iff
% 5.25/5.51 thf(fact_4228_divide__less__eq__numeral1_I2_J,axiom,
% 5.25/5.51 ! [B: real,W: num,A: real] :
% 5.25/5.51 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.25/5.51 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % divide_less_eq_numeral1(2)
% 5.25/5.51 thf(fact_4229_divide__less__eq__numeral1_I2_J,axiom,
% 5.25/5.51 ! [B: rat,W: num,A: rat] :
% 5.25/5.51 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.25/5.51 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % divide_less_eq_numeral1(2)
% 5.25/5.51 thf(fact_4230_less__divide__eq__numeral1_I2_J,axiom,
% 5.25/5.51 ! [A: real,B: real,W: num] :
% 5.25/5.51 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.25/5.51 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_divide_eq_numeral1(2)
% 5.25/5.51 thf(fact_4231_less__divide__eq__numeral1_I2_J,axiom,
% 5.25/5.51 ! [A: rat,B: rat,W: num] :
% 5.25/5.51 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.25/5.51 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_divide_eq_numeral1(2)
% 5.25/5.51 thf(fact_4232_power2__minus,axiom,
% 5.25/5.51 ! [A: int] :
% 5.25/5.51 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.51 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % power2_minus
% 5.25/5.51 thf(fact_4233_power2__minus,axiom,
% 5.25/5.51 ! [A: real] :
% 5.25/5.51 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.51 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % power2_minus
% 5.25/5.51 thf(fact_4234_power2__minus,axiom,
% 5.25/5.51 ! [A: complex] :
% 5.25/5.51 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.51 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % power2_minus
% 5.25/5.51 thf(fact_4235_power2__minus,axiom,
% 5.25/5.51 ! [A: code_integer] :
% 5.25/5.51 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.51 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % power2_minus
% 5.25/5.51 thf(fact_4236_power2__minus,axiom,
% 5.25/5.51 ! [A: rat] :
% 5.25/5.51 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.51 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % power2_minus
% 5.25/5.51 thf(fact_4237_add__neg__numeral__special_I9_J,axiom,
% 5.25/5.51 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(9)
% 5.25/5.51 thf(fact_4238_add__neg__numeral__special_I9_J,axiom,
% 5.25/5.51 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.51 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(9)
% 5.25/5.51 thf(fact_4239_add__neg__numeral__special_I9_J,axiom,
% 5.25/5.51 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(9)
% 5.25/5.51 thf(fact_4240_add__neg__numeral__special_I9_J,axiom,
% 5.25/5.51 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(9)
% 5.25/5.51 thf(fact_4241_add__neg__numeral__special_I9_J,axiom,
% 5.25/5.51 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.51 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_neg_numeral_special(9)
% 5.25/5.51 thf(fact_4242_diff__numeral__special_I11_J,axiom,
% 5.25/5.51 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.51 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(11)
% 5.25/5.51 thf(fact_4243_diff__numeral__special_I11_J,axiom,
% 5.25/5.51 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.51 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(11)
% 5.25/5.51 thf(fact_4244_diff__numeral__special_I11_J,axiom,
% 5.25/5.51 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.25/5.51 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(11)
% 5.25/5.51 thf(fact_4245_diff__numeral__special_I11_J,axiom,
% 5.25/5.51 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.51 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(11)
% 5.25/5.51 thf(fact_4246_diff__numeral__special_I11_J,axiom,
% 5.25/5.51 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.51 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(11)
% 5.25/5.51 thf(fact_4247_diff__numeral__special_I10_J,axiom,
% 5.25/5.51 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.25/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(10)
% 5.25/5.51 thf(fact_4248_diff__numeral__special_I10_J,axiom,
% 5.25/5.51 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.25/5.51 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(10)
% 5.25/5.51 thf(fact_4249_diff__numeral__special_I10_J,axiom,
% 5.25/5.51 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(10)
% 5.25/5.51 thf(fact_4250_diff__numeral__special_I10_J,axiom,
% 5.25/5.51 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(10)
% 5.25/5.51 thf(fact_4251_diff__numeral__special_I10_J,axiom,
% 5.25/5.51 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.25/5.51 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(10)
% 5.25/5.51 thf(fact_4252_minus__1__div__2__eq,axiom,
% 5.25/5.51 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.51 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_1_div_2_eq
% 5.25/5.51 thf(fact_4253_minus__1__div__2__eq,axiom,
% 5.25/5.51 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_1_div_2_eq
% 5.25/5.51 thf(fact_4254_bits__minus__1__mod__2__eq,axiom,
% 5.25/5.51 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.51 = one_one_int ) ).
% 5.25/5.51
% 5.25/5.51 % bits_minus_1_mod_2_eq
% 5.25/5.51 thf(fact_4255_bits__minus__1__mod__2__eq,axiom,
% 5.25/5.51 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.51 = one_one_Code_integer ) ).
% 5.25/5.51
% 5.25/5.51 % bits_minus_1_mod_2_eq
% 5.25/5.51 thf(fact_4256_minus__1__mod__2__eq,axiom,
% 5.25/5.51 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.51 = one_one_int ) ).
% 5.25/5.51
% 5.25/5.51 % minus_1_mod_2_eq
% 5.25/5.51 thf(fact_4257_minus__1__mod__2__eq,axiom,
% 5.25/5.51 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.51 = one_one_Code_integer ) ).
% 5.25/5.51
% 5.25/5.51 % minus_1_mod_2_eq
% 5.25/5.51 thf(fact_4258_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.25/5.51 ! [A: int,N: nat] :
% 5.25/5.51 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.51 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Power.ring_1_class.power_minus_even
% 5.25/5.51 thf(fact_4259_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.25/5.51 ! [A: real,N: nat] :
% 5.25/5.51 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.51 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Power.ring_1_class.power_minus_even
% 5.25/5.51 thf(fact_4260_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.25/5.51 ! [A: complex,N: nat] :
% 5.25/5.51 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.51 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Power.ring_1_class.power_minus_even
% 5.25/5.51 thf(fact_4261_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.25/5.51 ! [A: code_integer,N: nat] :
% 5.25/5.51 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.51 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Power.ring_1_class.power_minus_even
% 5.25/5.51 thf(fact_4262_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.25/5.51 ! [A: rat,N: nat] :
% 5.25/5.51 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.51 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Power.ring_1_class.power_minus_even
% 5.25/5.51 thf(fact_4263_power__minus__odd,axiom,
% 5.25/5.51 ! [N: nat,A: int] :
% 5.25/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.25/5.51 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % power_minus_odd
% 5.25/5.51 thf(fact_4264_power__minus__odd,axiom,
% 5.25/5.51 ! [N: nat,A: real] :
% 5.25/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.25/5.51 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % power_minus_odd
% 5.25/5.51 thf(fact_4265_power__minus__odd,axiom,
% 5.25/5.51 ! [N: nat,A: complex] :
% 5.25/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % power_minus_odd
% 5.25/5.51 thf(fact_4266_power__minus__odd,axiom,
% 5.25/5.51 ! [N: nat,A: code_integer] :
% 5.25/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % power_minus_odd
% 5.25/5.51 thf(fact_4267_power__minus__odd,axiom,
% 5.25/5.51 ! [N: nat,A: rat] :
% 5.25/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.25/5.51 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % power_minus_odd
% 5.25/5.51 thf(fact_4268_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.25/5.51 ! [N: nat,A: int] :
% 5.25/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.25/5.51 = ( power_power_int @ A @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Parity.ring_1_class.power_minus_even
% 5.25/5.51 thf(fact_4269_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.25/5.51 ! [N: nat,A: real] :
% 5.25/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.25/5.51 = ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Parity.ring_1_class.power_minus_even
% 5.25/5.51 thf(fact_4270_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.25/5.51 ! [N: nat,A: complex] :
% 5.25/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.25/5.51 = ( power_power_complex @ A @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Parity.ring_1_class.power_minus_even
% 5.25/5.51 thf(fact_4271_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.25/5.51 ! [N: nat,A: code_integer] :
% 5.25/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.25/5.51 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Parity.ring_1_class.power_minus_even
% 5.25/5.51 thf(fact_4272_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.25/5.51 ! [N: nat,A: rat] :
% 5.25/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.25/5.51 = ( power_power_rat @ A @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Parity.ring_1_class.power_minus_even
% 5.25/5.51 thf(fact_4273_odd__Suc__minus__one,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.25/5.51 = N ) ) ).
% 5.25/5.51
% 5.25/5.51 % odd_Suc_minus_one
% 5.25/5.51 thf(fact_4274_even__diff__nat,axiom,
% 5.25/5.51 ! [M: nat,N: nat] :
% 5.25/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 5.25/5.51 = ( ( ord_less_nat @ M @ N )
% 5.25/5.51 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % even_diff_nat
% 5.25/5.51 thf(fact_4275_diff__numeral__special_I3_J,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.51 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(3)
% 5.25/5.51 thf(fact_4276_diff__numeral__special_I3_J,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.25/5.51 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(3)
% 5.25/5.51 thf(fact_4277_diff__numeral__special_I3_J,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.25/5.51 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(3)
% 5.25/5.51 thf(fact_4278_diff__numeral__special_I3_J,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.25/5.51 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(3)
% 5.25/5.51 thf(fact_4279_diff__numeral__special_I3_J,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.25/5.51 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(3)
% 5.25/5.51 thf(fact_4280_diff__numeral__special_I4_J,axiom,
% 5.25/5.51 ! [M: num] :
% 5.25/5.51 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 5.25/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(4)
% 5.25/5.51 thf(fact_4281_diff__numeral__special_I4_J,axiom,
% 5.25/5.51 ! [M: num] :
% 5.25/5.51 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 5.25/5.51 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(4)
% 5.25/5.51 thf(fact_4282_diff__numeral__special_I4_J,axiom,
% 5.25/5.51 ! [M: num] :
% 5.25/5.51 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(4)
% 5.25/5.51 thf(fact_4283_diff__numeral__special_I4_J,axiom,
% 5.25/5.51 ! [M: num] :
% 5.25/5.51 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(4)
% 5.25/5.51 thf(fact_4284_diff__numeral__special_I4_J,axiom,
% 5.25/5.51 ! [M: num] :
% 5.25/5.51 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 5.25/5.51 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_numeral_special(4)
% 5.25/5.51 thf(fact_4285_dbl__simps_I4_J,axiom,
% 5.25/5.51 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_simps(4)
% 5.25/5.51 thf(fact_4286_dbl__simps_I4_J,axiom,
% 5.25/5.51 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.51 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_simps(4)
% 5.25/5.51 thf(fact_4287_dbl__simps_I4_J,axiom,
% 5.25/5.51 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_simps(4)
% 5.25/5.51 thf(fact_4288_dbl__simps_I4_J,axiom,
% 5.25/5.51 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_simps(4)
% 5.25/5.51 thf(fact_4289_dbl__simps_I4_J,axiom,
% 5.25/5.51 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.51 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dbl_simps(4)
% 5.25/5.51 thf(fact_4290_power__minus1__even,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.51 = one_one_int ) ).
% 5.25/5.51
% 5.25/5.51 % power_minus1_even
% 5.25/5.51 thf(fact_4291_power__minus1__even,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.51 = one_one_real ) ).
% 5.25/5.51
% 5.25/5.51 % power_minus1_even
% 5.25/5.51 thf(fact_4292_power__minus1__even,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.51 = one_one_complex ) ).
% 5.25/5.51
% 5.25/5.51 % power_minus1_even
% 5.25/5.51 thf(fact_4293_power__minus1__even,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.51 = one_one_Code_integer ) ).
% 5.25/5.51
% 5.25/5.51 % power_minus1_even
% 5.25/5.51 thf(fact_4294_power__minus1__even,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.51 = one_one_rat ) ).
% 5.25/5.51
% 5.25/5.51 % power_minus1_even
% 5.25/5.51 thf(fact_4295_neg__one__odd__power,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.25/5.51 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_odd_power
% 5.25/5.51 thf(fact_4296_neg__one__odd__power,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.25/5.51 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_odd_power
% 5.25/5.51 thf(fact_4297_neg__one__odd__power,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_odd_power
% 5.25/5.51 thf(fact_4298_neg__one__odd__power,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_odd_power
% 5.25/5.51 thf(fact_4299_neg__one__odd__power,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.25/5.51 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_odd_power
% 5.25/5.51 thf(fact_4300_neg__one__even__power,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.25/5.51 = one_one_int ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_even_power
% 5.25/5.51 thf(fact_4301_neg__one__even__power,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.25/5.51 = one_one_real ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_even_power
% 5.25/5.51 thf(fact_4302_neg__one__even__power,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.25/5.51 = one_one_complex ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_even_power
% 5.25/5.51 thf(fact_4303_neg__one__even__power,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.25/5.51 = one_one_Code_integer ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_even_power
% 5.25/5.51 thf(fact_4304_neg__one__even__power,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.25/5.51 = one_one_rat ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_even_power
% 5.25/5.51 thf(fact_4305_signed__take__bit__0,axiom,
% 5.25/5.51 ! [A: code_integer] :
% 5.25/5.51 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % signed_take_bit_0
% 5.25/5.51 thf(fact_4306_signed__take__bit__0,axiom,
% 5.25/5.51 ! [A: int] :
% 5.25/5.51 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.25/5.51 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % signed_take_bit_0
% 5.25/5.51 thf(fact_4307_odd__two__times__div__two__nat,axiom,
% 5.25/5.51 ! [N: nat] :
% 5.25/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.51 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.51 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % odd_two_times_div_two_nat
% 5.25/5.51 thf(fact_4308_signed__take__bit__Suc__minus__bit0,axiom,
% 5.25/5.51 ! [N: nat,K: num] :
% 5.25/5.51 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.25/5.51 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % signed_take_bit_Suc_minus_bit0
% 5.25/5.51 thf(fact_4309_signed__take__bit__numeral__bit0,axiom,
% 5.25/5.51 ! [L2: num,K: num] :
% 5.25/5.51 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.25/5.51 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % signed_take_bit_numeral_bit0
% 5.25/5.51 thf(fact_4310_signed__take__bit__numeral__minus__bit0,axiom,
% 5.25/5.51 ! [L2: num,K: num] :
% 5.25/5.51 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.25/5.51 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % signed_take_bit_numeral_minus_bit0
% 5.25/5.51 thf(fact_4311_signed__take__bit__numeral__minus__bit1,axiom,
% 5.25/5.51 ! [L2: num,K: num] :
% 5.25/5.51 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.25/5.51 = ( 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 ) ) ).
% 5.25/5.51
% 5.25/5.51 % signed_take_bit_numeral_minus_bit1
% 5.25/5.51 thf(fact_4312_eq__diff__eq_H,axiom,
% 5.25/5.51 ! [X3: real,Y: real,Z: real] :
% 5.25/5.51 ( ( X3
% 5.25/5.51 = ( minus_minus_real @ Y @ Z ) )
% 5.25/5.51 = ( Y
% 5.25/5.51 = ( plus_plus_real @ X3 @ Z ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % eq_diff_eq'
% 5.25/5.51 thf(fact_4313_dvd__antisym,axiom,
% 5.25/5.51 ! [M: nat,N: nat] :
% 5.25/5.51 ( ( dvd_dvd_nat @ M @ N )
% 5.25/5.51 => ( ( dvd_dvd_nat @ N @ M )
% 5.25/5.51 => ( M = N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dvd_antisym
% 5.25/5.51 thf(fact_4314_dvd__diff__nat,axiom,
% 5.25/5.51 ! [K: nat,M: nat,N: nat] :
% 5.25/5.51 ( ( dvd_dvd_nat @ K @ M )
% 5.25/5.51 => ( ( dvd_dvd_nat @ K @ N )
% 5.25/5.51 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dvd_diff_nat
% 5.25/5.51 thf(fact_4315_minus__equation__iff,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( ( uminus_uminus_int @ A )
% 5.25/5.51 = B )
% 5.25/5.51 = ( ( uminus_uminus_int @ B )
% 5.25/5.51 = A ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_equation_iff
% 5.25/5.51 thf(fact_4316_minus__equation__iff,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( ( uminus_uminus_real @ A )
% 5.25/5.51 = B )
% 5.25/5.51 = ( ( uminus_uminus_real @ B )
% 5.25/5.51 = A ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_equation_iff
% 5.25/5.51 thf(fact_4317_minus__equation__iff,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( ( uminus1482373934393186551omplex @ A )
% 5.25/5.51 = B )
% 5.25/5.51 = ( ( uminus1482373934393186551omplex @ B )
% 5.25/5.51 = A ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_equation_iff
% 5.25/5.51 thf(fact_4318_minus__equation__iff,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( ( uminus1351360451143612070nteger @ A )
% 5.25/5.51 = B )
% 5.25/5.51 = ( ( uminus1351360451143612070nteger @ B )
% 5.25/5.51 = A ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_equation_iff
% 5.25/5.51 thf(fact_4319_minus__equation__iff,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( ( uminus_uminus_rat @ A )
% 5.25/5.51 = B )
% 5.25/5.51 = ( ( uminus_uminus_rat @ B )
% 5.25/5.51 = A ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_equation_iff
% 5.25/5.51 thf(fact_4320_equation__minus__iff,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( A
% 5.25/5.51 = ( uminus_uminus_int @ B ) )
% 5.25/5.51 = ( B
% 5.25/5.51 = ( uminus_uminus_int @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % equation_minus_iff
% 5.25/5.51 thf(fact_4321_equation__minus__iff,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( A
% 5.25/5.51 = ( uminus_uminus_real @ B ) )
% 5.25/5.51 = ( B
% 5.25/5.51 = ( uminus_uminus_real @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % equation_minus_iff
% 5.25/5.51 thf(fact_4322_equation__minus__iff,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( A
% 5.25/5.51 = ( uminus1482373934393186551omplex @ B ) )
% 5.25/5.51 = ( B
% 5.25/5.51 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % equation_minus_iff
% 5.25/5.51 thf(fact_4323_equation__minus__iff,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( A
% 5.25/5.51 = ( uminus1351360451143612070nteger @ B ) )
% 5.25/5.51 = ( B
% 5.25/5.51 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % equation_minus_iff
% 5.25/5.51 thf(fact_4324_equation__minus__iff,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( A
% 5.25/5.51 = ( uminus_uminus_rat @ B ) )
% 5.25/5.51 = ( B
% 5.25/5.51 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % equation_minus_iff
% 5.25/5.51 thf(fact_4325_pred__numeral__def,axiom,
% 5.25/5.51 ( pred_numeral
% 5.25/5.51 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % pred_numeral_def
% 5.25/5.51 thf(fact_4326_le__minus__iff,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.25/5.51 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_minus_iff
% 5.25/5.51 thf(fact_4327_le__minus__iff,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.25/5.51 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_minus_iff
% 5.25/5.51 thf(fact_4328_le__minus__iff,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.25/5.51 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_minus_iff
% 5.25/5.51 thf(fact_4329_le__minus__iff,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.25/5.51 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_minus_iff
% 5.25/5.51 thf(fact_4330_minus__le__iff,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.25/5.51 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_le_iff
% 5.25/5.51 thf(fact_4331_minus__le__iff,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.25/5.51 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_le_iff
% 5.25/5.51 thf(fact_4332_minus__le__iff,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.25/5.51 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_le_iff
% 5.25/5.51 thf(fact_4333_minus__le__iff,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.25/5.51 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_le_iff
% 5.25/5.51 thf(fact_4334_le__imp__neg__le,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.51 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_imp_neg_le
% 5.25/5.51 thf(fact_4335_le__imp__neg__le,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.25/5.51 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_imp_neg_le
% 5.25/5.51 thf(fact_4336_le__imp__neg__le,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.51 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_imp_neg_le
% 5.25/5.51 thf(fact_4337_le__imp__neg__le,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.51 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_imp_neg_le
% 5.25/5.51 thf(fact_4338_less__minus__iff,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.25/5.51 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_minus_iff
% 5.25/5.51 thf(fact_4339_less__minus__iff,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.25/5.51 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_minus_iff
% 5.25/5.51 thf(fact_4340_less__minus__iff,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.25/5.51 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_minus_iff
% 5.25/5.51 thf(fact_4341_less__minus__iff,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.25/5.51 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_minus_iff
% 5.25/5.51 thf(fact_4342_minus__less__iff,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.25/5.51 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_less_iff
% 5.25/5.51 thf(fact_4343_minus__less__iff,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.25/5.51 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_less_iff
% 5.25/5.51 thf(fact_4344_minus__less__iff,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.25/5.51 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_less_iff
% 5.25/5.51 thf(fact_4345_minus__less__iff,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.25/5.51 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_less_iff
% 5.25/5.51 thf(fact_4346_verit__negate__coefficient_I2_J,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( ord_less_int @ A @ B )
% 5.25/5.51 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % verit_negate_coefficient(2)
% 5.25/5.51 thf(fact_4347_verit__negate__coefficient_I2_J,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( ord_less_real @ A @ B )
% 5.25/5.51 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % verit_negate_coefficient(2)
% 5.25/5.51 thf(fact_4348_verit__negate__coefficient_I2_J,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.25/5.51 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % verit_negate_coefficient(2)
% 5.25/5.51 thf(fact_4349_verit__negate__coefficient_I2_J,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( ord_less_rat @ A @ B )
% 5.25/5.51 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % verit_negate_coefficient(2)
% 5.25/5.51 thf(fact_4350_neg__numeral__neq__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.25/5.51 != ( numeral_numeral_int @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_neq_numeral
% 5.25/5.51 thf(fact_4351_neg__numeral__neq__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.25/5.51 != ( numeral_numeral_real @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_neq_numeral
% 5.25/5.51 thf(fact_4352_neg__numeral__neq__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.25/5.51 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_neq_numeral
% 5.25/5.51 thf(fact_4353_neg__numeral__neq__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.25/5.51 != ( numera6620942414471956472nteger @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_neq_numeral
% 5.25/5.51 thf(fact_4354_neg__numeral__neq__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.25/5.51 != ( numeral_numeral_rat @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_neq_numeral
% 5.25/5.51 thf(fact_4355_numeral__neq__neg__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( numeral_numeral_int @ M )
% 5.25/5.51 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_neq_neg_numeral
% 5.25/5.51 thf(fact_4356_numeral__neq__neg__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( numeral_numeral_real @ M )
% 5.25/5.51 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_neq_neg_numeral
% 5.25/5.51 thf(fact_4357_numeral__neq__neg__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( numera6690914467698888265omplex @ M )
% 5.25/5.51 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_neq_neg_numeral
% 5.25/5.51 thf(fact_4358_numeral__neq__neg__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( numera6620942414471956472nteger @ M )
% 5.25/5.51 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_neq_neg_numeral
% 5.25/5.51 thf(fact_4359_numeral__neq__neg__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ( ( numeral_numeral_rat @ M )
% 5.25/5.51 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_neq_neg_numeral
% 5.25/5.51 thf(fact_4360_square__eq__iff,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( ( times_times_int @ A @ A )
% 5.25/5.51 = ( times_times_int @ B @ B ) )
% 5.25/5.51 = ( ( A = B )
% 5.25/5.51 | ( A
% 5.25/5.51 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % square_eq_iff
% 5.25/5.51 thf(fact_4361_square__eq__iff,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( ( times_times_real @ A @ A )
% 5.25/5.51 = ( times_times_real @ B @ B ) )
% 5.25/5.51 = ( ( A = B )
% 5.25/5.51 | ( A
% 5.25/5.51 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % square_eq_iff
% 5.25/5.51 thf(fact_4362_square__eq__iff,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( ( times_times_complex @ A @ A )
% 5.25/5.51 = ( times_times_complex @ B @ B ) )
% 5.25/5.51 = ( ( A = B )
% 5.25/5.51 | ( A
% 5.25/5.51 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % square_eq_iff
% 5.25/5.51 thf(fact_4363_square__eq__iff,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.25/5.51 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.25/5.51 = ( ( A = B )
% 5.25/5.51 | ( A
% 5.25/5.51 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % square_eq_iff
% 5.25/5.51 thf(fact_4364_square__eq__iff,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( ( times_times_rat @ A @ A )
% 5.25/5.51 = ( times_times_rat @ B @ B ) )
% 5.25/5.51 = ( ( A = B )
% 5.25/5.51 | ( A
% 5.25/5.51 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % square_eq_iff
% 5.25/5.51 thf(fact_4365_minus__mult__commute,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.25/5.51 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_mult_commute
% 5.25/5.51 thf(fact_4366_minus__mult__commute,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.25/5.51 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_mult_commute
% 5.25/5.51 thf(fact_4367_minus__mult__commute,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.25/5.51 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_mult_commute
% 5.25/5.51 thf(fact_4368_minus__mult__commute,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.25/5.51 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_mult_commute
% 5.25/5.51 thf(fact_4369_minus__mult__commute,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.25/5.51 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_mult_commute
% 5.25/5.51 thf(fact_4370_one__neq__neg__one,axiom,
% 5.25/5.51 ( one_one_int
% 5.25/5.51 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.51
% 5.25/5.51 % one_neq_neg_one
% 5.25/5.51 thf(fact_4371_one__neq__neg__one,axiom,
% 5.25/5.51 ( one_one_real
% 5.25/5.51 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.51
% 5.25/5.51 % one_neq_neg_one
% 5.25/5.51 thf(fact_4372_one__neq__neg__one,axiom,
% 5.25/5.51 ( one_one_complex
% 5.25/5.51 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.25/5.51
% 5.25/5.51 % one_neq_neg_one
% 5.25/5.51 thf(fact_4373_one__neq__neg__one,axiom,
% 5.25/5.51 ( one_one_Code_integer
% 5.25/5.51 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.51
% 5.25/5.51 % one_neq_neg_one
% 5.25/5.51 thf(fact_4374_one__neq__neg__one,axiom,
% 5.25/5.51 ( one_one_rat
% 5.25/5.51 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.51
% 5.25/5.51 % one_neq_neg_one
% 5.25/5.51 thf(fact_4375_is__num__normalize_I8_J,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.25/5.51 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % is_num_normalize(8)
% 5.25/5.51 thf(fact_4376_is__num__normalize_I8_J,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.25/5.51 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % is_num_normalize(8)
% 5.25/5.51 thf(fact_4377_is__num__normalize_I8_J,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.25/5.51 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % is_num_normalize(8)
% 5.25/5.51 thf(fact_4378_is__num__normalize_I8_J,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.25/5.51 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % is_num_normalize(8)
% 5.25/5.51 thf(fact_4379_is__num__normalize_I8_J,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.25/5.51 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % is_num_normalize(8)
% 5.25/5.51 thf(fact_4380_group__cancel_Oneg1,axiom,
% 5.25/5.51 ! [A2: int,K: int,A: int] :
% 5.25/5.51 ( ( A2
% 5.25/5.51 = ( plus_plus_int @ K @ A ) )
% 5.25/5.51 => ( ( uminus_uminus_int @ A2 )
% 5.25/5.51 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % group_cancel.neg1
% 5.25/5.51 thf(fact_4381_group__cancel_Oneg1,axiom,
% 5.25/5.51 ! [A2: real,K: real,A: real] :
% 5.25/5.51 ( ( A2
% 5.25/5.51 = ( plus_plus_real @ K @ A ) )
% 5.25/5.51 => ( ( uminus_uminus_real @ A2 )
% 5.25/5.51 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % group_cancel.neg1
% 5.25/5.51 thf(fact_4382_group__cancel_Oneg1,axiom,
% 5.25/5.51 ! [A2: complex,K: complex,A: complex] :
% 5.25/5.51 ( ( A2
% 5.25/5.51 = ( plus_plus_complex @ K @ A ) )
% 5.25/5.51 => ( ( uminus1482373934393186551omplex @ A2 )
% 5.25/5.51 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % group_cancel.neg1
% 5.25/5.51 thf(fact_4383_group__cancel_Oneg1,axiom,
% 5.25/5.51 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 5.25/5.51 ( ( A2
% 5.25/5.51 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.25/5.51 => ( ( uminus1351360451143612070nteger @ A2 )
% 5.25/5.51 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % group_cancel.neg1
% 5.25/5.51 thf(fact_4384_group__cancel_Oneg1,axiom,
% 5.25/5.51 ! [A2: rat,K: rat,A: rat] :
% 5.25/5.51 ( ( A2
% 5.25/5.51 = ( plus_plus_rat @ K @ A ) )
% 5.25/5.51 => ( ( uminus_uminus_rat @ A2 )
% 5.25/5.51 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % group_cancel.neg1
% 5.25/5.51 thf(fact_4385_add_Oinverse__distrib__swap,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.25/5.51 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add.inverse_distrib_swap
% 5.25/5.51 thf(fact_4386_add_Oinverse__distrib__swap,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.25/5.51 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add.inverse_distrib_swap
% 5.25/5.51 thf(fact_4387_add_Oinverse__distrib__swap,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.25/5.51 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add.inverse_distrib_swap
% 5.25/5.51 thf(fact_4388_add_Oinverse__distrib__swap,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.25/5.51 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add.inverse_distrib_swap
% 5.25/5.51 thf(fact_4389_add_Oinverse__distrib__swap,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.25/5.51 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add.inverse_distrib_swap
% 5.25/5.51 thf(fact_4390_minus__diff__commute,axiom,
% 5.25/5.51 ! [B: int,A: int] :
% 5.25/5.51 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 5.25/5.51 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_diff_commute
% 5.25/5.51 thf(fact_4391_minus__diff__commute,axiom,
% 5.25/5.51 ! [B: real,A: real] :
% 5.25/5.51 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 5.25/5.51 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_diff_commute
% 5.25/5.51 thf(fact_4392_minus__diff__commute,axiom,
% 5.25/5.51 ! [B: complex,A: complex] :
% 5.25/5.51 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 5.25/5.51 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_diff_commute
% 5.25/5.51 thf(fact_4393_minus__diff__commute,axiom,
% 5.25/5.51 ! [B: code_integer,A: code_integer] :
% 5.25/5.51 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 5.25/5.51 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_diff_commute
% 5.25/5.51 thf(fact_4394_minus__diff__commute,axiom,
% 5.25/5.51 ! [B: rat,A: rat] :
% 5.25/5.51 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 5.25/5.51 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_diff_commute
% 5.25/5.51 thf(fact_4395_minus__diff__minus,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.25/5.51 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_diff_minus
% 5.25/5.51 thf(fact_4396_minus__diff__minus,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.25/5.51 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_diff_minus
% 5.25/5.51 thf(fact_4397_minus__diff__minus,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.25/5.51 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_diff_minus
% 5.25/5.51 thf(fact_4398_minus__diff__minus,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_diff_minus
% 5.25/5.51 thf(fact_4399_minus__diff__minus,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.25/5.51 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_diff_minus
% 5.25/5.51 thf(fact_4400_div__minus__right,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.25/5.51 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % div_minus_right
% 5.25/5.51 thf(fact_4401_div__minus__right,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.25/5.51 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % div_minus_right
% 5.25/5.51 thf(fact_4402_minus__divide__right,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.25/5.51 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_divide_right
% 5.25/5.51 thf(fact_4403_minus__divide__right,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.25/5.51 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_divide_right
% 5.25/5.51 thf(fact_4404_minus__divide__right,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.25/5.51 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_divide_right
% 5.25/5.51 thf(fact_4405_minus__divide__divide,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.25/5.51 = ( divide_divide_real @ A @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_divide_divide
% 5.25/5.51 thf(fact_4406_minus__divide__divide,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.25/5.51 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_divide_divide
% 5.25/5.51 thf(fact_4407_minus__divide__divide,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.25/5.51 = ( divide_divide_rat @ A @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_divide_divide
% 5.25/5.51 thf(fact_4408_minus__divide__left,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.25/5.51 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_divide_left
% 5.25/5.51 thf(fact_4409_minus__divide__left,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.25/5.51 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_divide_left
% 5.25/5.51 thf(fact_4410_minus__divide__left,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.25/5.51 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % minus_divide_left
% 5.25/5.51 thf(fact_4411_zero__induct__lemma,axiom,
% 5.25/5.51 ! [P: nat > $o,K: nat,I2: nat] :
% 5.25/5.51 ( ( P @ K )
% 5.25/5.51 => ( ! [N3: nat] :
% 5.25/5.51 ( ( P @ ( suc @ N3 ) )
% 5.25/5.51 => ( P @ N3 ) )
% 5.25/5.51 => ( P @ ( minus_minus_nat @ K @ I2 ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % zero_induct_lemma
% 5.25/5.51 thf(fact_4412_minus__nat_Odiff__0,axiom,
% 5.25/5.51 ! [M: nat] :
% 5.25/5.51 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.25/5.51 = M ) ).
% 5.25/5.51
% 5.25/5.51 % minus_nat.diff_0
% 5.25/5.51 thf(fact_4413_diffs0__imp__equal,axiom,
% 5.25/5.51 ! [M: nat,N: nat] :
% 5.25/5.51 ( ( ( minus_minus_nat @ M @ N )
% 5.25/5.51 = zero_zero_nat )
% 5.25/5.51 => ( ( ( minus_minus_nat @ N @ M )
% 5.25/5.51 = zero_zero_nat )
% 5.25/5.51 => ( M = N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diffs0_imp_equal
% 5.25/5.51 thf(fact_4414_diff__less__mono2,axiom,
% 5.25/5.51 ! [M: nat,N: nat,L2: nat] :
% 5.25/5.51 ( ( ord_less_nat @ M @ N )
% 5.25/5.51 => ( ( ord_less_nat @ M @ L2 )
% 5.25/5.51 => ( ord_less_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_less_mono2
% 5.25/5.51 thf(fact_4415_less__imp__diff__less,axiom,
% 5.25/5.51 ! [J2: nat,K: nat,N: nat] :
% 5.25/5.51 ( ( ord_less_nat @ J2 @ K )
% 5.25/5.51 => ( ord_less_nat @ ( minus_minus_nat @ J2 @ N ) @ K ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_imp_diff_less
% 5.25/5.51 thf(fact_4416_dvd__minus__self,axiom,
% 5.25/5.51 ! [M: nat,N: nat] :
% 5.25/5.51 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 5.25/5.51 = ( ( ord_less_nat @ N @ M )
% 5.25/5.51 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dvd_minus_self
% 5.25/5.51 thf(fact_4417_eq__diff__iff,axiom,
% 5.25/5.51 ! [K: nat,M: nat,N: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ K @ M )
% 5.25/5.51 => ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.51 => ( ( ( minus_minus_nat @ M @ K )
% 5.25/5.51 = ( minus_minus_nat @ N @ K ) )
% 5.25/5.51 = ( M = N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % eq_diff_iff
% 5.25/5.51 thf(fact_4418_le__diff__iff,axiom,
% 5.25/5.51 ! [K: nat,M: nat,N: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ K @ M )
% 5.25/5.51 => ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.51 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.25/5.51 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_diff_iff
% 5.25/5.51 thf(fact_4419_Nat_Odiff__diff__eq,axiom,
% 5.25/5.51 ! [K: nat,M: nat,N: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ K @ M )
% 5.25/5.51 => ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.51 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.25/5.51 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % Nat.diff_diff_eq
% 5.25/5.51 thf(fact_4420_diff__le__mono,axiom,
% 5.25/5.51 ! [M: nat,N: nat,L2: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.51 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L2 ) @ ( minus_minus_nat @ N @ L2 ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_le_mono
% 5.25/5.51 thf(fact_4421_diff__le__self,axiom,
% 5.25/5.51 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 5.25/5.51
% 5.25/5.51 % diff_le_self
% 5.25/5.51 thf(fact_4422_le__diff__iff_H,axiom,
% 5.25/5.51 ! [A: nat,C: nat,B: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ A @ C )
% 5.25/5.51 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.51 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.25/5.51 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_diff_iff'
% 5.25/5.51 thf(fact_4423_diff__le__mono2,axiom,
% 5.25/5.51 ! [M: nat,N: nat,L2: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.51 => ( ord_less_eq_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_le_mono2
% 5.25/5.51 thf(fact_4424_less__eq__dvd__minus,axiom,
% 5.25/5.51 ! [M: nat,N: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.51 => ( ( dvd_dvd_nat @ M @ N )
% 5.25/5.51 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_eq_dvd_minus
% 5.25/5.51 thf(fact_4425_dvd__diffD1,axiom,
% 5.25/5.51 ! [K: nat,M: nat,N: nat] :
% 5.25/5.51 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.25/5.51 => ( ( dvd_dvd_nat @ K @ M )
% 5.25/5.51 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.51 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dvd_diffD1
% 5.25/5.51 thf(fact_4426_dvd__diffD,axiom,
% 5.25/5.51 ! [K: nat,M: nat,N: nat] :
% 5.25/5.51 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.25/5.51 => ( ( dvd_dvd_nat @ K @ N )
% 5.25/5.51 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.51 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % dvd_diffD
% 5.25/5.51 thf(fact_4427_mod__minus__right,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.25/5.51 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mod_minus_right
% 5.25/5.51 thf(fact_4428_mod__minus__right,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.25/5.51 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mod_minus_right
% 5.25/5.51 thf(fact_4429_mod__minus__cong,axiom,
% 5.25/5.51 ! [A: int,B: int,A4: int] :
% 5.25/5.51 ( ( ( modulo_modulo_int @ A @ B )
% 5.25/5.51 = ( modulo_modulo_int @ A4 @ B ) )
% 5.25/5.51 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.25/5.51 = ( modulo_modulo_int @ ( uminus_uminus_int @ A4 ) @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mod_minus_cong
% 5.25/5.51 thf(fact_4430_mod__minus__cong,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer,A4: code_integer] :
% 5.25/5.51 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.25/5.51 = ( modulo364778990260209775nteger @ A4 @ B ) )
% 5.25/5.51 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.25/5.51 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A4 ) @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % mod_minus_cong
% 5.25/5.51 thf(fact_4431_mod__minus__eq,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 5.25/5.51 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % mod_minus_eq
% 5.25/5.51 thf(fact_4432_mod__minus__eq,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 5.25/5.51 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.25/5.51
% 5.25/5.51 % mod_minus_eq
% 5.25/5.51 thf(fact_4433_Nat_Odiff__cancel,axiom,
% 5.25/5.51 ! [K: nat,M: nat,N: nat] :
% 5.25/5.51 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.25/5.51 = ( minus_minus_nat @ M @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % Nat.diff_cancel
% 5.25/5.51 thf(fact_4434_diff__cancel2,axiom,
% 5.25/5.51 ! [M: nat,K: nat,N: nat] :
% 5.25/5.51 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 5.25/5.51 = ( minus_minus_nat @ M @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_cancel2
% 5.25/5.51 thf(fact_4435_diff__add__inverse,axiom,
% 5.25/5.51 ! [N: nat,M: nat] :
% 5.25/5.51 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 5.25/5.51 = M ) ).
% 5.25/5.51
% 5.25/5.51 % diff_add_inverse
% 5.25/5.51 thf(fact_4436_diff__add__inverse2,axiom,
% 5.25/5.51 ! [M: nat,N: nat] :
% 5.25/5.51 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 5.25/5.51 = M ) ).
% 5.25/5.51
% 5.25/5.51 % diff_add_inverse2
% 5.25/5.51 thf(fact_4437_diff__mult__distrib,axiom,
% 5.25/5.51 ! [M: nat,N: nat,K: nat] :
% 5.25/5.51 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 5.25/5.51 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_mult_distrib
% 5.25/5.51 thf(fact_4438_diff__mult__distrib2,axiom,
% 5.25/5.51 ! [K: nat,M: nat,N: nat] :
% 5.25/5.51 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.25/5.51 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % diff_mult_distrib2
% 5.25/5.51 thf(fact_4439_bezout1__nat,axiom,
% 5.25/5.51 ! [A: nat,B: nat] :
% 5.25/5.51 ? [D3: nat,X5: nat,Y3: nat] :
% 5.25/5.51 ( ( dvd_dvd_nat @ D3 @ A )
% 5.25/5.51 & ( dvd_dvd_nat @ D3 @ B )
% 5.25/5.51 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X5 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.25/5.51 = D3 )
% 5.25/5.51 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X5 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.25/5.51 = D3 ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % bezout1_nat
% 5.25/5.51 thf(fact_4440_signed__take__bit__minus,axiom,
% 5.25/5.51 ! [N: nat,K: int] :
% 5.25/5.51 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 5.25/5.51 = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % signed_take_bit_minus
% 5.25/5.51 thf(fact_4441_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.25/5.51 ! [K: nat,N: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.51 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 5.25/5.51 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_power_add_eq_neg_one_power_diff
% 5.25/5.51 thf(fact_4442_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.25/5.51 ! [K: nat,N: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.51 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 5.25/5.51 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_power_add_eq_neg_one_power_diff
% 5.25/5.51 thf(fact_4443_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.25/5.51 ! [K: nat,N: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.51 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 5.25/5.51 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_power_add_eq_neg_one_power_diff
% 5.25/5.51 thf(fact_4444_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.25/5.51 ! [K: nat,N: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.51 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 5.25/5.51 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_power_add_eq_neg_one_power_diff
% 5.25/5.51 thf(fact_4445_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.25/5.51 ! [K: nat,N: nat] :
% 5.25/5.51 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.51 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 5.25/5.51 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_one_power_add_eq_neg_one_power_diff
% 5.25/5.51 thf(fact_4446_neg__numeral__le__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_le_numeral
% 5.25/5.51 thf(fact_4447_neg__numeral__le__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_le_numeral
% 5.25/5.51 thf(fact_4448_neg__numeral__le__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_le_numeral
% 5.25/5.51 thf(fact_4449_neg__numeral__le__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_le_numeral
% 5.25/5.51 thf(fact_4450_not__numeral__le__neg__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % not_numeral_le_neg_numeral
% 5.25/5.51 thf(fact_4451_not__numeral__le__neg__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % not_numeral_le_neg_numeral
% 5.25/5.51 thf(fact_4452_not__numeral__le__neg__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % not_numeral_le_neg_numeral
% 5.25/5.51 thf(fact_4453_not__numeral__le__neg__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % not_numeral_le_neg_numeral
% 5.25/5.51 thf(fact_4454_zero__neq__neg__numeral,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( zero_zero_int
% 5.25/5.51 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % zero_neq_neg_numeral
% 5.25/5.51 thf(fact_4455_zero__neq__neg__numeral,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( zero_zero_real
% 5.25/5.51 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % zero_neq_neg_numeral
% 5.25/5.51 thf(fact_4456_zero__neq__neg__numeral,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( zero_zero_complex
% 5.25/5.51 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % zero_neq_neg_numeral
% 5.25/5.51 thf(fact_4457_zero__neq__neg__numeral,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( zero_z3403309356797280102nteger
% 5.25/5.51 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % zero_neq_neg_numeral
% 5.25/5.51 thf(fact_4458_zero__neq__neg__numeral,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( zero_zero_rat
% 5.25/5.51 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % zero_neq_neg_numeral
% 5.25/5.51 thf(fact_4459_neg__numeral__less__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_less_numeral
% 5.25/5.51 thf(fact_4460_neg__numeral__less__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_less_numeral
% 5.25/5.51 thf(fact_4461_neg__numeral__less__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_less_numeral
% 5.25/5.51 thf(fact_4462_neg__numeral__less__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_numeral_less_numeral
% 5.25/5.51 thf(fact_4463_not__numeral__less__neg__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % not_numeral_less_neg_numeral
% 5.25/5.51 thf(fact_4464_not__numeral__less__neg__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % not_numeral_less_neg_numeral
% 5.25/5.51 thf(fact_4465_not__numeral__less__neg__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % not_numeral_less_neg_numeral
% 5.25/5.51 thf(fact_4466_not__numeral__less__neg__numeral,axiom,
% 5.25/5.51 ! [M: num,N: num] :
% 5.25/5.51 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % not_numeral_less_neg_numeral
% 5.25/5.51 thf(fact_4467_le__minus__one__simps_I2_J,axiom,
% 5.25/5.51 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.25/5.51
% 5.25/5.51 % le_minus_one_simps(2)
% 5.25/5.51 thf(fact_4468_le__minus__one__simps_I2_J,axiom,
% 5.25/5.51 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.25/5.51
% 5.25/5.51 % le_minus_one_simps(2)
% 5.25/5.51 thf(fact_4469_le__minus__one__simps_I2_J,axiom,
% 5.25/5.51 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.25/5.51
% 5.25/5.51 % le_minus_one_simps(2)
% 5.25/5.51 thf(fact_4470_le__minus__one__simps_I2_J,axiom,
% 5.25/5.51 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.25/5.51
% 5.25/5.51 % le_minus_one_simps(2)
% 5.25/5.51 thf(fact_4471_le__minus__one__simps_I4_J,axiom,
% 5.25/5.51 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_minus_one_simps(4)
% 5.25/5.51 thf(fact_4472_le__minus__one__simps_I4_J,axiom,
% 5.25/5.51 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_minus_one_simps(4)
% 5.25/5.51 thf(fact_4473_le__minus__one__simps_I4_J,axiom,
% 5.25/5.51 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_minus_one_simps(4)
% 5.25/5.51 thf(fact_4474_le__minus__one__simps_I4_J,axiom,
% 5.25/5.51 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.51
% 5.25/5.51 % le_minus_one_simps(4)
% 5.25/5.51 thf(fact_4475_zero__neq__neg__one,axiom,
% 5.25/5.51 ( zero_zero_int
% 5.25/5.51 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.51
% 5.25/5.51 % zero_neq_neg_one
% 5.25/5.51 thf(fact_4476_zero__neq__neg__one,axiom,
% 5.25/5.51 ( zero_zero_real
% 5.25/5.51 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.51
% 5.25/5.51 % zero_neq_neg_one
% 5.25/5.51 thf(fact_4477_zero__neq__neg__one,axiom,
% 5.25/5.51 ( zero_zero_complex
% 5.25/5.51 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.25/5.51
% 5.25/5.51 % zero_neq_neg_one
% 5.25/5.51 thf(fact_4478_zero__neq__neg__one,axiom,
% 5.25/5.51 ( zero_z3403309356797280102nteger
% 5.25/5.51 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.51
% 5.25/5.51 % zero_neq_neg_one
% 5.25/5.51 thf(fact_4479_zero__neq__neg__one,axiom,
% 5.25/5.51 ( zero_zero_rat
% 5.25/5.51 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.51
% 5.25/5.51 % zero_neq_neg_one
% 5.25/5.51 thf(fact_4480_add__eq__0__iff,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( ( plus_plus_int @ A @ B )
% 5.25/5.51 = zero_zero_int )
% 5.25/5.51 = ( B
% 5.25/5.51 = ( uminus_uminus_int @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_eq_0_iff
% 5.25/5.51 thf(fact_4481_add__eq__0__iff,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( ( plus_plus_real @ A @ B )
% 5.25/5.51 = zero_zero_real )
% 5.25/5.51 = ( B
% 5.25/5.51 = ( uminus_uminus_real @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_eq_0_iff
% 5.25/5.51 thf(fact_4482_add__eq__0__iff,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( ( plus_plus_complex @ A @ B )
% 5.25/5.51 = zero_zero_complex )
% 5.25/5.51 = ( B
% 5.25/5.51 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_eq_0_iff
% 5.25/5.51 thf(fact_4483_add__eq__0__iff,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.25/5.51 = zero_z3403309356797280102nteger )
% 5.25/5.51 = ( B
% 5.25/5.51 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_eq_0_iff
% 5.25/5.51 thf(fact_4484_add__eq__0__iff,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( ( plus_plus_rat @ A @ B )
% 5.25/5.51 = zero_zero_rat )
% 5.25/5.51 = ( B
% 5.25/5.51 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % add_eq_0_iff
% 5.25/5.51 thf(fact_4485_ab__group__add__class_Oab__left__minus,axiom,
% 5.25/5.51 ! [A: int] :
% 5.25/5.51 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.25/5.51 = zero_zero_int ) ).
% 5.25/5.51
% 5.25/5.51 % ab_group_add_class.ab_left_minus
% 5.25/5.51 thf(fact_4486_ab__group__add__class_Oab__left__minus,axiom,
% 5.25/5.51 ! [A: real] :
% 5.25/5.51 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.25/5.51 = zero_zero_real ) ).
% 5.25/5.51
% 5.25/5.51 % ab_group_add_class.ab_left_minus
% 5.25/5.51 thf(fact_4487_ab__group__add__class_Oab__left__minus,axiom,
% 5.25/5.51 ! [A: complex] :
% 5.25/5.51 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.25/5.51 = zero_zero_complex ) ).
% 5.25/5.51
% 5.25/5.51 % ab_group_add_class.ab_left_minus
% 5.25/5.51 thf(fact_4488_ab__group__add__class_Oab__left__minus,axiom,
% 5.25/5.51 ! [A: code_integer] :
% 5.25/5.51 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.25/5.51 = zero_z3403309356797280102nteger ) ).
% 5.25/5.51
% 5.25/5.51 % ab_group_add_class.ab_left_minus
% 5.25/5.51 thf(fact_4489_ab__group__add__class_Oab__left__minus,axiom,
% 5.25/5.51 ! [A: rat] :
% 5.25/5.51 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.25/5.51 = zero_zero_rat ) ).
% 5.25/5.51
% 5.25/5.51 % ab_group_add_class.ab_left_minus
% 5.25/5.51 thf(fact_4490_add_Oinverse__unique,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( ( plus_plus_int @ A @ B )
% 5.25/5.51 = zero_zero_int )
% 5.25/5.51 => ( ( uminus_uminus_int @ A )
% 5.25/5.51 = B ) ) ).
% 5.25/5.51
% 5.25/5.51 % add.inverse_unique
% 5.25/5.51 thf(fact_4491_add_Oinverse__unique,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( ( plus_plus_real @ A @ B )
% 5.25/5.51 = zero_zero_real )
% 5.25/5.51 => ( ( uminus_uminus_real @ A )
% 5.25/5.51 = B ) ) ).
% 5.25/5.51
% 5.25/5.51 % add.inverse_unique
% 5.25/5.51 thf(fact_4492_add_Oinverse__unique,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( ( plus_plus_complex @ A @ B )
% 5.25/5.51 = zero_zero_complex )
% 5.25/5.51 => ( ( uminus1482373934393186551omplex @ A )
% 5.25/5.51 = B ) ) ).
% 5.25/5.51
% 5.25/5.51 % add.inverse_unique
% 5.25/5.51 thf(fact_4493_add_Oinverse__unique,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.25/5.51 = zero_z3403309356797280102nteger )
% 5.25/5.51 => ( ( uminus1351360451143612070nteger @ A )
% 5.25/5.51 = B ) ) ).
% 5.25/5.51
% 5.25/5.51 % add.inverse_unique
% 5.25/5.51 thf(fact_4494_add_Oinverse__unique,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( ( plus_plus_rat @ A @ B )
% 5.25/5.51 = zero_zero_rat )
% 5.25/5.51 => ( ( uminus_uminus_rat @ A )
% 5.25/5.51 = B ) ) ).
% 5.25/5.51
% 5.25/5.51 % add.inverse_unique
% 5.25/5.51 thf(fact_4495_eq__neg__iff__add__eq__0,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( A
% 5.25/5.51 = ( uminus_uminus_int @ B ) )
% 5.25/5.51 = ( ( plus_plus_int @ A @ B )
% 5.25/5.51 = zero_zero_int ) ) ).
% 5.25/5.51
% 5.25/5.51 % eq_neg_iff_add_eq_0
% 5.25/5.51 thf(fact_4496_eq__neg__iff__add__eq__0,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( A
% 5.25/5.51 = ( uminus_uminus_real @ B ) )
% 5.25/5.51 = ( ( plus_plus_real @ A @ B )
% 5.25/5.51 = zero_zero_real ) ) ).
% 5.25/5.51
% 5.25/5.51 % eq_neg_iff_add_eq_0
% 5.25/5.51 thf(fact_4497_eq__neg__iff__add__eq__0,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( A
% 5.25/5.51 = ( uminus1482373934393186551omplex @ B ) )
% 5.25/5.51 = ( ( plus_plus_complex @ A @ B )
% 5.25/5.51 = zero_zero_complex ) ) ).
% 5.25/5.51
% 5.25/5.51 % eq_neg_iff_add_eq_0
% 5.25/5.51 thf(fact_4498_eq__neg__iff__add__eq__0,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( A
% 5.25/5.51 = ( uminus1351360451143612070nteger @ B ) )
% 5.25/5.51 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.25/5.51 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.51
% 5.25/5.51 % eq_neg_iff_add_eq_0
% 5.25/5.51 thf(fact_4499_eq__neg__iff__add__eq__0,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( A
% 5.25/5.51 = ( uminus_uminus_rat @ B ) )
% 5.25/5.51 = ( ( plus_plus_rat @ A @ B )
% 5.25/5.51 = zero_zero_rat ) ) ).
% 5.25/5.51
% 5.25/5.51 % eq_neg_iff_add_eq_0
% 5.25/5.51 thf(fact_4500_neg__eq__iff__add__eq__0,axiom,
% 5.25/5.51 ! [A: int,B: int] :
% 5.25/5.51 ( ( ( uminus_uminus_int @ A )
% 5.25/5.51 = B )
% 5.25/5.51 = ( ( plus_plus_int @ A @ B )
% 5.25/5.51 = zero_zero_int ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_eq_iff_add_eq_0
% 5.25/5.51 thf(fact_4501_neg__eq__iff__add__eq__0,axiom,
% 5.25/5.51 ! [A: real,B: real] :
% 5.25/5.51 ( ( ( uminus_uminus_real @ A )
% 5.25/5.51 = B )
% 5.25/5.51 = ( ( plus_plus_real @ A @ B )
% 5.25/5.51 = zero_zero_real ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_eq_iff_add_eq_0
% 5.25/5.51 thf(fact_4502_neg__eq__iff__add__eq__0,axiom,
% 5.25/5.51 ! [A: complex,B: complex] :
% 5.25/5.51 ( ( ( uminus1482373934393186551omplex @ A )
% 5.25/5.51 = B )
% 5.25/5.51 = ( ( plus_plus_complex @ A @ B )
% 5.25/5.51 = zero_zero_complex ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_eq_iff_add_eq_0
% 5.25/5.51 thf(fact_4503_neg__eq__iff__add__eq__0,axiom,
% 5.25/5.51 ! [A: code_integer,B: code_integer] :
% 5.25/5.51 ( ( ( uminus1351360451143612070nteger @ A )
% 5.25/5.51 = B )
% 5.25/5.51 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.25/5.51 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_eq_iff_add_eq_0
% 5.25/5.51 thf(fact_4504_neg__eq__iff__add__eq__0,axiom,
% 5.25/5.51 ! [A: rat,B: rat] :
% 5.25/5.51 ( ( ( uminus_uminus_rat @ A )
% 5.25/5.51 = B )
% 5.25/5.51 = ( ( plus_plus_rat @ A @ B )
% 5.25/5.51 = zero_zero_rat ) ) ).
% 5.25/5.51
% 5.25/5.51 % neg_eq_iff_add_eq_0
% 5.25/5.51 thf(fact_4505_less__minus__one__simps_I2_J,axiom,
% 5.25/5.51 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.25/5.51
% 5.25/5.51 % less_minus_one_simps(2)
% 5.25/5.51 thf(fact_4506_less__minus__one__simps_I2_J,axiom,
% 5.25/5.51 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.25/5.51
% 5.25/5.51 % less_minus_one_simps(2)
% 5.25/5.51 thf(fact_4507_less__minus__one__simps_I2_J,axiom,
% 5.25/5.51 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.25/5.51
% 5.25/5.51 % less_minus_one_simps(2)
% 5.25/5.51 thf(fact_4508_less__minus__one__simps_I2_J,axiom,
% 5.25/5.51 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.25/5.51
% 5.25/5.51 % less_minus_one_simps(2)
% 5.25/5.51 thf(fact_4509_less__minus__one__simps_I4_J,axiom,
% 5.25/5.51 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_minus_one_simps(4)
% 5.25/5.51 thf(fact_4510_less__minus__one__simps_I4_J,axiom,
% 5.25/5.51 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_minus_one_simps(4)
% 5.25/5.51 thf(fact_4511_less__minus__one__simps_I4_J,axiom,
% 5.25/5.51 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_minus_one_simps(4)
% 5.25/5.51 thf(fact_4512_less__minus__one__simps_I4_J,axiom,
% 5.25/5.51 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.51
% 5.25/5.51 % less_minus_one_simps(4)
% 5.25/5.51 thf(fact_4513_numeral__times__minus__swap,axiom,
% 5.25/5.51 ! [W: num,X3: int] :
% 5.25/5.51 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X3 ) )
% 5.25/5.51 = ( times_times_int @ X3 @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_times_minus_swap
% 5.25/5.51 thf(fact_4514_numeral__times__minus__swap,axiom,
% 5.25/5.51 ! [W: num,X3: real] :
% 5.25/5.51 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X3 ) )
% 5.25/5.51 = ( times_times_real @ X3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_times_minus_swap
% 5.25/5.51 thf(fact_4515_numeral__times__minus__swap,axiom,
% 5.25/5.51 ! [W: num,X3: complex] :
% 5.25/5.51 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X3 ) )
% 5.25/5.51 = ( times_times_complex @ X3 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_times_minus_swap
% 5.25/5.51 thf(fact_4516_numeral__times__minus__swap,axiom,
% 5.25/5.51 ! [W: num,X3: code_integer] :
% 5.25/5.51 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X3 ) )
% 5.25/5.51 = ( times_3573771949741848930nteger @ X3 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_times_minus_swap
% 5.25/5.51 thf(fact_4517_numeral__times__minus__swap,axiom,
% 5.25/5.51 ! [W: num,X3: rat] :
% 5.25/5.51 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X3 ) )
% 5.25/5.51 = ( times_times_rat @ X3 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_times_minus_swap
% 5.25/5.51 thf(fact_4518_nonzero__minus__divide__right,axiom,
% 5.25/5.51 ! [B: real,A: real] :
% 5.25/5.51 ( ( B != zero_zero_real )
% 5.25/5.51 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.25/5.51 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % nonzero_minus_divide_right
% 5.25/5.51 thf(fact_4519_nonzero__minus__divide__right,axiom,
% 5.25/5.51 ! [B: complex,A: complex] :
% 5.25/5.51 ( ( B != zero_zero_complex )
% 5.25/5.51 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.25/5.51 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % nonzero_minus_divide_right
% 5.25/5.51 thf(fact_4520_nonzero__minus__divide__right,axiom,
% 5.25/5.51 ! [B: rat,A: rat] :
% 5.25/5.51 ( ( B != zero_zero_rat )
% 5.25/5.51 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.25/5.51 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % nonzero_minus_divide_right
% 5.25/5.51 thf(fact_4521_nonzero__minus__divide__divide,axiom,
% 5.25/5.51 ! [B: real,A: real] :
% 5.25/5.51 ( ( B != zero_zero_real )
% 5.25/5.51 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.25/5.51 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % nonzero_minus_divide_divide
% 5.25/5.51 thf(fact_4522_nonzero__minus__divide__divide,axiom,
% 5.25/5.51 ! [B: complex,A: complex] :
% 5.25/5.51 ( ( B != zero_zero_complex )
% 5.25/5.51 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.25/5.51 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % nonzero_minus_divide_divide
% 5.25/5.51 thf(fact_4523_nonzero__minus__divide__divide,axiom,
% 5.25/5.51 ! [B: rat,A: rat] :
% 5.25/5.51 ( ( B != zero_zero_rat )
% 5.25/5.51 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.25/5.51 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % nonzero_minus_divide_divide
% 5.25/5.51 thf(fact_4524_one__neq__neg__numeral,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( one_one_int
% 5.25/5.51 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % one_neq_neg_numeral
% 5.25/5.51 thf(fact_4525_one__neq__neg__numeral,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( one_one_real
% 5.25/5.51 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % one_neq_neg_numeral
% 5.25/5.51 thf(fact_4526_one__neq__neg__numeral,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( one_one_complex
% 5.25/5.51 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % one_neq_neg_numeral
% 5.25/5.51 thf(fact_4527_one__neq__neg__numeral,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( one_one_Code_integer
% 5.25/5.51 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % one_neq_neg_numeral
% 5.25/5.51 thf(fact_4528_one__neq__neg__numeral,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( one_one_rat
% 5.25/5.51 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % one_neq_neg_numeral
% 5.25/5.51 thf(fact_4529_numeral__neq__neg__one,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( numeral_numeral_int @ N )
% 5.25/5.51 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_neq_neg_one
% 5.25/5.51 thf(fact_4530_numeral__neq__neg__one,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( numeral_numeral_real @ N )
% 5.25/5.51 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_neq_neg_one
% 5.25/5.51 thf(fact_4531_numeral__neq__neg__one,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( numera6690914467698888265omplex @ N )
% 5.25/5.51 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_neq_neg_one
% 5.25/5.51 thf(fact_4532_numeral__neq__neg__one,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( numera6620942414471956472nteger @ N )
% 5.25/5.51 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_neq_neg_one
% 5.25/5.51 thf(fact_4533_numeral__neq__neg__one,axiom,
% 5.25/5.51 ! [N: num] :
% 5.25/5.51 ( ( numeral_numeral_rat @ N )
% 5.25/5.51 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.51
% 5.25/5.51 % numeral_neq_neg_one
% 5.25/5.51 thf(fact_4534_square__eq__1__iff,axiom,
% 5.25/5.51 ! [X3: int] :
% 5.25/5.51 ( ( ( times_times_int @ X3 @ X3 )
% 5.25/5.51 = one_one_int )
% 5.25/5.51 = ( ( X3 = one_one_int )
% 5.25/5.51 | ( X3
% 5.25/5.51 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % square_eq_1_iff
% 5.25/5.51 thf(fact_4535_square__eq__1__iff,axiom,
% 5.25/5.51 ! [X3: real] :
% 5.25/5.51 ( ( ( times_times_real @ X3 @ X3 )
% 5.25/5.51 = one_one_real )
% 5.25/5.51 = ( ( X3 = one_one_real )
% 5.25/5.51 | ( X3
% 5.25/5.51 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.25/5.51
% 5.25/5.51 % square_eq_1_iff
% 5.25/5.51 thf(fact_4536_square__eq__1__iff,axiom,
% 5.25/5.51 ! [X3: complex] :
% 5.25/5.51 ( ( ( times_times_complex @ X3 @ X3 )
% 5.25/5.51 = one_one_complex )
% 5.25/5.51 = ( ( X3 = one_one_complex )
% 5.25/5.52 | ( X3
% 5.25/5.52 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % square_eq_1_iff
% 5.25/5.52 thf(fact_4537_square__eq__1__iff,axiom,
% 5.25/5.52 ! [X3: code_integer] :
% 5.25/5.52 ( ( ( times_3573771949741848930nteger @ X3 @ X3 )
% 5.25/5.52 = one_one_Code_integer )
% 5.25/5.52 = ( ( X3 = one_one_Code_integer )
% 5.25/5.52 | ( X3
% 5.25/5.52 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % square_eq_1_iff
% 5.25/5.52 thf(fact_4538_square__eq__1__iff,axiom,
% 5.25/5.52 ! [X3: rat] :
% 5.25/5.52 ( ( ( times_times_rat @ X3 @ X3 )
% 5.25/5.52 = one_one_rat )
% 5.25/5.52 = ( ( X3 = one_one_rat )
% 5.25/5.52 | ( X3
% 5.25/5.52 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % square_eq_1_iff
% 5.25/5.52 thf(fact_4539_group__cancel_Osub2,axiom,
% 5.25/5.52 ! [B3: int,K: int,B: int,A: int] :
% 5.25/5.52 ( ( B3
% 5.25/5.52 = ( plus_plus_int @ K @ B ) )
% 5.25/5.52 => ( ( minus_minus_int @ A @ B3 )
% 5.25/5.52 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % group_cancel.sub2
% 5.25/5.52 thf(fact_4540_group__cancel_Osub2,axiom,
% 5.25/5.52 ! [B3: real,K: real,B: real,A: real] :
% 5.25/5.52 ( ( B3
% 5.25/5.52 = ( plus_plus_real @ K @ B ) )
% 5.25/5.52 => ( ( minus_minus_real @ A @ B3 )
% 5.25/5.52 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % group_cancel.sub2
% 5.25/5.52 thf(fact_4541_group__cancel_Osub2,axiom,
% 5.25/5.52 ! [B3: complex,K: complex,B: complex,A: complex] :
% 5.25/5.52 ( ( B3
% 5.25/5.52 = ( plus_plus_complex @ K @ B ) )
% 5.25/5.52 => ( ( minus_minus_complex @ A @ B3 )
% 5.25/5.52 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % group_cancel.sub2
% 5.25/5.52 thf(fact_4542_group__cancel_Osub2,axiom,
% 5.25/5.52 ! [B3: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.52 ( ( B3
% 5.25/5.52 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 5.25/5.52 => ( ( minus_8373710615458151222nteger @ A @ B3 )
% 5.25/5.52 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % group_cancel.sub2
% 5.25/5.52 thf(fact_4543_group__cancel_Osub2,axiom,
% 5.25/5.52 ! [B3: rat,K: rat,B: rat,A: rat] :
% 5.25/5.52 ( ( B3
% 5.25/5.52 = ( plus_plus_rat @ K @ B ) )
% 5.25/5.52 => ( ( minus_minus_rat @ A @ B3 )
% 5.25/5.52 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % group_cancel.sub2
% 5.25/5.52 thf(fact_4544_diff__conv__add__uminus,axiom,
% 5.25/5.52 ( minus_minus_int
% 5.25/5.52 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % diff_conv_add_uminus
% 5.25/5.52 thf(fact_4545_diff__conv__add__uminus,axiom,
% 5.25/5.52 ( minus_minus_real
% 5.25/5.52 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % diff_conv_add_uminus
% 5.25/5.52 thf(fact_4546_diff__conv__add__uminus,axiom,
% 5.25/5.52 ( minus_minus_complex
% 5.25/5.52 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % diff_conv_add_uminus
% 5.25/5.52 thf(fact_4547_diff__conv__add__uminus,axiom,
% 5.25/5.52 ( minus_8373710615458151222nteger
% 5.25/5.52 = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % diff_conv_add_uminus
% 5.25/5.52 thf(fact_4548_diff__conv__add__uminus,axiom,
% 5.25/5.52 ( minus_minus_rat
% 5.25/5.52 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % diff_conv_add_uminus
% 5.25/5.52 thf(fact_4549_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.25/5.52 ( minus_minus_int
% 5.25/5.52 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.25/5.52 thf(fact_4550_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.25/5.52 ( minus_minus_real
% 5.25/5.52 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.25/5.52 thf(fact_4551_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.25/5.52 ( minus_minus_complex
% 5.25/5.52 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.25/5.52 thf(fact_4552_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.25/5.52 ( minus_8373710615458151222nteger
% 5.25/5.52 = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.25/5.52 thf(fact_4553_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.25/5.52 ( minus_minus_rat
% 5.25/5.52 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.25/5.52 thf(fact_4554_replicate__eqI,axiom,
% 5.25/5.52 ! [Xs: list_real,N: nat,X3: real] :
% 5.25/5.52 ( ( ( size_size_list_real @ Xs )
% 5.25/5.52 = N )
% 5.25/5.52 => ( ! [Y3: real] :
% 5.25/5.52 ( ( member_real @ Y3 @ ( set_real2 @ Xs ) )
% 5.25/5.52 => ( Y3 = X3 ) )
% 5.25/5.52 => ( Xs
% 5.25/5.52 = ( replicate_real @ N @ X3 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % replicate_eqI
% 5.25/5.52 thf(fact_4555_replicate__eqI,axiom,
% 5.25/5.52 ! [Xs: list_complex,N: nat,X3: complex] :
% 5.25/5.52 ( ( ( size_s3451745648224563538omplex @ Xs )
% 5.25/5.52 = N )
% 5.25/5.52 => ( ! [Y3: complex] :
% 5.25/5.52 ( ( member_complex @ Y3 @ ( set_complex2 @ Xs ) )
% 5.25/5.52 => ( Y3 = X3 ) )
% 5.25/5.52 => ( Xs
% 5.25/5.52 = ( replicate_complex @ N @ X3 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % replicate_eqI
% 5.25/5.52 thf(fact_4556_replicate__eqI,axiom,
% 5.25/5.52 ! [Xs: list_P6011104703257516679at_nat,N: nat,X3: product_prod_nat_nat] :
% 5.25/5.52 ( ( ( size_s5460976970255530739at_nat @ Xs )
% 5.25/5.52 = N )
% 5.25/5.52 => ( ! [Y3: product_prod_nat_nat] :
% 5.25/5.52 ( ( member8440522571783428010at_nat @ Y3 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 5.25/5.52 => ( Y3 = X3 ) )
% 5.25/5.52 => ( Xs
% 5.25/5.52 = ( replic4235873036481779905at_nat @ N @ X3 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % replicate_eqI
% 5.25/5.52 thf(fact_4557_replicate__eqI,axiom,
% 5.25/5.52 ! [Xs: list_VEBT_VEBT,N: nat,X3: vEBT_VEBT] :
% 5.25/5.52 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.25/5.52 = N )
% 5.25/5.52 => ( ! [Y3: vEBT_VEBT] :
% 5.25/5.52 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.25/5.52 => ( Y3 = X3 ) )
% 5.25/5.52 => ( Xs
% 5.25/5.52 = ( replicate_VEBT_VEBT @ N @ X3 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % replicate_eqI
% 5.25/5.52 thf(fact_4558_replicate__eqI,axiom,
% 5.25/5.52 ! [Xs: list_o,N: nat,X3: $o] :
% 5.25/5.52 ( ( ( size_size_list_o @ Xs )
% 5.25/5.52 = N )
% 5.25/5.52 => ( ! [Y3: $o] :
% 5.25/5.52 ( ( member_o @ Y3 @ ( set_o2 @ Xs ) )
% 5.25/5.52 => ( Y3 = X3 ) )
% 5.25/5.52 => ( Xs
% 5.25/5.52 = ( replicate_o @ N @ X3 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % replicate_eqI
% 5.25/5.52 thf(fact_4559_replicate__eqI,axiom,
% 5.25/5.52 ! [Xs: list_nat,N: nat,X3: nat] :
% 5.25/5.52 ( ( ( size_size_list_nat @ Xs )
% 5.25/5.52 = N )
% 5.25/5.52 => ( ! [Y3: nat] :
% 5.25/5.52 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs ) )
% 5.25/5.52 => ( Y3 = X3 ) )
% 5.25/5.52 => ( Xs
% 5.25/5.52 = ( replicate_nat @ N @ X3 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % replicate_eqI
% 5.25/5.52 thf(fact_4560_replicate__eqI,axiom,
% 5.25/5.52 ! [Xs: list_int,N: nat,X3: int] :
% 5.25/5.52 ( ( ( size_size_list_int @ Xs )
% 5.25/5.52 = N )
% 5.25/5.52 => ( ! [Y3: int] :
% 5.25/5.52 ( ( member_int @ Y3 @ ( set_int2 @ Xs ) )
% 5.25/5.52 => ( Y3 = X3 ) )
% 5.25/5.52 => ( Xs
% 5.25/5.52 = ( replicate_int @ N @ X3 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % replicate_eqI
% 5.25/5.52 thf(fact_4561_replicate__length__same,axiom,
% 5.25/5.52 ! [Xs: list_VEBT_VEBT,X3: vEBT_VEBT] :
% 5.25/5.52 ( ! [X5: vEBT_VEBT] :
% 5.25/5.52 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.25/5.52 => ( X5 = X3 ) )
% 5.25/5.52 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs ) @ X3 )
% 5.25/5.52 = Xs ) ) ).
% 5.25/5.52
% 5.25/5.52 % replicate_length_same
% 5.25/5.52 thf(fact_4562_replicate__length__same,axiom,
% 5.25/5.52 ! [Xs: list_o,X3: $o] :
% 5.25/5.52 ( ! [X5: $o] :
% 5.25/5.52 ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 5.25/5.52 => ( X5 = X3 ) )
% 5.25/5.52 => ( ( replicate_o @ ( size_size_list_o @ Xs ) @ X3 )
% 5.25/5.52 = Xs ) ) ).
% 5.25/5.52
% 5.25/5.52 % replicate_length_same
% 5.25/5.52 thf(fact_4563_replicate__length__same,axiom,
% 5.25/5.52 ! [Xs: list_nat,X3: nat] :
% 5.25/5.52 ( ! [X5: nat] :
% 5.25/5.52 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 5.25/5.52 => ( X5 = X3 ) )
% 5.25/5.52 => ( ( replicate_nat @ ( size_size_list_nat @ Xs ) @ X3 )
% 5.25/5.52 = Xs ) ) ).
% 5.25/5.52
% 5.25/5.52 % replicate_length_same
% 5.25/5.52 thf(fact_4564_replicate__length__same,axiom,
% 5.25/5.52 ! [Xs: list_int,X3: int] :
% 5.25/5.52 ( ! [X5: int] :
% 5.25/5.52 ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 5.25/5.52 => ( X5 = X3 ) )
% 5.25/5.52 => ( ( replicate_int @ ( size_size_list_int @ Xs ) @ X3 )
% 5.25/5.52 = Xs ) ) ).
% 5.25/5.52
% 5.25/5.52 % replicate_length_same
% 5.25/5.52 thf(fact_4565_dvd__neg__div,axiom,
% 5.25/5.52 ! [B: int,A: int] :
% 5.25/5.52 ( ( dvd_dvd_int @ B @ A )
% 5.25/5.52 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.25/5.52 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dvd_neg_div
% 5.25/5.52 thf(fact_4566_dvd__neg__div,axiom,
% 5.25/5.52 ! [B: real,A: real] :
% 5.25/5.52 ( ( dvd_dvd_real @ B @ A )
% 5.25/5.52 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.25/5.52 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dvd_neg_div
% 5.25/5.52 thf(fact_4567_dvd__neg__div,axiom,
% 5.25/5.52 ! [B: complex,A: complex] :
% 5.25/5.52 ( ( dvd_dvd_complex @ B @ A )
% 5.25/5.52 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dvd_neg_div
% 5.25/5.52 thf(fact_4568_dvd__neg__div,axiom,
% 5.25/5.52 ! [B: code_integer,A: code_integer] :
% 5.25/5.52 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.52 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.25/5.52 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dvd_neg_div
% 5.25/5.52 thf(fact_4569_dvd__neg__div,axiom,
% 5.25/5.52 ! [B: rat,A: rat] :
% 5.25/5.52 ( ( dvd_dvd_rat @ B @ A )
% 5.25/5.52 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.25/5.52 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dvd_neg_div
% 5.25/5.52 thf(fact_4570_dvd__div__neg,axiom,
% 5.25/5.52 ! [B: int,A: int] :
% 5.25/5.52 ( ( dvd_dvd_int @ B @ A )
% 5.25/5.52 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.25/5.52 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dvd_div_neg
% 5.25/5.52 thf(fact_4571_dvd__div__neg,axiom,
% 5.25/5.52 ! [B: real,A: real] :
% 5.25/5.52 ( ( dvd_dvd_real @ B @ A )
% 5.25/5.52 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.25/5.52 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dvd_div_neg
% 5.25/5.52 thf(fact_4572_dvd__div__neg,axiom,
% 5.25/5.52 ! [B: complex,A: complex] :
% 5.25/5.52 ( ( dvd_dvd_complex @ B @ A )
% 5.25/5.52 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dvd_div_neg
% 5.25/5.52 thf(fact_4573_dvd__div__neg,axiom,
% 5.25/5.52 ! [B: code_integer,A: code_integer] :
% 5.25/5.52 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.52 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.25/5.52 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dvd_div_neg
% 5.25/5.52 thf(fact_4574_dvd__div__neg,axiom,
% 5.25/5.52 ! [B: rat,A: rat] :
% 5.25/5.52 ( ( dvd_dvd_rat @ B @ A )
% 5.25/5.52 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.25/5.52 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dvd_div_neg
% 5.25/5.52 thf(fact_4575_Suc__diff__Suc,axiom,
% 5.25/5.52 ! [N: nat,M: nat] :
% 5.25/5.52 ( ( ord_less_nat @ N @ M )
% 5.25/5.52 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 5.25/5.52 = ( minus_minus_nat @ M @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Suc_diff_Suc
% 5.25/5.52 thf(fact_4576_diff__less__Suc,axiom,
% 5.25/5.52 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 5.25/5.52
% 5.25/5.52 % diff_less_Suc
% 5.25/5.52 thf(fact_4577_diff__less,axiom,
% 5.25/5.52 ! [N: nat,M: nat] :
% 5.25/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.52 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.52 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % diff_less
% 5.25/5.52 thf(fact_4578_Suc__diff__le,axiom,
% 5.25/5.52 ! [N: nat,M: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.52 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.25/5.52 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Suc_diff_le
% 5.25/5.52 thf(fact_4579_less__diff__iff,axiom,
% 5.25/5.52 ! [K: nat,M: nat,N: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ K @ M )
% 5.25/5.52 => ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.52 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.25/5.52 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_diff_iff
% 5.25/5.52 thf(fact_4580_diff__less__mono,axiom,
% 5.25/5.52 ! [A: nat,B: nat,C: nat] :
% 5.25/5.52 ( ( ord_less_nat @ A @ B )
% 5.25/5.52 => ( ( ord_less_eq_nat @ C @ A )
% 5.25/5.52 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % diff_less_mono
% 5.25/5.52 thf(fact_4581_diff__add__0,axiom,
% 5.25/5.52 ! [N: nat,M: nat] :
% 5.25/5.52 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 5.25/5.52 = zero_zero_nat ) ).
% 5.25/5.52
% 5.25/5.52 % diff_add_0
% 5.25/5.52 thf(fact_4582_add__diff__inverse__nat,axiom,
% 5.25/5.52 ! [M: nat,N: nat] :
% 5.25/5.52 ( ~ ( ord_less_nat @ M @ N )
% 5.25/5.52 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 5.25/5.52 = M ) ) ).
% 5.25/5.52
% 5.25/5.52 % add_diff_inverse_nat
% 5.25/5.52 thf(fact_4583_less__diff__conv,axiom,
% 5.25/5.52 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.52 ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J2 @ K ) )
% 5.25/5.52 = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J2 ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_diff_conv
% 5.25/5.52 thf(fact_4584_Nat_Ole__imp__diff__is__add,axiom,
% 5.25/5.52 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.52 => ( ( ( minus_minus_nat @ J2 @ I2 )
% 5.25/5.52 = K )
% 5.25/5.52 = ( J2
% 5.25/5.52 = ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Nat.le_imp_diff_is_add
% 5.25/5.52 thf(fact_4585_Nat_Odiff__add__assoc2,axiom,
% 5.25/5.52 ! [K: nat,J2: nat,I2: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ K @ J2 )
% 5.25/5.52 => ( ( minus_minus_nat @ ( plus_plus_nat @ J2 @ I2 ) @ K )
% 5.25/5.52 = ( plus_plus_nat @ ( minus_minus_nat @ J2 @ K ) @ I2 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Nat.diff_add_assoc2
% 5.25/5.52 thf(fact_4586_Nat_Odiff__add__assoc,axiom,
% 5.25/5.52 ! [K: nat,J2: nat,I2: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ K @ J2 )
% 5.25/5.52 => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K )
% 5.25/5.52 = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J2 @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Nat.diff_add_assoc
% 5.25/5.52 thf(fact_4587_Nat_Ole__diff__conv2,axiom,
% 5.25/5.52 ! [K: nat,J2: nat,I2: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ K @ J2 )
% 5.25/5.52 => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J2 @ K ) )
% 5.25/5.52 = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J2 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Nat.le_diff_conv2
% 5.25/5.52 thf(fact_4588_le__diff__conv,axiom,
% 5.25/5.52 ! [J2: nat,K: nat,I2: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J2 @ K ) @ I2 )
% 5.25/5.52 = ( ord_less_eq_nat @ J2 @ ( plus_plus_nat @ I2 @ K ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % le_diff_conv
% 5.25/5.52 thf(fact_4589_diff__Suc__eq__diff__pred,axiom,
% 5.25/5.52 ! [M: nat,N: nat] :
% 5.25/5.52 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.25/5.52 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 5.25/5.52
% 5.25/5.52 % diff_Suc_eq_diff_pred
% 5.25/5.52 thf(fact_4590_pos__zmult__eq__1__iff__lemma,axiom,
% 5.25/5.52 ! [M: int,N: int] :
% 5.25/5.52 ( ( ( times_times_int @ M @ N )
% 5.25/5.52 = one_one_int )
% 5.25/5.52 => ( ( M = one_one_int )
% 5.25/5.52 | ( M
% 5.25/5.52 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % pos_zmult_eq_1_iff_lemma
% 5.25/5.52 thf(fact_4591_zmult__eq__1__iff,axiom,
% 5.25/5.52 ! [M: int,N: int] :
% 5.25/5.52 ( ( ( times_times_int @ M @ N )
% 5.25/5.52 = one_one_int )
% 5.25/5.52 = ( ( ( M = one_one_int )
% 5.25/5.52 & ( N = one_one_int ) )
% 5.25/5.52 | ( ( M
% 5.25/5.52 = ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.52 & ( N
% 5.25/5.52 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % zmult_eq_1_iff
% 5.25/5.52 thf(fact_4592_mod__geq,axiom,
% 5.25/5.52 ! [M: nat,N: nat] :
% 5.25/5.52 ( ~ ( ord_less_nat @ M @ N )
% 5.25/5.52 => ( ( modulo_modulo_nat @ M @ N )
% 5.25/5.52 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % mod_geq
% 5.25/5.52 thf(fact_4593_mod__if,axiom,
% 5.25/5.52 ( modulo_modulo_nat
% 5.25/5.52 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( ord_less_nat @ M6 @ N2 ) @ M6 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % mod_if
% 5.25/5.52 thf(fact_4594_le__mod__geq,axiom,
% 5.25/5.52 ! [N: nat,M: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.52 => ( ( modulo_modulo_nat @ M @ N )
% 5.25/5.52 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % le_mod_geq
% 5.25/5.52 thf(fact_4595_mod__eq__dvd__iff__nat,axiom,
% 5.25/5.52 ! [N: nat,M: nat,Q2: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.52 => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.25/5.52 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.25/5.52 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % mod_eq_dvd_iff_nat
% 5.25/5.52 thf(fact_4596_numeral__eq__Suc,axiom,
% 5.25/5.52 ( numeral_numeral_nat
% 5.25/5.52 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % numeral_eq_Suc
% 5.25/5.52 thf(fact_4597_zmod__zminus1__not__zero,axiom,
% 5.25/5.52 ! [K: int,L2: int] :
% 5.25/5.52 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 5.25/5.52 != zero_zero_int )
% 5.25/5.52 => ( ( modulo_modulo_int @ K @ L2 )
% 5.25/5.52 != zero_zero_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % zmod_zminus1_not_zero
% 5.25/5.52 thf(fact_4598_zmod__zminus2__not__zero,axiom,
% 5.25/5.52 ! [K: int,L2: int] :
% 5.25/5.52 ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L2 ) )
% 5.25/5.52 != zero_zero_int )
% 5.25/5.52 => ( ( modulo_modulo_int @ K @ L2 )
% 5.25/5.52 != zero_zero_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % zmod_zminus2_not_zero
% 5.25/5.52 thf(fact_4599_nat__minus__add__max,axiom,
% 5.25/5.52 ! [N: nat,M: nat] :
% 5.25/5.52 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 5.25/5.52 = ( ord_max_nat @ N @ M ) ) ).
% 5.25/5.52
% 5.25/5.52 % nat_minus_add_max
% 5.25/5.52 thf(fact_4600_add__diff__assoc__enat,axiom,
% 5.25/5.52 ! [Z: extended_enat,Y: extended_enat,X3: extended_enat] :
% 5.25/5.52 ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 5.25/5.52 => ( ( plus_p3455044024723400733d_enat @ X3 @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 5.25/5.52 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X3 @ Y ) @ Z ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % add_diff_assoc_enat
% 5.25/5.52 thf(fact_4601_neg__numeral__le__zero,axiom,
% 5.25/5.52 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_le_zero
% 5.25/5.52 thf(fact_4602_neg__numeral__le__zero,axiom,
% 5.25/5.52 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_le_zero
% 5.25/5.52 thf(fact_4603_neg__numeral__le__zero,axiom,
% 5.25/5.52 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_le_zero
% 5.25/5.52 thf(fact_4604_neg__numeral__le__zero,axiom,
% 5.25/5.52 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_le_zero
% 5.25/5.52 thf(fact_4605_not__zero__le__neg__numeral,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_zero_le_neg_numeral
% 5.25/5.52 thf(fact_4606_not__zero__le__neg__numeral,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_zero_le_neg_numeral
% 5.25/5.52 thf(fact_4607_not__zero__le__neg__numeral,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_zero_le_neg_numeral
% 5.25/5.52 thf(fact_4608_not__zero__le__neg__numeral,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_zero_le_neg_numeral
% 5.25/5.52 thf(fact_4609_neg__numeral__less__zero,axiom,
% 5.25/5.52 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_less_zero
% 5.25/5.52 thf(fact_4610_neg__numeral__less__zero,axiom,
% 5.25/5.52 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_less_zero
% 5.25/5.52 thf(fact_4611_neg__numeral__less__zero,axiom,
% 5.25/5.52 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_less_zero
% 5.25/5.52 thf(fact_4612_neg__numeral__less__zero,axiom,
% 5.25/5.52 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_less_zero
% 5.25/5.52 thf(fact_4613_not__zero__less__neg__numeral,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_zero_less_neg_numeral
% 5.25/5.52 thf(fact_4614_not__zero__less__neg__numeral,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_zero_less_neg_numeral
% 5.25/5.52 thf(fact_4615_not__zero__less__neg__numeral,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_zero_less_neg_numeral
% 5.25/5.52 thf(fact_4616_not__zero__less__neg__numeral,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_zero_less_neg_numeral
% 5.25/5.52 thf(fact_4617_le__minus__one__simps_I3_J,axiom,
% 5.25/5.52 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.52
% 5.25/5.52 % le_minus_one_simps(3)
% 5.25/5.52 thf(fact_4618_le__minus__one__simps_I3_J,axiom,
% 5.25/5.52 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.52
% 5.25/5.52 % le_minus_one_simps(3)
% 5.25/5.52 thf(fact_4619_le__minus__one__simps_I3_J,axiom,
% 5.25/5.52 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.52
% 5.25/5.52 % le_minus_one_simps(3)
% 5.25/5.52 thf(fact_4620_le__minus__one__simps_I3_J,axiom,
% 5.25/5.52 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % le_minus_one_simps(3)
% 5.25/5.52 thf(fact_4621_le__minus__one__simps_I1_J,axiom,
% 5.25/5.52 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.25/5.52
% 5.25/5.52 % le_minus_one_simps(1)
% 5.25/5.52 thf(fact_4622_le__minus__one__simps_I1_J,axiom,
% 5.25/5.52 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.25/5.52
% 5.25/5.52 % le_minus_one_simps(1)
% 5.25/5.52 thf(fact_4623_le__minus__one__simps_I1_J,axiom,
% 5.25/5.52 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.25/5.52
% 5.25/5.52 % le_minus_one_simps(1)
% 5.25/5.52 thf(fact_4624_le__minus__one__simps_I1_J,axiom,
% 5.25/5.52 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.25/5.52
% 5.25/5.52 % le_minus_one_simps(1)
% 5.25/5.52 thf(fact_4625_less__minus__one__simps_I3_J,axiom,
% 5.25/5.52 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_minus_one_simps(3)
% 5.25/5.52 thf(fact_4626_less__minus__one__simps_I3_J,axiom,
% 5.25/5.52 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_minus_one_simps(3)
% 5.25/5.52 thf(fact_4627_less__minus__one__simps_I3_J,axiom,
% 5.25/5.52 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_minus_one_simps(3)
% 5.25/5.52 thf(fact_4628_less__minus__one__simps_I3_J,axiom,
% 5.25/5.52 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_minus_one_simps(3)
% 5.25/5.52 thf(fact_4629_less__minus__one__simps_I1_J,axiom,
% 5.25/5.52 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.25/5.52
% 5.25/5.52 % less_minus_one_simps(1)
% 5.25/5.52 thf(fact_4630_less__minus__one__simps_I1_J,axiom,
% 5.25/5.52 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.25/5.52
% 5.25/5.52 % less_minus_one_simps(1)
% 5.25/5.52 thf(fact_4631_less__minus__one__simps_I1_J,axiom,
% 5.25/5.52 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.25/5.52
% 5.25/5.52 % less_minus_one_simps(1)
% 5.25/5.52 thf(fact_4632_less__minus__one__simps_I1_J,axiom,
% 5.25/5.52 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.25/5.52
% 5.25/5.52 % less_minus_one_simps(1)
% 5.25/5.52 thf(fact_4633_neg__numeral__le__one,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_le_one
% 5.25/5.52 thf(fact_4634_neg__numeral__le__one,axiom,
% 5.25/5.52 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_le_one
% 5.25/5.52 thf(fact_4635_neg__numeral__le__one,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_le_one
% 5.25/5.52 thf(fact_4636_neg__numeral__le__one,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_le_one
% 5.25/5.52 thf(fact_4637_neg__one__le__numeral,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_one_le_numeral
% 5.25/5.52 thf(fact_4638_neg__one__le__numeral,axiom,
% 5.25/5.52 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_one_le_numeral
% 5.25/5.52 thf(fact_4639_neg__one__le__numeral,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_one_le_numeral
% 5.25/5.52 thf(fact_4640_neg__one__le__numeral,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_one_le_numeral
% 5.25/5.52 thf(fact_4641_neg__numeral__le__neg__one,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_le_neg_one
% 5.25/5.52 thf(fact_4642_neg__numeral__le__neg__one,axiom,
% 5.25/5.52 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_le_neg_one
% 5.25/5.52 thf(fact_4643_neg__numeral__le__neg__one,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_le_neg_one
% 5.25/5.52 thf(fact_4644_neg__numeral__le__neg__one,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_le_neg_one
% 5.25/5.52 thf(fact_4645_not__numeral__le__neg__one,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_numeral_le_neg_one
% 5.25/5.52 thf(fact_4646_not__numeral__le__neg__one,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_numeral_le_neg_one
% 5.25/5.52 thf(fact_4647_not__numeral__le__neg__one,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_numeral_le_neg_one
% 5.25/5.52 thf(fact_4648_not__numeral__le__neg__one,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_numeral_le_neg_one
% 5.25/5.52 thf(fact_4649_not__one__le__neg__numeral,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_one_le_neg_numeral
% 5.25/5.52 thf(fact_4650_not__one__le__neg__numeral,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_one_le_neg_numeral
% 5.25/5.52 thf(fact_4651_not__one__le__neg__numeral,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_one_le_neg_numeral
% 5.25/5.52 thf(fact_4652_not__one__le__neg__numeral,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_one_le_neg_numeral
% 5.25/5.52 thf(fact_4653_neg__numeral__less__one,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_less_one
% 5.25/5.52 thf(fact_4654_neg__numeral__less__one,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_less_one
% 5.25/5.52 thf(fact_4655_neg__numeral__less__one,axiom,
% 5.25/5.52 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_less_one
% 5.25/5.52 thf(fact_4656_neg__numeral__less__one,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.25/5.52
% 5.25/5.52 % neg_numeral_less_one
% 5.25/5.52 thf(fact_4657_neg__one__less__numeral,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_one_less_numeral
% 5.25/5.52 thf(fact_4658_neg__one__less__numeral,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_one_less_numeral
% 5.25/5.52 thf(fact_4659_neg__one__less__numeral,axiom,
% 5.25/5.52 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_one_less_numeral
% 5.25/5.52 thf(fact_4660_neg__one__less__numeral,axiom,
% 5.25/5.52 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_one_less_numeral
% 5.25/5.52 thf(fact_4661_not__numeral__less__neg__one,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_numeral_less_neg_one
% 5.25/5.52 thf(fact_4662_not__numeral__less__neg__one,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_numeral_less_neg_one
% 5.25/5.52 thf(fact_4663_not__numeral__less__neg__one,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_numeral_less_neg_one
% 5.25/5.52 thf(fact_4664_not__numeral__less__neg__one,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_numeral_less_neg_one
% 5.25/5.52 thf(fact_4665_not__one__less__neg__numeral,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_one_less_neg_numeral
% 5.25/5.52 thf(fact_4666_not__one__less__neg__numeral,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_one_less_neg_numeral
% 5.25/5.52 thf(fact_4667_not__one__less__neg__numeral,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_one_less_neg_numeral
% 5.25/5.52 thf(fact_4668_not__one__less__neg__numeral,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_one_less_neg_numeral
% 5.25/5.52 thf(fact_4669_not__neg__one__less__neg__numeral,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_neg_one_less_neg_numeral
% 5.25/5.52 thf(fact_4670_not__neg__one__less__neg__numeral,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_neg_one_less_neg_numeral
% 5.25/5.52 thf(fact_4671_not__neg__one__less__neg__numeral,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_neg_one_less_neg_numeral
% 5.25/5.52 thf(fact_4672_not__neg__one__less__neg__numeral,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % not_neg_one_less_neg_numeral
% 5.25/5.52 thf(fact_4673_nonzero__neg__divide__eq__eq2,axiom,
% 5.25/5.52 ! [B: real,C: real,A: real] :
% 5.25/5.52 ( ( B != zero_zero_real )
% 5.25/5.52 => ( ( C
% 5.25/5.52 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.25/5.52 = ( ( times_times_real @ C @ B )
% 5.25/5.52 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nonzero_neg_divide_eq_eq2
% 5.25/5.52 thf(fact_4674_nonzero__neg__divide__eq__eq2,axiom,
% 5.25/5.52 ! [B: complex,C: complex,A: complex] :
% 5.25/5.52 ( ( B != zero_zero_complex )
% 5.25/5.52 => ( ( C
% 5.25/5.52 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.25/5.52 = ( ( times_times_complex @ C @ B )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nonzero_neg_divide_eq_eq2
% 5.25/5.52 thf(fact_4675_nonzero__neg__divide__eq__eq2,axiom,
% 5.25/5.52 ! [B: rat,C: rat,A: rat] :
% 5.25/5.52 ( ( B != zero_zero_rat )
% 5.25/5.52 => ( ( C
% 5.25/5.52 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.25/5.52 = ( ( times_times_rat @ C @ B )
% 5.25/5.52 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nonzero_neg_divide_eq_eq2
% 5.25/5.52 thf(fact_4676_nonzero__neg__divide__eq__eq,axiom,
% 5.25/5.52 ! [B: real,A: real,C: real] :
% 5.25/5.52 ( ( B != zero_zero_real )
% 5.25/5.52 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.25/5.52 = C )
% 5.25/5.52 = ( ( uminus_uminus_real @ A )
% 5.25/5.52 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nonzero_neg_divide_eq_eq
% 5.25/5.52 thf(fact_4677_nonzero__neg__divide__eq__eq,axiom,
% 5.25/5.52 ! [B: complex,A: complex,C: complex] :
% 5.25/5.52 ( ( B != zero_zero_complex )
% 5.25/5.52 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.25/5.52 = C )
% 5.25/5.52 = ( ( uminus1482373934393186551omplex @ A )
% 5.25/5.52 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nonzero_neg_divide_eq_eq
% 5.25/5.52 thf(fact_4678_nonzero__neg__divide__eq__eq,axiom,
% 5.25/5.52 ! [B: rat,A: rat,C: rat] :
% 5.25/5.52 ( ( B != zero_zero_rat )
% 5.25/5.52 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.25/5.52 = C )
% 5.25/5.52 = ( ( uminus_uminus_rat @ A )
% 5.25/5.52 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nonzero_neg_divide_eq_eq
% 5.25/5.52 thf(fact_4679_minus__divide__eq__eq,axiom,
% 5.25/5.52 ! [B: real,C: real,A: real] :
% 5.25/5.52 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.25/5.52 = A )
% 5.25/5.52 = ( ( ( C != zero_zero_real )
% 5.25/5.52 => ( ( uminus_uminus_real @ B )
% 5.25/5.52 = ( times_times_real @ A @ C ) ) )
% 5.25/5.52 & ( ( C = zero_zero_real )
% 5.25/5.52 => ( A = zero_zero_real ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_divide_eq_eq
% 5.25/5.52 thf(fact_4680_minus__divide__eq__eq,axiom,
% 5.25/5.52 ! [B: complex,C: complex,A: complex] :
% 5.25/5.52 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.52 = A )
% 5.25/5.52 = ( ( ( C != zero_zero_complex )
% 5.25/5.52 => ( ( uminus1482373934393186551omplex @ B )
% 5.25/5.52 = ( times_times_complex @ A @ C ) ) )
% 5.25/5.52 & ( ( C = zero_zero_complex )
% 5.25/5.52 => ( A = zero_zero_complex ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_divide_eq_eq
% 5.25/5.52 thf(fact_4681_minus__divide__eq__eq,axiom,
% 5.25/5.52 ! [B: rat,C: rat,A: rat] :
% 5.25/5.52 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.52 = A )
% 5.25/5.52 = ( ( ( C != zero_zero_rat )
% 5.25/5.52 => ( ( uminus_uminus_rat @ B )
% 5.25/5.52 = ( times_times_rat @ A @ C ) ) )
% 5.25/5.52 & ( ( C = zero_zero_rat )
% 5.25/5.52 => ( A = zero_zero_rat ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_divide_eq_eq
% 5.25/5.52 thf(fact_4682_eq__minus__divide__eq,axiom,
% 5.25/5.52 ! [A: real,B: real,C: real] :
% 5.25/5.52 ( ( A
% 5.25/5.52 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.25/5.52 = ( ( ( C != zero_zero_real )
% 5.25/5.52 => ( ( times_times_real @ A @ C )
% 5.25/5.52 = ( uminus_uminus_real @ B ) ) )
% 5.25/5.52 & ( ( C = zero_zero_real )
% 5.25/5.52 => ( A = zero_zero_real ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % eq_minus_divide_eq
% 5.25/5.52 thf(fact_4683_eq__minus__divide__eq,axiom,
% 5.25/5.52 ! [A: complex,B: complex,C: complex] :
% 5.25/5.52 ( ( A
% 5.25/5.52 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.25/5.52 = ( ( ( C != zero_zero_complex )
% 5.25/5.52 => ( ( times_times_complex @ A @ C )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.25/5.52 & ( ( C = zero_zero_complex )
% 5.25/5.52 => ( A = zero_zero_complex ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % eq_minus_divide_eq
% 5.25/5.52 thf(fact_4684_eq__minus__divide__eq,axiom,
% 5.25/5.52 ! [A: rat,B: rat,C: rat] :
% 5.25/5.52 ( ( A
% 5.25/5.52 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.25/5.52 = ( ( ( C != zero_zero_rat )
% 5.25/5.52 => ( ( times_times_rat @ A @ C )
% 5.25/5.52 = ( uminus_uminus_rat @ B ) ) )
% 5.25/5.52 & ( ( C = zero_zero_rat )
% 5.25/5.52 => ( A = zero_zero_rat ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % eq_minus_divide_eq
% 5.25/5.52 thf(fact_4685_divide__eq__minus__1__iff,axiom,
% 5.25/5.52 ! [A: real,B: real] :
% 5.25/5.52 ( ( ( divide_divide_real @ A @ B )
% 5.25/5.52 = ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.52 = ( ( B != zero_zero_real )
% 5.25/5.52 & ( A
% 5.25/5.52 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divide_eq_minus_1_iff
% 5.25/5.52 thf(fact_4686_divide__eq__minus__1__iff,axiom,
% 5.25/5.52 ! [A: complex,B: complex] :
% 5.25/5.52 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.25/5.52 = ( ( B != zero_zero_complex )
% 5.25/5.52 & ( A
% 5.25/5.52 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divide_eq_minus_1_iff
% 5.25/5.52 thf(fact_4687_divide__eq__minus__1__iff,axiom,
% 5.25/5.52 ! [A: rat,B: rat] :
% 5.25/5.52 ( ( ( divide_divide_rat @ A @ B )
% 5.25/5.52 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.52 = ( ( B != zero_zero_rat )
% 5.25/5.52 & ( A
% 5.25/5.52 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divide_eq_minus_1_iff
% 5.25/5.52 thf(fact_4688_mult__1s__ring__1_I2_J,axiom,
% 5.25/5.52 ! [B: int] :
% 5.25/5.52 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.25/5.52 = ( uminus_uminus_int @ B ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_1s_ring_1(2)
% 5.25/5.52 thf(fact_4689_mult__1s__ring__1_I2_J,axiom,
% 5.25/5.52 ! [B: real] :
% 5.25/5.52 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.25/5.52 = ( uminus_uminus_real @ B ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_1s_ring_1(2)
% 5.25/5.52 thf(fact_4690_mult__1s__ring__1_I2_J,axiom,
% 5.25/5.52 ! [B: complex] :
% 5.25/5.52 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_1s_ring_1(2)
% 5.25/5.52 thf(fact_4691_mult__1s__ring__1_I2_J,axiom,
% 5.25/5.52 ! [B: code_integer] :
% 5.25/5.52 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.25/5.52 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_1s_ring_1(2)
% 5.25/5.52 thf(fact_4692_mult__1s__ring__1_I2_J,axiom,
% 5.25/5.52 ! [B: rat] :
% 5.25/5.52 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.25/5.52 = ( uminus_uminus_rat @ B ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_1s_ring_1(2)
% 5.25/5.52 thf(fact_4693_mult__1s__ring__1_I1_J,axiom,
% 5.25/5.52 ! [B: int] :
% 5.25/5.52 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.25/5.52 = ( uminus_uminus_int @ B ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_1s_ring_1(1)
% 5.25/5.52 thf(fact_4694_mult__1s__ring__1_I1_J,axiom,
% 5.25/5.52 ! [B: real] :
% 5.25/5.52 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.25/5.52 = ( uminus_uminus_real @ B ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_1s_ring_1(1)
% 5.25/5.52 thf(fact_4695_mult__1s__ring__1_I1_J,axiom,
% 5.25/5.52 ! [B: complex] :
% 5.25/5.52 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_1s_ring_1(1)
% 5.25/5.52 thf(fact_4696_mult__1s__ring__1_I1_J,axiom,
% 5.25/5.52 ! [B: code_integer] :
% 5.25/5.52 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.25/5.52 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_1s_ring_1(1)
% 5.25/5.52 thf(fact_4697_mult__1s__ring__1_I1_J,axiom,
% 5.25/5.52 ! [B: rat] :
% 5.25/5.52 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.25/5.52 = ( uminus_uminus_rat @ B ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_1s_ring_1(1)
% 5.25/5.52 thf(fact_4698_uminus__numeral__One,axiom,
% 5.25/5.52 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.25/5.52 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % uminus_numeral_One
% 5.25/5.52 thf(fact_4699_uminus__numeral__One,axiom,
% 5.25/5.52 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.25/5.52 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.52
% 5.25/5.52 % uminus_numeral_One
% 5.25/5.52 thf(fact_4700_uminus__numeral__One,axiom,
% 5.25/5.52 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.25/5.52
% 5.25/5.52 % uminus_numeral_One
% 5.25/5.52 thf(fact_4701_uminus__numeral__One,axiom,
% 5.25/5.52 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.25/5.52 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.52
% 5.25/5.52 % uminus_numeral_One
% 5.25/5.52 thf(fact_4702_uminus__numeral__One,axiom,
% 5.25/5.52 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.25/5.52 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.52
% 5.25/5.52 % uminus_numeral_One
% 5.25/5.52 thf(fact_4703_power__minus,axiom,
% 5.25/5.52 ! [A: int,N: nat] :
% 5.25/5.52 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.25/5.52 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus
% 5.25/5.52 thf(fact_4704_power__minus,axiom,
% 5.25/5.52 ! [A: real,N: nat] :
% 5.25/5.52 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.25/5.52 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus
% 5.25/5.52 thf(fact_4705_power__minus,axiom,
% 5.25/5.52 ! [A: complex,N: nat] :
% 5.25/5.52 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.25/5.52 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus
% 5.25/5.52 thf(fact_4706_power__minus,axiom,
% 5.25/5.52 ! [A: code_integer,N: nat] :
% 5.25/5.52 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.25/5.52 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus
% 5.25/5.52 thf(fact_4707_power__minus,axiom,
% 5.25/5.52 ! [A: rat,N: nat] :
% 5.25/5.52 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.25/5.52 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus
% 5.25/5.52 thf(fact_4708_power__minus__Bit0,axiom,
% 5.25/5.52 ! [X3: int,K: num] :
% 5.25/5.52 ( ( power_power_int @ ( uminus_uminus_int @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.25/5.52 = ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_Bit0
% 5.25/5.52 thf(fact_4709_power__minus__Bit0,axiom,
% 5.25/5.52 ! [X3: real,K: num] :
% 5.25/5.52 ( ( power_power_real @ ( uminus_uminus_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.25/5.52 = ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_Bit0
% 5.25/5.52 thf(fact_4710_power__minus__Bit0,axiom,
% 5.25/5.52 ! [X3: complex,K: num] :
% 5.25/5.52 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.25/5.52 = ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_Bit0
% 5.25/5.52 thf(fact_4711_power__minus__Bit0,axiom,
% 5.25/5.52 ! [X3: code_integer,K: num] :
% 5.25/5.52 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.25/5.52 = ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_Bit0
% 5.25/5.52 thf(fact_4712_power__minus__Bit0,axiom,
% 5.25/5.52 ! [X3: rat,K: num] :
% 5.25/5.52 ( ( power_power_rat @ ( uminus_uminus_rat @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.25/5.52 = ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_Bit0
% 5.25/5.52 thf(fact_4713_power__minus__Bit1,axiom,
% 5.25/5.52 ! [X3: int,K: num] :
% 5.25/5.52 ( ( power_power_int @ ( uminus_uminus_int @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.25/5.52 = ( uminus_uminus_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_Bit1
% 5.25/5.52 thf(fact_4714_power__minus__Bit1,axiom,
% 5.25/5.52 ! [X3: real,K: num] :
% 5.25/5.52 ( ( power_power_real @ ( uminus_uminus_real @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.25/5.52 = ( uminus_uminus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_Bit1
% 5.25/5.52 thf(fact_4715_power__minus__Bit1,axiom,
% 5.25/5.52 ! [X3: complex,K: num] :
% 5.25/5.52 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_Bit1
% 5.25/5.52 thf(fact_4716_power__minus__Bit1,axiom,
% 5.25/5.52 ! [X3: code_integer,K: num] :
% 5.25/5.52 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.25/5.52 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_Bit1
% 5.25/5.52 thf(fact_4717_power__minus__Bit1,axiom,
% 5.25/5.52 ! [X3: rat,K: num] :
% 5.25/5.52 ( ( power_power_rat @ ( uminus_uminus_rat @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.25/5.52 = ( uminus_uminus_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_Bit1
% 5.25/5.52 thf(fact_4718_diff__Suc__less,axiom,
% 5.25/5.52 ! [N: nat,I2: nat] :
% 5.25/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.52 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 5.25/5.52
% 5.25/5.52 % diff_Suc_less
% 5.25/5.52 thf(fact_4719_nat__diff__split__asm,axiom,
% 5.25/5.52 ! [P: nat > $o,A: nat,B: nat] :
% 5.25/5.52 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.25/5.52 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.25/5.52 & ~ ( P @ zero_zero_nat ) )
% 5.25/5.52 | ? [D2: nat] :
% 5.25/5.52 ( ( A
% 5.25/5.52 = ( plus_plus_nat @ B @ D2 ) )
% 5.25/5.52 & ~ ( P @ D2 ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nat_diff_split_asm
% 5.25/5.52 thf(fact_4720_nat__diff__split,axiom,
% 5.25/5.52 ! [P: nat > $o,A: nat,B: nat] :
% 5.25/5.52 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.25/5.52 = ( ( ( ord_less_nat @ A @ B )
% 5.25/5.52 => ( P @ zero_zero_nat ) )
% 5.25/5.52 & ! [D2: nat] :
% 5.25/5.52 ( ( A
% 5.25/5.52 = ( plus_plus_nat @ B @ D2 ) )
% 5.25/5.52 => ( P @ D2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nat_diff_split
% 5.25/5.52 thf(fact_4721_less__diff__conv2,axiom,
% 5.25/5.52 ! [K: nat,J2: nat,I2: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ K @ J2 )
% 5.25/5.52 => ( ( ord_less_nat @ ( minus_minus_nat @ J2 @ K ) @ I2 )
% 5.25/5.52 = ( ord_less_nat @ J2 @ ( plus_plus_nat @ I2 @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_diff_conv2
% 5.25/5.52 thf(fact_4722_nat__diff__add__eq2,axiom,
% 5.25/5.52 ! [I2: nat,J2: nat,U: nat,M: nat,N: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.52 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.25/5.52 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nat_diff_add_eq2
% 5.25/5.52 thf(fact_4723_nat__diff__add__eq1,axiom,
% 5.25/5.52 ! [J2: nat,I2: nat,U: nat,M: nat,N: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ J2 @ I2 )
% 5.25/5.52 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.25/5.52 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M ) @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nat_diff_add_eq1
% 5.25/5.52 thf(fact_4724_nat__le__add__iff2,axiom,
% 5.25/5.52 ! [I2: nat,J2: nat,U: nat,M: nat,N: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.52 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.25/5.52 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nat_le_add_iff2
% 5.25/5.52 thf(fact_4725_nat__le__add__iff1,axiom,
% 5.25/5.52 ! [J2: nat,I2: nat,U: nat,M: nat,N: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ J2 @ I2 )
% 5.25/5.52 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.25/5.52 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M ) @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nat_le_add_iff1
% 5.25/5.52 thf(fact_4726_nat__eq__add__iff2,axiom,
% 5.25/5.52 ! [I2: nat,J2: nat,U: nat,M: nat,N: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.52 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 5.25/5.52 = ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.25/5.52 = ( M
% 5.25/5.52 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nat_eq_add_iff2
% 5.25/5.52 thf(fact_4727_nat__eq__add__iff1,axiom,
% 5.25/5.52 ! [J2: nat,I2: nat,U: nat,M: nat,N: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ J2 @ I2 )
% 5.25/5.52 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 5.25/5.52 = ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.25/5.52 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M )
% 5.25/5.52 = N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nat_eq_add_iff1
% 5.25/5.52 thf(fact_4728_dvd__minus__add,axiom,
% 5.25/5.52 ! [Q2: nat,N: nat,R2: nat,M: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ Q2 @ N )
% 5.25/5.52 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R2 @ M ) )
% 5.25/5.52 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 5.25/5.52 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q2 ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dvd_minus_add
% 5.25/5.52 thf(fact_4729_mod__nat__eqI,axiom,
% 5.25/5.52 ! [R2: nat,N: nat,M: nat] :
% 5.25/5.52 ( ( ord_less_nat @ R2 @ N )
% 5.25/5.52 => ( ( ord_less_eq_nat @ R2 @ M )
% 5.25/5.52 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R2 ) )
% 5.25/5.52 => ( ( modulo_modulo_nat @ M @ N )
% 5.25/5.52 = R2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % mod_nat_eqI
% 5.25/5.52 thf(fact_4730_modulo__nat__def,axiom,
% 5.25/5.52 ( modulo_modulo_nat
% 5.25/5.52 = ( ^ [M6: nat,N2: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N2 ) @ N2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % modulo_nat_def
% 5.25/5.52 thf(fact_4731_zmod__zminus1__eq__if,axiom,
% 5.25/5.52 ! [A: int,B: int] :
% 5.25/5.52 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.25/5.52 = zero_zero_int )
% 5.25/5.52 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.25/5.52 = zero_zero_int ) )
% 5.25/5.52 & ( ( ( modulo_modulo_int @ A @ B )
% 5.25/5.52 != zero_zero_int )
% 5.25/5.52 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.25/5.52 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % zmod_zminus1_eq_if
% 5.25/5.52 thf(fact_4732_zmod__zminus2__eq__if,axiom,
% 5.25/5.52 ! [A: int,B: int] :
% 5.25/5.52 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.25/5.52 = zero_zero_int )
% 5.25/5.52 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.25/5.52 = zero_zero_int ) )
% 5.25/5.52 & ( ( ( modulo_modulo_int @ A @ B )
% 5.25/5.52 != zero_zero_int )
% 5.25/5.52 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.25/5.52 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % zmod_zminus2_eq_if
% 5.25/5.52 thf(fact_4733_pos__minus__divide__less__eq,axiom,
% 5.25/5.52 ! [C: real,B: real,A: real] :
% 5.25/5.52 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.25/5.52 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % pos_minus_divide_less_eq
% 5.25/5.52 thf(fact_4734_pos__minus__divide__less__eq,axiom,
% 5.25/5.52 ! [C: rat,B: rat,A: rat] :
% 5.25/5.52 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.25/5.52 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % pos_minus_divide_less_eq
% 5.25/5.52 thf(fact_4735_pos__less__minus__divide__eq,axiom,
% 5.25/5.52 ! [C: real,A: real,B: real] :
% 5.25/5.52 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.25/5.52 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % pos_less_minus_divide_eq
% 5.25/5.52 thf(fact_4736_pos__less__minus__divide__eq,axiom,
% 5.25/5.52 ! [C: rat,A: rat,B: rat] :
% 5.25/5.52 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.25/5.52 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % pos_less_minus_divide_eq
% 5.25/5.52 thf(fact_4737_neg__minus__divide__less__eq,axiom,
% 5.25/5.52 ! [C: real,B: real,A: real] :
% 5.25/5.52 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.25/5.52 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_minus_divide_less_eq
% 5.25/5.52 thf(fact_4738_neg__minus__divide__less__eq,axiom,
% 5.25/5.52 ! [C: rat,B: rat,A: rat] :
% 5.25/5.52 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.25/5.52 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_minus_divide_less_eq
% 5.25/5.52 thf(fact_4739_neg__less__minus__divide__eq,axiom,
% 5.25/5.52 ! [C: real,A: real,B: real] :
% 5.25/5.52 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.25/5.52 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_less_minus_divide_eq
% 5.25/5.52 thf(fact_4740_neg__less__minus__divide__eq,axiom,
% 5.25/5.52 ! [C: rat,A: rat,B: rat] :
% 5.25/5.52 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.25/5.52 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_less_minus_divide_eq
% 5.25/5.52 thf(fact_4741_minus__divide__less__eq,axiom,
% 5.25/5.52 ! [B: real,C: real,A: real] :
% 5.25/5.52 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.25/5.52 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_divide_less_eq
% 5.25/5.52 thf(fact_4742_minus__divide__less__eq,axiom,
% 5.25/5.52 ! [B: rat,C: rat,A: rat] :
% 5.25/5.52 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.25/5.52 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_divide_less_eq
% 5.25/5.52 thf(fact_4743_less__minus__divide__eq,axiom,
% 5.25/5.52 ! [A: real,B: real,C: real] :
% 5.25/5.52 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.25/5.52 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_minus_divide_eq
% 5.25/5.52 thf(fact_4744_less__minus__divide__eq,axiom,
% 5.25/5.52 ! [A: rat,B: rat,C: rat] :
% 5.25/5.52 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.25/5.52 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_minus_divide_eq
% 5.25/5.52 thf(fact_4745_eq__divide__eq__numeral_I2_J,axiom,
% 5.25/5.52 ! [W: num,B: real,C: real] :
% 5.25/5.52 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.25/5.52 = ( divide_divide_real @ B @ C ) )
% 5.25/5.52 = ( ( ( C != zero_zero_real )
% 5.25/5.52 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.25/5.52 = B ) )
% 5.25/5.52 & ( ( C = zero_zero_real )
% 5.25/5.52 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.25/5.52 = zero_zero_real ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % eq_divide_eq_numeral(2)
% 5.25/5.52 thf(fact_4746_eq__divide__eq__numeral_I2_J,axiom,
% 5.25/5.52 ! [W: num,B: complex,C: complex] :
% 5.25/5.52 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.25/5.52 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.52 = ( ( ( C != zero_zero_complex )
% 5.25/5.52 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.25/5.52 = B ) )
% 5.25/5.52 & ( ( C = zero_zero_complex )
% 5.25/5.52 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.25/5.52 = zero_zero_complex ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % eq_divide_eq_numeral(2)
% 5.25/5.52 thf(fact_4747_eq__divide__eq__numeral_I2_J,axiom,
% 5.25/5.52 ! [W: num,B: rat,C: rat] :
% 5.25/5.52 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.25/5.52 = ( divide_divide_rat @ B @ C ) )
% 5.25/5.52 = ( ( ( C != zero_zero_rat )
% 5.25/5.52 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 5.25/5.52 = B ) )
% 5.25/5.52 & ( ( C = zero_zero_rat )
% 5.25/5.52 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.25/5.52 = zero_zero_rat ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % eq_divide_eq_numeral(2)
% 5.25/5.52 thf(fact_4748_divide__eq__eq__numeral_I2_J,axiom,
% 5.25/5.52 ! [B: real,C: real,W: num] :
% 5.25/5.52 ( ( ( divide_divide_real @ B @ C )
% 5.25/5.52 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.52 = ( ( ( C != zero_zero_real )
% 5.25/5.52 => ( B
% 5.25/5.52 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.25/5.52 & ( ( C = zero_zero_real )
% 5.25/5.52 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.25/5.52 = zero_zero_real ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divide_eq_eq_numeral(2)
% 5.25/5.52 thf(fact_4749_divide__eq__eq__numeral_I2_J,axiom,
% 5.25/5.52 ! [B: complex,C: complex,W: num] :
% 5.25/5.52 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.25/5.52 = ( ( ( C != zero_zero_complex )
% 5.25/5.52 => ( B
% 5.25/5.52 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.25/5.52 & ( ( C = zero_zero_complex )
% 5.25/5.52 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.25/5.52 = zero_zero_complex ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divide_eq_eq_numeral(2)
% 5.25/5.52 thf(fact_4750_divide__eq__eq__numeral_I2_J,axiom,
% 5.25/5.52 ! [B: rat,C: rat,W: num] :
% 5.25/5.52 ( ( ( divide_divide_rat @ B @ C )
% 5.25/5.52 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.25/5.52 = ( ( ( C != zero_zero_rat )
% 5.25/5.52 => ( B
% 5.25/5.52 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.25/5.52 & ( ( C = zero_zero_rat )
% 5.25/5.52 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.25/5.52 = zero_zero_rat ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divide_eq_eq_numeral(2)
% 5.25/5.52 thf(fact_4751_add__divide__eq__if__simps_I3_J,axiom,
% 5.25/5.52 ! [Z: real,A: real,B: real] :
% 5.25/5.52 ( ( ( Z = zero_zero_real )
% 5.25/5.52 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.25/5.52 = B ) )
% 5.25/5.52 & ( ( Z != zero_zero_real )
% 5.25/5.52 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.25/5.52 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % add_divide_eq_if_simps(3)
% 5.25/5.52 thf(fact_4752_add__divide__eq__if__simps_I3_J,axiom,
% 5.25/5.52 ! [Z: complex,A: complex,B: complex] :
% 5.25/5.52 ( ( ( Z = zero_zero_complex )
% 5.25/5.52 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.25/5.52 = B ) )
% 5.25/5.52 & ( ( Z != zero_zero_complex )
% 5.25/5.52 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.25/5.52 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % add_divide_eq_if_simps(3)
% 5.25/5.52 thf(fact_4753_add__divide__eq__if__simps_I3_J,axiom,
% 5.25/5.52 ! [Z: rat,A: rat,B: rat] :
% 5.25/5.52 ( ( ( Z = zero_zero_rat )
% 5.25/5.52 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.25/5.52 = B ) )
% 5.25/5.52 & ( ( Z != zero_zero_rat )
% 5.25/5.52 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.25/5.52 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % add_divide_eq_if_simps(3)
% 5.25/5.52 thf(fact_4754_minus__divide__add__eq__iff,axiom,
% 5.25/5.52 ! [Z: real,X3: real,Y: real] :
% 5.25/5.52 ( ( Z != zero_zero_real )
% 5.25/5.52 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X3 @ Z ) ) @ Y )
% 5.25/5.52 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X3 ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_divide_add_eq_iff
% 5.25/5.52 thf(fact_4755_minus__divide__add__eq__iff,axiom,
% 5.25/5.52 ! [Z: complex,X3: complex,Y: complex] :
% 5.25/5.52 ( ( Z != zero_zero_complex )
% 5.25/5.52 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X3 @ Z ) ) @ Y )
% 5.25/5.52 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_divide_add_eq_iff
% 5.25/5.52 thf(fact_4756_minus__divide__add__eq__iff,axiom,
% 5.25/5.52 ! [Z: rat,X3: rat,Y: rat] :
% 5.25/5.52 ( ( Z != zero_zero_rat )
% 5.25/5.52 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X3 @ Z ) ) @ Y )
% 5.25/5.52 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X3 ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_divide_add_eq_iff
% 5.25/5.52 thf(fact_4757_minus__divide__diff__eq__iff,axiom,
% 5.25/5.52 ! [Z: real,X3: real,Y: real] :
% 5.25/5.52 ( ( Z != zero_zero_real )
% 5.25/5.52 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X3 @ Z ) ) @ Y )
% 5.25/5.52 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X3 ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_divide_diff_eq_iff
% 5.25/5.52 thf(fact_4758_minus__divide__diff__eq__iff,axiom,
% 5.25/5.52 ! [Z: complex,X3: complex,Y: complex] :
% 5.25/5.52 ( ( Z != zero_zero_complex )
% 5.25/5.52 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X3 @ Z ) ) @ Y )
% 5.25/5.52 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X3 ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_divide_diff_eq_iff
% 5.25/5.52 thf(fact_4759_minus__divide__diff__eq__iff,axiom,
% 5.25/5.52 ! [Z: rat,X3: rat,Y: rat] :
% 5.25/5.52 ( ( Z != zero_zero_rat )
% 5.25/5.52 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X3 @ Z ) ) @ Y )
% 5.25/5.52 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X3 ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_divide_diff_eq_iff
% 5.25/5.52 thf(fact_4760_add__divide__eq__if__simps_I5_J,axiom,
% 5.25/5.52 ! [Z: real,A: real,B: real] :
% 5.25/5.52 ( ( ( Z = zero_zero_real )
% 5.25/5.52 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.25/5.52 = ( uminus_uminus_real @ B ) ) )
% 5.25/5.52 & ( ( Z != zero_zero_real )
% 5.25/5.52 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.25/5.52 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % add_divide_eq_if_simps(5)
% 5.25/5.52 thf(fact_4761_add__divide__eq__if__simps_I5_J,axiom,
% 5.25/5.52 ! [Z: complex,A: complex,B: complex] :
% 5.25/5.52 ( ( ( Z = zero_zero_complex )
% 5.25/5.52 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.25/5.52 & ( ( Z != zero_zero_complex )
% 5.25/5.52 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.25/5.52 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % add_divide_eq_if_simps(5)
% 5.25/5.52 thf(fact_4762_add__divide__eq__if__simps_I5_J,axiom,
% 5.25/5.52 ! [Z: rat,A: rat,B: rat] :
% 5.25/5.52 ( ( ( Z = zero_zero_rat )
% 5.25/5.52 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.25/5.52 = ( uminus_uminus_rat @ B ) ) )
% 5.25/5.52 & ( ( Z != zero_zero_rat )
% 5.25/5.52 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.25/5.52 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % add_divide_eq_if_simps(5)
% 5.25/5.52 thf(fact_4763_add__divide__eq__if__simps_I6_J,axiom,
% 5.25/5.52 ! [Z: real,A: real,B: real] :
% 5.25/5.52 ( ( ( Z = zero_zero_real )
% 5.25/5.52 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.25/5.52 = ( uminus_uminus_real @ B ) ) )
% 5.25/5.52 & ( ( Z != zero_zero_real )
% 5.25/5.52 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.25/5.52 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % add_divide_eq_if_simps(6)
% 5.25/5.52 thf(fact_4764_add__divide__eq__if__simps_I6_J,axiom,
% 5.25/5.52 ! [Z: complex,A: complex,B: complex] :
% 5.25/5.52 ( ( ( Z = zero_zero_complex )
% 5.25/5.52 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.25/5.52 & ( ( Z != zero_zero_complex )
% 5.25/5.52 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.25/5.52 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % add_divide_eq_if_simps(6)
% 5.25/5.52 thf(fact_4765_add__divide__eq__if__simps_I6_J,axiom,
% 5.25/5.52 ! [Z: rat,A: rat,B: rat] :
% 5.25/5.52 ( ( ( Z = zero_zero_rat )
% 5.25/5.52 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.25/5.52 = ( uminus_uminus_rat @ B ) ) )
% 5.25/5.52 & ( ( Z != zero_zero_rat )
% 5.25/5.52 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.25/5.52 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % add_divide_eq_if_simps(6)
% 5.25/5.52 thf(fact_4766_even__minus,axiom,
% 5.25/5.52 ! [A: int] :
% 5.25/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.25/5.52 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.25/5.52
% 5.25/5.52 % even_minus
% 5.25/5.52 thf(fact_4767_even__minus,axiom,
% 5.25/5.52 ! [A: code_integer] :
% 5.25/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.25/5.52 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.25/5.52
% 5.25/5.52 % even_minus
% 5.25/5.52 thf(fact_4768_power2__eq__iff,axiom,
% 5.25/5.52 ! [X3: int,Y: int] :
% 5.25/5.52 ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.52 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.52 = ( ( X3 = Y )
% 5.25/5.52 | ( X3
% 5.25/5.52 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power2_eq_iff
% 5.25/5.52 thf(fact_4769_power2__eq__iff,axiom,
% 5.25/5.52 ! [X3: real,Y: real] :
% 5.25/5.52 ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.52 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.52 = ( ( X3 = Y )
% 5.25/5.52 | ( X3
% 5.25/5.52 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power2_eq_iff
% 5.25/5.52 thf(fact_4770_power2__eq__iff,axiom,
% 5.25/5.52 ! [X3: complex,Y: complex] :
% 5.25/5.52 ( ( ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.52 = ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.52 = ( ( X3 = Y )
% 5.25/5.52 | ( X3
% 5.25/5.52 = ( uminus1482373934393186551omplex @ Y ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power2_eq_iff
% 5.25/5.52 thf(fact_4771_power2__eq__iff,axiom,
% 5.25/5.52 ! [X3: code_integer,Y: code_integer] :
% 5.25/5.52 ( ( ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.52 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.52 = ( ( X3 = Y )
% 5.25/5.52 | ( X3
% 5.25/5.52 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power2_eq_iff
% 5.25/5.52 thf(fact_4772_power2__eq__iff,axiom,
% 5.25/5.52 ! [X3: rat,Y: rat] :
% 5.25/5.52 ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.52 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.52 = ( ( X3 = Y )
% 5.25/5.52 | ( X3
% 5.25/5.52 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power2_eq_iff
% 5.25/5.52 thf(fact_4773_uminus__power__if,axiom,
% 5.25/5.52 ! [N: nat,A: int] :
% 5.25/5.52 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.25/5.52 = ( power_power_int @ A @ N ) ) )
% 5.25/5.52 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.25/5.52 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % uminus_power_if
% 5.25/5.52 thf(fact_4774_uminus__power__if,axiom,
% 5.25/5.52 ! [N: nat,A: real] :
% 5.25/5.52 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.25/5.52 = ( power_power_real @ A @ N ) ) )
% 5.25/5.52 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.25/5.52 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % uminus_power_if
% 5.25/5.52 thf(fact_4775_uminus__power__if,axiom,
% 5.25/5.52 ! [N: nat,A: complex] :
% 5.25/5.52 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.25/5.52 = ( power_power_complex @ A @ N ) ) )
% 5.25/5.52 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % uminus_power_if
% 5.25/5.52 thf(fact_4776_uminus__power__if,axiom,
% 5.25/5.52 ! [N: nat,A: code_integer] :
% 5.25/5.52 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.25/5.52 = ( power_8256067586552552935nteger @ A @ N ) ) )
% 5.25/5.52 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.25/5.52 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % uminus_power_if
% 5.25/5.52 thf(fact_4777_uminus__power__if,axiom,
% 5.25/5.52 ! [N: nat,A: rat] :
% 5.25/5.52 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.25/5.52 = ( power_power_rat @ A @ N ) ) )
% 5.25/5.52 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.25/5.52 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % uminus_power_if
% 5.25/5.52 thf(fact_4778_power__diff,axiom,
% 5.25/5.52 ! [A: complex,N: nat,M: nat] :
% 5.25/5.52 ( ( A != zero_zero_complex )
% 5.25/5.52 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.52 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 5.25/5.52 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_diff
% 5.25/5.52 thf(fact_4779_power__diff,axiom,
% 5.25/5.52 ! [A: real,N: nat,M: nat] :
% 5.25/5.52 ( ( A != zero_zero_real )
% 5.25/5.52 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.52 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 5.25/5.52 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_diff
% 5.25/5.52 thf(fact_4780_power__diff,axiom,
% 5.25/5.52 ! [A: rat,N: nat,M: nat] :
% 5.25/5.52 ( ( A != zero_zero_rat )
% 5.25/5.52 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.52 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.25/5.52 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_diff
% 5.25/5.52 thf(fact_4781_power__diff,axiom,
% 5.25/5.52 ! [A: nat,N: nat,M: nat] :
% 5.25/5.52 ( ( A != zero_zero_nat )
% 5.25/5.52 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.52 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.25/5.52 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_diff
% 5.25/5.52 thf(fact_4782_power__diff,axiom,
% 5.25/5.52 ! [A: int,N: nat,M: nat] :
% 5.25/5.52 ( ( A != zero_zero_int )
% 5.25/5.52 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.52 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 5.25/5.52 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_diff
% 5.25/5.52 thf(fact_4783_dbl__inc__def,axiom,
% 5.25/5.52 ( neg_nu8557863876264182079omplex
% 5.25/5.52 = ( ^ [X2: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_inc_def
% 5.25/5.52 thf(fact_4784_dbl__inc__def,axiom,
% 5.25/5.52 ( neg_nu8295874005876285629c_real
% 5.25/5.52 = ( ^ [X2: real] : ( plus_plus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_inc_def
% 5.25/5.52 thf(fact_4785_dbl__inc__def,axiom,
% 5.25/5.52 ( neg_nu5219082963157363817nc_rat
% 5.25/5.52 = ( ^ [X2: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_inc_def
% 5.25/5.52 thf(fact_4786_dbl__inc__def,axiom,
% 5.25/5.52 ( neg_nu5851722552734809277nc_int
% 5.25/5.52 = ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_inc_def
% 5.25/5.52 thf(fact_4787_Suc__pred_H,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.52 => ( N
% 5.25/5.52 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Suc_pred'
% 5.25/5.52 thf(fact_4788_Suc__diff__eq__diff__pred,axiom,
% 5.25/5.52 ! [N: nat,M: nat] :
% 5.25/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.52 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.25/5.52 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Suc_diff_eq_diff_pred
% 5.25/5.52 thf(fact_4789_div__geq,axiom,
% 5.25/5.52 ! [N: nat,M: nat] :
% 5.25/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.52 => ( ~ ( ord_less_nat @ M @ N )
% 5.25/5.52 => ( ( divide_divide_nat @ M @ N )
% 5.25/5.52 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % div_geq
% 5.25/5.52 thf(fact_4790_div__if,axiom,
% 5.25/5.52 ( divide_divide_nat
% 5.25/5.52 = ( ^ [M6: nat,N2: nat] :
% 5.25/5.52 ( if_nat
% 5.25/5.52 @ ( ( ord_less_nat @ M6 @ N2 )
% 5.25/5.52 | ( N2 = zero_zero_nat ) )
% 5.25/5.52 @ zero_zero_nat
% 5.25/5.52 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % div_if
% 5.25/5.52 thf(fact_4791_add__eq__if,axiom,
% 5.25/5.52 ( plus_plus_nat
% 5.25/5.52 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % add_eq_if
% 5.25/5.52 thf(fact_4792_nat__less__add__iff1,axiom,
% 5.25/5.52 ! [J2: nat,I2: nat,U: nat,M: nat,N: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ J2 @ I2 )
% 5.25/5.52 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.25/5.52 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M ) @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nat_less_add_iff1
% 5.25/5.52 thf(fact_4793_nat__less__add__iff2,axiom,
% 5.25/5.52 ! [I2: nat,J2: nat,U: nat,M: nat,N: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.52 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.25/5.52 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % nat_less_add_iff2
% 5.25/5.52 thf(fact_4794_mult__eq__if,axiom,
% 5.25/5.52 ( times_times_nat
% 5.25/5.52 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_eq_if
% 5.25/5.52 thf(fact_4795_verit__less__mono__div__int2,axiom,
% 5.25/5.52 ! [A2: int,B3: int,N: int] :
% 5.25/5.52 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.25/5.52 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 5.25/5.52 => ( ord_less_eq_int @ ( divide_divide_int @ B3 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % verit_less_mono_div_int2
% 5.25/5.52 thf(fact_4796_div__eq__minus1,axiom,
% 5.25/5.52 ! [B: int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.52 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.25/5.52 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % div_eq_minus1
% 5.25/5.52 thf(fact_4797_pos__minus__divide__le__eq,axiom,
% 5.25/5.52 ! [C: real,B: real,A: real] :
% 5.25/5.52 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.25/5.52 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % pos_minus_divide_le_eq
% 5.25/5.52 thf(fact_4798_pos__minus__divide__le__eq,axiom,
% 5.25/5.52 ! [C: rat,B: rat,A: rat] :
% 5.25/5.52 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.25/5.52 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % pos_minus_divide_le_eq
% 5.25/5.52 thf(fact_4799_pos__le__minus__divide__eq,axiom,
% 5.25/5.52 ! [C: real,A: real,B: real] :
% 5.25/5.52 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.25/5.52 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % pos_le_minus_divide_eq
% 5.25/5.52 thf(fact_4800_pos__le__minus__divide__eq,axiom,
% 5.25/5.52 ! [C: rat,A: rat,B: rat] :
% 5.25/5.52 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.25/5.52 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % pos_le_minus_divide_eq
% 5.25/5.52 thf(fact_4801_neg__minus__divide__le__eq,axiom,
% 5.25/5.52 ! [C: real,B: real,A: real] :
% 5.25/5.52 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.25/5.52 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_minus_divide_le_eq
% 5.25/5.52 thf(fact_4802_neg__minus__divide__le__eq,axiom,
% 5.25/5.52 ! [C: rat,B: rat,A: rat] :
% 5.25/5.52 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.25/5.52 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_minus_divide_le_eq
% 5.25/5.52 thf(fact_4803_neg__le__minus__divide__eq,axiom,
% 5.25/5.52 ! [C: real,A: real,B: real] :
% 5.25/5.52 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.25/5.52 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_le_minus_divide_eq
% 5.25/5.52 thf(fact_4804_neg__le__minus__divide__eq,axiom,
% 5.25/5.52 ! [C: rat,A: rat,B: rat] :
% 5.25/5.52 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.25/5.52 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % neg_le_minus_divide_eq
% 5.25/5.52 thf(fact_4805_minus__divide__le__eq,axiom,
% 5.25/5.52 ! [B: real,C: real,A: real] :
% 5.25/5.52 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.25/5.52 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_divide_le_eq
% 5.25/5.52 thf(fact_4806_minus__divide__le__eq,axiom,
% 5.25/5.52 ! [B: rat,C: rat,A: rat] :
% 5.25/5.52 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.25/5.52 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_divide_le_eq
% 5.25/5.52 thf(fact_4807_le__minus__divide__eq,axiom,
% 5.25/5.52 ! [A: real,B: real,C: real] :
% 5.25/5.52 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.25/5.52 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % le_minus_divide_eq
% 5.25/5.52 thf(fact_4808_le__minus__divide__eq,axiom,
% 5.25/5.52 ! [A: rat,B: rat,C: rat] :
% 5.25/5.52 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.25/5.52 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % le_minus_divide_eq
% 5.25/5.52 thf(fact_4809_less__divide__eq__numeral_I2_J,axiom,
% 5.25/5.52 ! [W: num,B: real,C: real] :
% 5.25/5.52 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.25/5.52 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_divide_eq_numeral(2)
% 5.25/5.52 thf(fact_4810_less__divide__eq__numeral_I2_J,axiom,
% 5.25/5.52 ! [W: num,B: rat,C: rat] :
% 5.25/5.52 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.52 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_divide_eq_numeral(2)
% 5.25/5.52 thf(fact_4811_divide__less__eq__numeral_I2_J,axiom,
% 5.25/5.52 ! [B: real,C: real,W: num] :
% 5.25/5.52 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.52 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divide_less_eq_numeral(2)
% 5.25/5.52 thf(fact_4812_divide__less__eq__numeral_I2_J,axiom,
% 5.25/5.52 ! [B: rat,C: rat,W: num] :
% 5.25/5.52 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.25/5.52 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divide_less_eq_numeral(2)
% 5.25/5.52 thf(fact_4813_signed__take__bit__rec,axiom,
% 5.25/5.52 ( bit_ri6519982836138164636nteger
% 5.25/5.52 = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % signed_take_bit_rec
% 5.25/5.52 thf(fact_4814_signed__take__bit__rec,axiom,
% 5.25/5.52 ( bit_ri631733984087533419it_int
% 5.25/5.52 = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % signed_take_bit_rec
% 5.25/5.52 thf(fact_4815_power2__eq__1__iff,axiom,
% 5.25/5.52 ! [A: int] :
% 5.25/5.52 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.52 = one_one_int )
% 5.25/5.52 = ( ( A = one_one_int )
% 5.25/5.52 | ( A
% 5.25/5.52 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power2_eq_1_iff
% 5.25/5.52 thf(fact_4816_power2__eq__1__iff,axiom,
% 5.25/5.52 ! [A: real] :
% 5.25/5.52 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.52 = one_one_real )
% 5.25/5.52 = ( ( A = one_one_real )
% 5.25/5.52 | ( A
% 5.25/5.52 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power2_eq_1_iff
% 5.25/5.52 thf(fact_4817_power2__eq__1__iff,axiom,
% 5.25/5.52 ! [A: complex] :
% 5.25/5.52 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.52 = one_one_complex )
% 5.25/5.52 = ( ( A = one_one_complex )
% 5.25/5.52 | ( A
% 5.25/5.52 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power2_eq_1_iff
% 5.25/5.52 thf(fact_4818_power2__eq__1__iff,axiom,
% 5.25/5.52 ! [A: code_integer] :
% 5.25/5.52 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.52 = one_one_Code_integer )
% 5.25/5.52 = ( ( A = one_one_Code_integer )
% 5.25/5.52 | ( A
% 5.25/5.52 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power2_eq_1_iff
% 5.25/5.52 thf(fact_4819_power2__eq__1__iff,axiom,
% 5.25/5.52 ! [A: rat] :
% 5.25/5.52 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.52 = one_one_rat )
% 5.25/5.52 = ( ( A = one_one_rat )
% 5.25/5.52 | ( A
% 5.25/5.52 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power2_eq_1_iff
% 5.25/5.52 thf(fact_4820_minus__one__power__iff,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.25/5.52 = one_one_int ) )
% 5.25/5.52 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.25/5.52 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_one_power_iff
% 5.25/5.52 thf(fact_4821_minus__one__power__iff,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.25/5.52 = one_one_real ) )
% 5.25/5.52 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.25/5.52 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_one_power_iff
% 5.25/5.52 thf(fact_4822_minus__one__power__iff,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.25/5.52 = one_one_complex ) )
% 5.25/5.52 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_one_power_iff
% 5.25/5.52 thf(fact_4823_minus__one__power__iff,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.25/5.52 = one_one_Code_integer ) )
% 5.25/5.52 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.25/5.52 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_one_power_iff
% 5.25/5.52 thf(fact_4824_minus__one__power__iff,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.25/5.52 = one_one_rat ) )
% 5.25/5.52 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.25/5.52 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_one_power_iff
% 5.25/5.52 thf(fact_4825_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.25/5.52 ! [N: nat,M: nat] :
% 5.25/5.52 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 != zero_zero_nat )
% 5.25/5.52 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.25/5.52 != zero_zero_nat ) ) ).
% 5.25/5.52
% 5.25/5.52 % exp_not_zero_imp_exp_diff_not_zero
% 5.25/5.52 thf(fact_4826_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.25/5.52 ! [N: nat,M: nat] :
% 5.25/5.52 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 != zero_zero_int )
% 5.25/5.52 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.25/5.52 != zero_zero_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % exp_not_zero_imp_exp_diff_not_zero
% 5.25/5.52 thf(fact_4827_power__diff__power__eq,axiom,
% 5.25/5.52 ! [A: nat,N: nat,M: nat] :
% 5.25/5.52 ( ( A != zero_zero_nat )
% 5.25/5.52 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.52 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.25/5.52 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.25/5.52 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.25/5.52 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.25/5.52 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_diff_power_eq
% 5.25/5.52 thf(fact_4828_power__diff__power__eq,axiom,
% 5.25/5.52 ! [A: int,N: nat,M: nat] :
% 5.25/5.52 ( ( A != zero_zero_int )
% 5.25/5.52 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.52 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.25/5.52 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.25/5.52 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.25/5.52 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.25/5.52 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_diff_power_eq
% 5.25/5.52 thf(fact_4829_power__eq__if,axiom,
% 5.25/5.52 ( power_power_complex
% 5.25/5.52 = ( ^ [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 ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_eq_if
% 5.25/5.52 thf(fact_4830_power__eq__if,axiom,
% 5.25/5.52 ( power_power_real
% 5.25/5.52 = ( ^ [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 ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_eq_if
% 5.25/5.52 thf(fact_4831_power__eq__if,axiom,
% 5.25/5.52 ( power_power_rat
% 5.25/5.52 = ( ^ [P4: rat,M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P4 @ ( power_power_rat @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_eq_if
% 5.25/5.52 thf(fact_4832_power__eq__if,axiom,
% 5.25/5.52 ( power_power_nat
% 5.25/5.52 = ( ^ [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 ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_eq_if
% 5.25/5.52 thf(fact_4833_power__eq__if,axiom,
% 5.25/5.52 ( power_power_int
% 5.25/5.52 = ( ^ [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 ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_eq_if
% 5.25/5.52 thf(fact_4834_power__minus__mult,axiom,
% 5.25/5.52 ! [N: nat,A: complex] :
% 5.25/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.52 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.25/5.52 = ( power_power_complex @ A @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_mult
% 5.25/5.52 thf(fact_4835_power__minus__mult,axiom,
% 5.25/5.52 ! [N: nat,A: real] :
% 5.25/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.52 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.25/5.52 = ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_mult
% 5.25/5.52 thf(fact_4836_power__minus__mult,axiom,
% 5.25/5.52 ! [N: nat,A: rat] :
% 5.25/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.52 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.25/5.52 = ( power_power_rat @ A @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_mult
% 5.25/5.52 thf(fact_4837_power__minus__mult,axiom,
% 5.25/5.52 ! [N: nat,A: nat] :
% 5.25/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.52 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.25/5.52 = ( power_power_nat @ A @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_mult
% 5.25/5.52 thf(fact_4838_power__minus__mult,axiom,
% 5.25/5.52 ! [N: nat,A: int] :
% 5.25/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.52 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.25/5.52 = ( power_power_int @ A @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus_mult
% 5.25/5.52 thf(fact_4839_diff__le__diff__pow,axiom,
% 5.25/5.52 ! [K: nat,M: nat,N: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.25/5.52 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % diff_le_diff_pow
% 5.25/5.52 thf(fact_4840_le__div__geq,axiom,
% 5.25/5.52 ! [N: nat,M: nat] :
% 5.25/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.52 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.52 => ( ( divide_divide_nat @ M @ N )
% 5.25/5.52 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % le_div_geq
% 5.25/5.52 thf(fact_4841_minus__mod__int__eq,axiom,
% 5.25/5.52 ! [L2: int,K: int] :
% 5.25/5.52 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 5.25/5.52 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 5.25/5.52 = ( minus_minus_int @ ( minus_minus_int @ L2 @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_mod_int_eq
% 5.25/5.52 thf(fact_4842_zmod__minus1,axiom,
% 5.25/5.52 ! [B: int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.52 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.25/5.52 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % zmod_minus1
% 5.25/5.52 thf(fact_4843_zdiv__zminus1__eq__if,axiom,
% 5.25/5.52 ! [B: int,A: int] :
% 5.25/5.52 ( ( B != zero_zero_int )
% 5.25/5.52 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.25/5.52 = zero_zero_int )
% 5.25/5.52 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.25/5.52 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.25/5.52 & ( ( ( modulo_modulo_int @ A @ B )
% 5.25/5.52 != zero_zero_int )
% 5.25/5.52 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.25/5.52 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % zdiv_zminus1_eq_if
% 5.25/5.52 thf(fact_4844_zdiv__zminus2__eq__if,axiom,
% 5.25/5.52 ! [B: int,A: int] :
% 5.25/5.52 ( ( B != zero_zero_int )
% 5.25/5.52 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.25/5.52 = zero_zero_int )
% 5.25/5.52 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.25/5.52 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.25/5.52 & ( ( ( modulo_modulo_int @ A @ B )
% 5.25/5.52 != zero_zero_int )
% 5.25/5.52 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.25/5.52 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % zdiv_zminus2_eq_if
% 5.25/5.52 thf(fact_4845_zminus1__lemma,axiom,
% 5.25/5.52 ! [A: int,B: int,Q2: int,R2: int] :
% 5.25/5.52 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.25/5.52 => ( ( B != zero_zero_int )
% 5.25/5.52 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R2 = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R2 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R2 ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % zminus1_lemma
% 5.25/5.52 thf(fact_4846_divide__le__eq__numeral_I2_J,axiom,
% 5.25/5.52 ! [B: real,C: real,W: num] :
% 5.25/5.52 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.52 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divide_le_eq_numeral(2)
% 5.25/5.52 thf(fact_4847_divide__le__eq__numeral_I2_J,axiom,
% 5.25/5.52 ! [B: rat,C: rat,W: num] :
% 5.25/5.52 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.25/5.52 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divide_le_eq_numeral(2)
% 5.25/5.52 thf(fact_4848_le__divide__eq__numeral_I2_J,axiom,
% 5.25/5.52 ! [W: num,B: real,C: real] :
% 5.25/5.52 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.25/5.52 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.52 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.52 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % le_divide_eq_numeral(2)
% 5.25/5.52 thf(fact_4849_le__divide__eq__numeral_I2_J,axiom,
% 5.25/5.52 ! [W: num,B: rat,C: rat] :
% 5.25/5.52 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.52 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.52 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.25/5.52 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.52 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % le_divide_eq_numeral(2)
% 5.25/5.52 thf(fact_4850_square__le__1,axiom,
% 5.25/5.52 ! [X3: real] :
% 5.25/5.52 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.52 => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 5.25/5.52 => ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % square_le_1
% 5.25/5.52 thf(fact_4851_square__le__1,axiom,
% 5.25/5.52 ! [X3: code_integer] :
% 5.25/5.52 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X3 )
% 5.25/5.52 => ( ( ord_le3102999989581377725nteger @ X3 @ one_one_Code_integer )
% 5.25/5.52 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % square_le_1
% 5.25/5.52 thf(fact_4852_square__le__1,axiom,
% 5.25/5.52 ! [X3: rat] :
% 5.25/5.52 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X3 )
% 5.25/5.52 => ( ( ord_less_eq_rat @ X3 @ one_one_rat )
% 5.25/5.52 => ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % square_le_1
% 5.25/5.52 thf(fact_4853_square__le__1,axiom,
% 5.25/5.52 ! [X3: int] :
% 5.25/5.52 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X3 )
% 5.25/5.52 => ( ( ord_less_eq_int @ X3 @ one_one_int )
% 5.25/5.52 => ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % square_le_1
% 5.25/5.52 thf(fact_4854_minus__power__mult__self,axiom,
% 5.25/5.52 ! [A: int,N: nat] :
% 5.25/5.52 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.25/5.52 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_power_mult_self
% 5.25/5.52 thf(fact_4855_minus__power__mult__self,axiom,
% 5.25/5.52 ! [A: real,N: nat] :
% 5.25/5.52 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.25/5.52 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_power_mult_self
% 5.25/5.52 thf(fact_4856_minus__power__mult__self,axiom,
% 5.25/5.52 ! [A: complex,N: nat] :
% 5.25/5.52 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 5.25/5.52 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_power_mult_self
% 5.25/5.52 thf(fact_4857_minus__power__mult__self,axiom,
% 5.25/5.52 ! [A: code_integer,N: nat] :
% 5.25/5.52 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.25/5.52 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_power_mult_self
% 5.25/5.52 thf(fact_4858_minus__power__mult__self,axiom,
% 5.25/5.52 ! [A: rat,N: nat] :
% 5.25/5.52 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.25/5.52 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_power_mult_self
% 5.25/5.52 thf(fact_4859_minus__1__div__exp__eq__int,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.52 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_1_div_exp_eq_int
% 5.25/5.52 thf(fact_4860_div__pos__neg__trivial,axiom,
% 5.25/5.52 ! [K: int,L2: int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.52 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.25/5.52 => ( ( divide_divide_int @ K @ L2 )
% 5.25/5.52 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % div_pos_neg_trivial
% 5.25/5.52 thf(fact_4861_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.25/5.52 ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 5.25/5.52
% 5.25/5.52 % signed_take_bit_int_greater_eq_minus_exp
% 5.25/5.52 thf(fact_4862_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.25/5.52 ! [N: nat,K: int] :
% 5.25/5.52 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.25/5.52 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 5.25/5.52
% 5.25/5.52 % signed_take_bit_int_less_eq_self_iff
% 5.25/5.52 thf(fact_4863_signed__take__bit__int__greater__self__iff,axiom,
% 5.25/5.52 ! [K: int,N: nat] :
% 5.25/5.52 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.25/5.52 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % signed_take_bit_int_greater_self_iff
% 5.25/5.52 thf(fact_4864_list__decode_Ocases,axiom,
% 5.25/5.52 ! [X3: nat] :
% 5.25/5.52 ( ( X3 != zero_zero_nat )
% 5.25/5.52 => ~ ! [N3: nat] :
% 5.25/5.52 ( X3
% 5.25/5.52 != ( suc @ N3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % list_decode.cases
% 5.25/5.52 thf(fact_4865_power__minus1__odd,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.52 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus1_odd
% 5.25/5.52 thf(fact_4866_power__minus1__odd,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.52 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus1_odd
% 5.25/5.52 thf(fact_4867_power__minus1__odd,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus1_odd
% 5.25/5.52 thf(fact_4868_power__minus1__odd,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.52 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus1_odd
% 5.25/5.52 thf(fact_4869_power__minus1__odd,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.52 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.52
% 5.25/5.52 % power_minus1_odd
% 5.25/5.52 thf(fact_4870_mult__exp__mod__exp__eq,axiom,
% 5.25/5.52 ! [M: nat,N: nat,A: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.52 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.52 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_exp_mod_exp_eq
% 5.25/5.52 thf(fact_4871_mult__exp__mod__exp__eq,axiom,
% 5.25/5.52 ! [M: nat,N: nat,A: int] :
% 5.25/5.52 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.52 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.52 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_exp_mod_exp_eq
% 5.25/5.52 thf(fact_4872_mult__exp__mod__exp__eq,axiom,
% 5.25/5.52 ! [M: nat,N: nat,A: code_integer] :
% 5.25/5.52 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.52 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.52 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_exp_mod_exp_eq
% 5.25/5.52 thf(fact_4873_even__mod__4__div__2,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.25/5.52 = ( suc @ zero_zero_nat ) )
% 5.25/5.52 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % even_mod_4_div_2
% 5.25/5.52 thf(fact_4874_int__bit__induct,axiom,
% 5.25/5.52 ! [P: int > $o,K: int] :
% 5.25/5.52 ( ( P @ zero_zero_int )
% 5.25/5.52 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.52 => ( ! [K2: int] :
% 5.25/5.52 ( ( P @ K2 )
% 5.25/5.52 => ( ( K2 != zero_zero_int )
% 5.25/5.52 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.52 => ( ! [K2: int] :
% 5.25/5.52 ( ( P @ K2 )
% 5.25/5.52 => ( ( K2
% 5.25/5.52 != ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.52 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.25/5.52 => ( P @ K ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % int_bit_induct
% 5.25/5.52 thf(fact_4875_int__power__div__base,axiom,
% 5.25/5.52 ! [M: nat,K: int] :
% 5.25/5.52 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.52 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.52 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.25/5.52 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % int_power_div_base
% 5.25/5.52 thf(fact_4876_signed__take__bit__int__eq__self__iff,axiom,
% 5.25/5.52 ! [N: nat,K: int] :
% 5.25/5.52 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.25/5.52 = K )
% 5.25/5.52 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.25/5.52 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % signed_take_bit_int_eq_self_iff
% 5.25/5.52 thf(fact_4877_signed__take__bit__int__eq__self,axiom,
% 5.25/5.52 ! [N: nat,K: int] :
% 5.25/5.52 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.25/5.52 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.52 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.25/5.52 = K ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % signed_take_bit_int_eq_self
% 5.25/5.52 thf(fact_4878_odd__mod__4__div__2,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.25/5.52 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.25/5.52 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % odd_mod_4_div_2
% 5.25/5.52 thf(fact_4879_signed__take__bit__int__greater__eq,axiom,
% 5.25/5.52 ! [K: int,N: nat] :
% 5.25/5.52 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.52 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % signed_take_bit_int_greater_eq
% 5.25/5.52 thf(fact_4880_vebt__buildup_Osimps_I3_J,axiom,
% 5.25/5.52 ! [Va2: nat] :
% 5.25/5.52 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.25/5.52 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 5.25/5.52 = ( 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 ) ) ) ) ) ) )
% 5.25/5.52 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.25/5.52 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 5.25/5.52 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % vebt_buildup.simps(3)
% 5.25/5.52 thf(fact_4881_even__mult__exp__div__exp__iff,axiom,
% 5.25/5.52 ! [A: code_integer,M: nat,N: nat] :
% 5.25/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.52 = ( ( ord_less_nat @ N @ M )
% 5.25/5.52 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 = zero_z3403309356797280102nteger )
% 5.25/5.52 | ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.52 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % even_mult_exp_div_exp_iff
% 5.25/5.52 thf(fact_4882_even__mult__exp__div__exp__iff,axiom,
% 5.25/5.52 ! [A: nat,M: nat,N: nat] :
% 5.25/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.52 = ( ( ord_less_nat @ N @ M )
% 5.25/5.52 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 = zero_zero_nat )
% 5.25/5.52 | ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.52 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % even_mult_exp_div_exp_iff
% 5.25/5.52 thf(fact_4883_even__mult__exp__div__exp__iff,axiom,
% 5.25/5.52 ! [A: int,M: nat,N: nat] :
% 5.25/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.52 = ( ( ord_less_nat @ N @ M )
% 5.25/5.52 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.25/5.52 = zero_zero_int )
% 5.25/5.52 | ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.52 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % even_mult_exp_div_exp_iff
% 5.25/5.52 thf(fact_4884_real__average__minus__second,axiom,
% 5.25/5.52 ! [B: real,A: real] :
% 5.25/5.52 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.25/5.52 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % real_average_minus_second
% 5.25/5.52 thf(fact_4885_real__average__minus__first,axiom,
% 5.25/5.52 ! [A: real,B: real] :
% 5.25/5.52 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.25/5.52 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % real_average_minus_first
% 5.25/5.52 thf(fact_4886_vebt__member_Opelims_I3_J,axiom,
% 5.25/5.52 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.52 ( ~ ( vEBT_vebt_member @ X3 @ Xa2 )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 5.25/5.52 => ( ! [A5: $o,B5: $o] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.25/5.52 => ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.52 => A5 )
% 5.25/5.52 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.52 => ( ( ( Xa2 = one_one_nat )
% 5.25/5.52 => B5 )
% 5.25/5.52 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.25/5.52 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) )
% 5.25/5.52 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 5.25/5.52 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 5.25/5.52 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.25/5.52 => ( ( Xa2 != Mi2 )
% 5.25/5.52 => ( ( Xa2 != Ma2 )
% 5.25/5.52 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.25/5.52 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.25/5.52 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.25/5.52 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.25/5.52 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.52 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.52 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % vebt_member.pelims(3)
% 5.25/5.52 thf(fact_4887_vebt__member_Opelims_I1_J,axiom,
% 5.25/5.52 ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.25/5.52 ( ( ( vEBT_vebt_member @ X3 @ Xa2 )
% 5.25/5.52 = Y )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 5.25/5.52 => ( ! [A5: $o,B5: $o] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.52 => ( ( Y
% 5.25/5.52 = ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.52 => A5 )
% 5.25/5.52 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.52 => ( ( ( Xa2 = one_one_nat )
% 5.25/5.52 => B5 )
% 5.25/5.52 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.25/5.52 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.25/5.52 => ( ~ Y
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) ) )
% 5.25/5.52 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.25/5.52 => ( ~ Y
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.25/5.52 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.25/5.52 => ( ~ Y
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.25/5.52 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.25/5.52 => ( ( Y
% 5.25/5.52 = ( ( Xa2 != Mi2 )
% 5.25/5.52 => ( ( Xa2 != Ma2 )
% 5.25/5.52 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.25/5.52 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.25/5.52 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.25/5.52 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.25/5.52 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.52 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.52 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % vebt_member.pelims(1)
% 5.25/5.52 thf(fact_4888_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.25/5.52 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.52 ( ~ ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 5.25/5.52 => ( ! [A5: $o,B5: $o] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.25/5.52 => ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.52 => A5 )
% 5.25/5.52 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.52 => ( ( ( Xa2 = one_one_nat )
% 5.25/5.52 => B5 )
% 5.25/5.52 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.25/5.52 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa2 ) ) )
% 5.25/5.52 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ Xa2 ) )
% 5.25/5.52 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.52 => ( 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 ) ) ) ) ) )
% 5.25/5.52 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % VEBT_internal.naive_member.pelims(3)
% 5.25/5.52 thf(fact_4889_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.25/5.52 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.52 ( ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 5.25/5.52 => ( ! [A5: $o,B5: $o] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.25/5.52 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.52 => A5 )
% 5.25/5.52 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.52 => ( ( ( Xa2 = one_one_nat )
% 5.25/5.52 => B5 )
% 5.25/5.52 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.25/5.52 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ Xa2 ) )
% 5.25/5.52 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.52 => ( 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 ) ) ) ) ) )
% 5.25/5.52 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % VEBT_internal.naive_member.pelims(2)
% 5.25/5.52 thf(fact_4890_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.25/5.52 ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.25/5.52 ( ( ( vEBT_V5719532721284313246member @ X3 @ Xa2 )
% 5.25/5.52 = Y )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 5.25/5.52 => ( ! [A5: $o,B5: $o] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.52 => ( ( Y
% 5.25/5.52 = ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.52 => A5 )
% 5.25/5.52 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.52 => ( ( ( Xa2 = one_one_nat )
% 5.25/5.52 => B5 )
% 5.25/5.52 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.25/5.52 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 5.25/5.52 => ( ~ Y
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa2 ) ) ) )
% 5.25/5.52 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.25/5.52 => ( ( Y
% 5.25/5.52 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.52 => ( 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 ) ) ) ) ) )
% 5.25/5.52 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % VEBT_internal.naive_member.pelims(1)
% 5.25/5.52 thf(fact_4891_vebt__member_Opelims_I2_J,axiom,
% 5.25/5.52 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.52 ( ( vEBT_vebt_member @ X3 @ Xa2 )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 5.25/5.52 => ( ! [A5: $o,B5: $o] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.25/5.52 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.52 => A5 )
% 5.25/5.52 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.52 => ( ( ( Xa2 = one_one_nat )
% 5.25/5.52 => B5 )
% 5.25/5.52 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.25/5.52 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.25/5.52 => ~ ( ( Xa2 != Mi2 )
% 5.25/5.52 => ( ( Xa2 != Ma2 )
% 5.25/5.52 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.25/5.52 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.25/5.52 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.25/5.52 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.25/5.52 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.52 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.52 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % vebt_member.pelims(2)
% 5.25/5.52 thf(fact_4892_real__add__minus__iff,axiom,
% 5.25/5.52 ! [X3: real,A: real] :
% 5.25/5.52 ( ( ( plus_plus_real @ X3 @ ( uminus_uminus_real @ A ) )
% 5.25/5.52 = zero_zero_real )
% 5.25/5.52 = ( X3 = A ) ) ).
% 5.25/5.52
% 5.25/5.52 % real_add_minus_iff
% 5.25/5.52 thf(fact_4893_diff__commute,axiom,
% 5.25/5.52 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.52 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J2 ) @ K )
% 5.25/5.52 = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J2 ) ) ).
% 5.25/5.52
% 5.25/5.52 % diff_commute
% 5.25/5.52 thf(fact_4894_minus__real__def,axiom,
% 5.25/5.52 ( minus_minus_real
% 5.25/5.52 = ( ^ [X2: real,Y6: real] : ( plus_plus_real @ X2 @ ( uminus_uminus_real @ Y6 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_real_def
% 5.25/5.52 thf(fact_4895_real__minus__mult__self__le,axiom,
% 5.25/5.52 ! [U: real,X3: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X3 @ X3 ) ) ).
% 5.25/5.52
% 5.25/5.52 % real_minus_mult_self_le
% 5.25/5.52 thf(fact_4896_real__0__less__add__iff,axiom,
% 5.25/5.52 ! [X3: real,Y: real] :
% 5.25/5.52 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X3 @ Y ) )
% 5.25/5.52 = ( ord_less_real @ ( uminus_uminus_real @ X3 ) @ Y ) ) ).
% 5.25/5.52
% 5.25/5.52 % real_0_less_add_iff
% 5.25/5.52 thf(fact_4897_real__add__less__0__iff,axiom,
% 5.25/5.52 ! [X3: real,Y: real] :
% 5.25/5.52 ( ( ord_less_real @ ( plus_plus_real @ X3 @ Y ) @ zero_zero_real )
% 5.25/5.52 = ( ord_less_real @ Y @ ( uminus_uminus_real @ X3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % real_add_less_0_iff
% 5.25/5.52 thf(fact_4898_real__0__le__add__iff,axiom,
% 5.25/5.52 ! [X3: real,Y: real] :
% 5.25/5.52 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X3 @ Y ) )
% 5.25/5.52 = ( ord_less_eq_real @ ( uminus_uminus_real @ X3 ) @ Y ) ) ).
% 5.25/5.52
% 5.25/5.52 % real_0_le_add_iff
% 5.25/5.52 thf(fact_4899_real__add__le__0__iff,axiom,
% 5.25/5.52 ! [X3: real,Y: real] :
% 5.25/5.52 ( ( ord_less_eq_real @ ( plus_plus_real @ X3 @ Y ) @ zero_zero_real )
% 5.25/5.52 = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % real_add_le_0_iff
% 5.25/5.52 thf(fact_4900_mult__commute__abs,axiom,
% 5.25/5.52 ! [C: real] :
% 5.25/5.52 ( ( ^ [X2: real] : ( times_times_real @ X2 @ C ) )
% 5.25/5.52 = ( times_times_real @ C ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_commute_abs
% 5.25/5.52 thf(fact_4901_mult__commute__abs,axiom,
% 5.25/5.52 ! [C: rat] :
% 5.25/5.52 ( ( ^ [X2: rat] : ( times_times_rat @ X2 @ C ) )
% 5.25/5.52 = ( times_times_rat @ C ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_commute_abs
% 5.25/5.52 thf(fact_4902_mult__commute__abs,axiom,
% 5.25/5.52 ! [C: nat] :
% 5.25/5.52 ( ( ^ [X2: nat] : ( times_times_nat @ X2 @ C ) )
% 5.25/5.52 = ( times_times_nat @ C ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_commute_abs
% 5.25/5.52 thf(fact_4903_mult__commute__abs,axiom,
% 5.25/5.52 ! [C: int] :
% 5.25/5.52 ( ( ^ [X2: int] : ( times_times_int @ X2 @ C ) )
% 5.25/5.52 = ( times_times_int @ C ) ) ).
% 5.25/5.52
% 5.25/5.52 % mult_commute_abs
% 5.25/5.52 thf(fact_4904_realpow__square__minus__le,axiom,
% 5.25/5.52 ! [U: real,X3: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % realpow_square_minus_le
% 5.25/5.52 thf(fact_4905_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.25/5.52 ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.25/5.52 ( ( ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 5.25/5.52 = Y )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 5.25/5.52 => ( ! [Uu: $o,Uv: $o] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.25/5.52 => ( ~ Y
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) ) )
% 5.25/5.52 => ( ! [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) )
% 5.25/5.52 => ( ~ Y
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) @ Xa2 ) ) ) )
% 5.25/5.52 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.25/5.52 => ( ( Y
% 5.25/5.52 = ( ( Xa2 = Mi2 )
% 5.25/5.52 | ( Xa2 = Ma2 ) ) )
% 5.25/5.52 => ~ ( 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 ) ) ) )
% 5.25/5.52 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.25/5.52 => ( ( Y
% 5.25/5.52 = ( ( Xa2 = Mi2 )
% 5.25/5.52 | ( Xa2 = Ma2 )
% 5.25/5.52 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.52 => ( 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 ) ) ) ) ) )
% 5.25/5.52 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) ) ) )
% 5.25/5.52 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.25/5.52 => ( ( Y
% 5.25/5.52 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.52 => ( 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 ) ) ) ) ) )
% 5.25/5.52 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % VEBT_internal.membermima.pelims(1)
% 5.25/5.52 thf(fact_4906_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.25/5.52 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.52 ( ~ ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 5.25/5.52 => ( ! [Uu: $o,Uv: $o] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) )
% 5.25/5.52 => ( ! [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) )
% 5.25/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) @ Xa2 ) ) )
% 5.25/5.52 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.25/5.52 => ( ( 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 ) )
% 5.25/5.52 => ( ( Xa2 = Mi2 )
% 5.25/5.52 | ( Xa2 = Ma2 ) ) ) )
% 5.25/5.52 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 5.25/5.52 => ( ( Xa2 = Mi2 )
% 5.25/5.52 | ( Xa2 = Ma2 )
% 5.25/5.52 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.52 => ( 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 ) ) ) ) ) )
% 5.25/5.52 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.25/5.52 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) )
% 5.25/5.52 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.52 => ( 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 ) ) ) ) ) )
% 5.25/5.52 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % VEBT_internal.membermima.pelims(3)
% 5.25/5.52 thf(fact_4907_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.25/5.52 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.52 ( ( vEBT_VEBT_membermima @ X3 @ Xa2 )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 5.25/5.52 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.25/5.52 => ( ( 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 ) )
% 5.25/5.52 => ~ ( ( Xa2 = Mi2 )
% 5.25/5.52 | ( Xa2 = Ma2 ) ) ) )
% 5.25/5.52 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 5.25/5.52 => ~ ( ( Xa2 = Mi2 )
% 5.25/5.52 | ( Xa2 = Ma2 )
% 5.25/5.52 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.52 => ( 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 ) ) ) ) ) )
% 5.25/5.52 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.25/5.52 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.25/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) )
% 5.25/5.52 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.25/5.52 => ( 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 ) ) ) ) ) )
% 5.25/5.52 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % VEBT_internal.membermima.pelims(2)
% 5.25/5.52 thf(fact_4908_inrange,axiom,
% 5.25/5.52 ! [T: vEBT_VEBT,N: nat] :
% 5.25/5.52 ( ( vEBT_invar_vebt @ T @ N )
% 5.25/5.52 => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % inrange
% 5.25/5.52 thf(fact_4909_psubsetI,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.52 => ( ( A2 != B3 )
% 5.25/5.52 => ( ord_less_set_int @ A2 @ B3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % psubsetI
% 5.25/5.52 thf(fact_4910_compl__le__compl__iff,axiom,
% 5.25/5.52 ! [X3: set_int,Y: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X3 ) @ ( uminus1532241313380277803et_int @ Y ) )
% 5.25/5.52 = ( ord_less_eq_set_int @ Y @ X3 ) ) ).
% 5.25/5.52
% 5.25/5.52 % compl_le_compl_iff
% 5.25/5.52 thf(fact_4911_subsetI,axiom,
% 5.25/5.52 ! [A2: set_nat,B3: set_nat] :
% 5.25/5.52 ( ! [X5: nat] :
% 5.25/5.52 ( ( member_nat @ X5 @ A2 )
% 5.25/5.52 => ( member_nat @ X5 @ B3 ) )
% 5.25/5.52 => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 5.25/5.52
% 5.25/5.52 % subsetI
% 5.25/5.52 thf(fact_4912_subsetI,axiom,
% 5.25/5.52 ! [A2: set_real,B3: set_real] :
% 5.25/5.52 ( ! [X5: real] :
% 5.25/5.52 ( ( member_real @ X5 @ A2 )
% 5.25/5.52 => ( member_real @ X5 @ B3 ) )
% 5.25/5.52 => ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 5.25/5.52
% 5.25/5.52 % subsetI
% 5.25/5.52 thf(fact_4913_subsetI,axiom,
% 5.25/5.52 ! [A2: set_complex,B3: set_complex] :
% 5.25/5.52 ( ! [X5: complex] :
% 5.25/5.52 ( ( member_complex @ X5 @ A2 )
% 5.25/5.52 => ( member_complex @ X5 @ B3 ) )
% 5.25/5.52 => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ).
% 5.25/5.52
% 5.25/5.52 % subsetI
% 5.25/5.52 thf(fact_4914_subsetI,axiom,
% 5.25/5.52 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.25/5.52 ( ! [X5: product_prod_nat_nat] :
% 5.25/5.52 ( ( member8440522571783428010at_nat @ X5 @ A2 )
% 5.25/5.52 => ( member8440522571783428010at_nat @ X5 @ B3 ) )
% 5.25/5.52 => ( ord_le3146513528884898305at_nat @ A2 @ B3 ) ) ).
% 5.25/5.52
% 5.25/5.52 % subsetI
% 5.25/5.52 thf(fact_4915_subsetI,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int] :
% 5.25/5.52 ( ! [X5: int] :
% 5.25/5.52 ( ( member_int @ X5 @ A2 )
% 5.25/5.52 => ( member_int @ X5 @ B3 ) )
% 5.25/5.52 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.25/5.52
% 5.25/5.52 % subsetI
% 5.25/5.52 thf(fact_4916_subset__antisym,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.52 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.25/5.52 => ( A2 = B3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_antisym
% 5.25/5.52 thf(fact_4917_Compl__subset__Compl__iff,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B3 ) )
% 5.25/5.52 = ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 5.25/5.52
% 5.25/5.52 % Compl_subset_Compl_iff
% 5.25/5.52 thf(fact_4918_Compl__anti__mono,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.52 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B3 ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Compl_anti_mono
% 5.25/5.52 thf(fact_4919_Icc__eq__Icc,axiom,
% 5.25/5.52 ! [L2: set_int,H2: set_int,L3: set_int,H3: set_int] :
% 5.25/5.52 ( ( ( set_or370866239135849197et_int @ L2 @ H2 )
% 5.25/5.52 = ( set_or370866239135849197et_int @ L3 @ H3 ) )
% 5.25/5.52 = ( ( ( L2 = L3 )
% 5.25/5.52 & ( H2 = H3 ) )
% 5.25/5.52 | ( ~ ( ord_less_eq_set_int @ L2 @ H2 )
% 5.25/5.52 & ~ ( ord_less_eq_set_int @ L3 @ H3 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Icc_eq_Icc
% 5.25/5.52 thf(fact_4920_Icc__eq__Icc,axiom,
% 5.25/5.52 ! [L2: rat,H2: rat,L3: rat,H3: rat] :
% 5.25/5.52 ( ( ( set_or633870826150836451st_rat @ L2 @ H2 )
% 5.25/5.52 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 5.25/5.52 = ( ( ( L2 = L3 )
% 5.25/5.52 & ( H2 = H3 ) )
% 5.25/5.52 | ( ~ ( ord_less_eq_rat @ L2 @ H2 )
% 5.25/5.52 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Icc_eq_Icc
% 5.25/5.52 thf(fact_4921_Icc__eq__Icc,axiom,
% 5.25/5.52 ! [L2: num,H2: num,L3: num,H3: num] :
% 5.25/5.52 ( ( ( set_or7049704709247886629st_num @ L2 @ H2 )
% 5.25/5.52 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.25/5.52 = ( ( ( L2 = L3 )
% 5.25/5.52 & ( H2 = H3 ) )
% 5.25/5.52 | ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 5.25/5.52 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Icc_eq_Icc
% 5.25/5.52 thf(fact_4922_Icc__eq__Icc,axiom,
% 5.25/5.52 ! [L2: nat,H2: nat,L3: nat,H3: nat] :
% 5.25/5.52 ( ( ( set_or1269000886237332187st_nat @ L2 @ H2 )
% 5.25/5.52 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.25/5.52 = ( ( ( L2 = L3 )
% 5.25/5.52 & ( H2 = H3 ) )
% 5.25/5.52 | ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 5.25/5.52 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Icc_eq_Icc
% 5.25/5.52 thf(fact_4923_Icc__eq__Icc,axiom,
% 5.25/5.52 ! [L2: int,H2: int,L3: int,H3: int] :
% 5.25/5.52 ( ( ( set_or1266510415728281911st_int @ L2 @ H2 )
% 5.25/5.52 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.25/5.52 = ( ( ( L2 = L3 )
% 5.25/5.52 & ( H2 = H3 ) )
% 5.25/5.52 | ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 5.25/5.52 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Icc_eq_Icc
% 5.25/5.52 thf(fact_4924_Icc__eq__Icc,axiom,
% 5.25/5.52 ! [L2: real,H2: real,L3: real,H3: real] :
% 5.25/5.52 ( ( ( set_or1222579329274155063t_real @ L2 @ H2 )
% 5.25/5.52 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 5.25/5.52 = ( ( ( L2 = L3 )
% 5.25/5.52 & ( H2 = H3 ) )
% 5.25/5.52 | ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 5.25/5.52 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Icc_eq_Icc
% 5.25/5.52 thf(fact_4925_atLeastAtMost__iff,axiom,
% 5.25/5.52 ! [I2: set_int,L2: set_int,U: set_int] :
% 5.25/5.52 ( ( member_set_int @ I2 @ ( set_or370866239135849197et_int @ L2 @ U ) )
% 5.25/5.52 = ( ( ord_less_eq_set_int @ L2 @ I2 )
% 5.25/5.52 & ( ord_less_eq_set_int @ I2 @ U ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastAtMost_iff
% 5.25/5.52 thf(fact_4926_atLeastAtMost__iff,axiom,
% 5.25/5.52 ! [I2: rat,L2: rat,U: rat] :
% 5.25/5.52 ( ( member_rat @ I2 @ ( set_or633870826150836451st_rat @ L2 @ U ) )
% 5.25/5.52 = ( ( ord_less_eq_rat @ L2 @ I2 )
% 5.25/5.52 & ( ord_less_eq_rat @ I2 @ U ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastAtMost_iff
% 5.25/5.52 thf(fact_4927_atLeastAtMost__iff,axiom,
% 5.25/5.52 ! [I2: num,L2: num,U: num] :
% 5.25/5.52 ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L2 @ U ) )
% 5.25/5.52 = ( ( ord_less_eq_num @ L2 @ I2 )
% 5.25/5.52 & ( ord_less_eq_num @ I2 @ U ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastAtMost_iff
% 5.25/5.52 thf(fact_4928_atLeastAtMost__iff,axiom,
% 5.25/5.52 ! [I2: nat,L2: nat,U: nat] :
% 5.25/5.52 ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 5.25/5.52 = ( ( ord_less_eq_nat @ L2 @ I2 )
% 5.25/5.52 & ( ord_less_eq_nat @ I2 @ U ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastAtMost_iff
% 5.25/5.52 thf(fact_4929_atLeastAtMost__iff,axiom,
% 5.25/5.52 ! [I2: int,L2: int,U: int] :
% 5.25/5.52 ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 5.25/5.52 = ( ( ord_less_eq_int @ L2 @ I2 )
% 5.25/5.52 & ( ord_less_eq_int @ I2 @ U ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastAtMost_iff
% 5.25/5.52 thf(fact_4930_atLeastAtMost__iff,axiom,
% 5.25/5.52 ! [I2: real,L2: real,U: real] :
% 5.25/5.52 ( ( member_real @ I2 @ ( set_or1222579329274155063t_real @ L2 @ U ) )
% 5.25/5.52 = ( ( ord_less_eq_real @ L2 @ I2 )
% 5.25/5.52 & ( ord_less_eq_real @ I2 @ U ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastAtMost_iff
% 5.25/5.52 thf(fact_4931_atLeastatMost__subset__iff,axiom,
% 5.25/5.52 ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 5.25/5.52 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 5.25/5.52 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.25/5.52 | ( ( ord_less_eq_set_int @ C @ A )
% 5.25/5.52 & ( ord_less_eq_set_int @ B @ D ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastatMost_subset_iff
% 5.25/5.52 thf(fact_4932_atLeastatMost__subset__iff,axiom,
% 5.25/5.52 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.52 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.25/5.52 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.25/5.52 | ( ( ord_less_eq_rat @ C @ A )
% 5.25/5.52 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastatMost_subset_iff
% 5.25/5.52 thf(fact_4933_atLeastatMost__subset__iff,axiom,
% 5.25/5.52 ! [A: num,B: num,C: num,D: num] :
% 5.25/5.52 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.25/5.52 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.25/5.52 | ( ( ord_less_eq_num @ C @ A )
% 5.25/5.52 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastatMost_subset_iff
% 5.25/5.52 thf(fact_4934_atLeastatMost__subset__iff,axiom,
% 5.25/5.52 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.52 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.25/5.52 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.25/5.52 | ( ( ord_less_eq_nat @ C @ A )
% 5.25/5.52 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastatMost_subset_iff
% 5.25/5.52 thf(fact_4935_atLeastatMost__subset__iff,axiom,
% 5.25/5.52 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.25/5.52 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.25/5.52 | ( ( ord_less_eq_int @ C @ A )
% 5.25/5.52 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastatMost_subset_iff
% 5.25/5.52 thf(fact_4936_atLeastatMost__subset__iff,axiom,
% 5.25/5.52 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.52 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.25/5.52 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.25/5.52 | ( ( ord_less_eq_real @ C @ A )
% 5.25/5.52 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastatMost_subset_iff
% 5.25/5.52 thf(fact_4937_all__nat__less,axiom,
% 5.25/5.52 ! [N: nat,P: nat > $o] :
% 5.25/5.52 ( ( ! [M6: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ M6 @ N )
% 5.25/5.52 => ( P @ M6 ) ) )
% 5.25/5.52 = ( ! [X2: nat] :
% 5.25/5.52 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.25/5.52 => ( P @ X2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % all_nat_less
% 5.25/5.52 thf(fact_4938_ex__nat__less,axiom,
% 5.25/5.52 ! [N: nat,P: nat > $o] :
% 5.25/5.52 ( ( ? [M6: nat] :
% 5.25/5.52 ( ( ord_less_eq_nat @ M6 @ N )
% 5.25/5.52 & ( P @ M6 ) ) )
% 5.25/5.52 = ( ? [X2: nat] :
% 5.25/5.52 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.25/5.52 & ( P @ X2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % ex_nat_less
% 5.25/5.52 thf(fact_4939_atLeastatMost__psubset__iff,axiom,
% 5.25/5.52 ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 5.25/5.52 ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 5.25/5.52 = ( ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.25/5.52 | ( ( ord_less_eq_set_int @ C @ A )
% 5.25/5.52 & ( ord_less_eq_set_int @ B @ D )
% 5.25/5.52 & ( ( ord_less_set_int @ C @ A )
% 5.25/5.52 | ( ord_less_set_int @ B @ D ) ) ) )
% 5.25/5.52 & ( ord_less_eq_set_int @ C @ D ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastatMost_psubset_iff
% 5.25/5.52 thf(fact_4940_atLeastatMost__psubset__iff,axiom,
% 5.25/5.52 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.52 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.25/5.52 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 5.25/5.52 | ( ( ord_less_eq_rat @ C @ A )
% 5.25/5.52 & ( ord_less_eq_rat @ B @ D )
% 5.25/5.52 & ( ( ord_less_rat @ C @ A )
% 5.25/5.52 | ( ord_less_rat @ B @ D ) ) ) )
% 5.25/5.52 & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastatMost_psubset_iff
% 5.25/5.52 thf(fact_4941_atLeastatMost__psubset__iff,axiom,
% 5.25/5.52 ! [A: num,B: num,C: num,D: num] :
% 5.25/5.52 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.25/5.52 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.25/5.52 | ( ( ord_less_eq_num @ C @ A )
% 5.25/5.52 & ( ord_less_eq_num @ B @ D )
% 5.25/5.52 & ( ( ord_less_num @ C @ A )
% 5.25/5.52 | ( ord_less_num @ B @ D ) ) ) )
% 5.25/5.52 & ( ord_less_eq_num @ C @ D ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastatMost_psubset_iff
% 5.25/5.52 thf(fact_4942_atLeastatMost__psubset__iff,axiom,
% 5.25/5.52 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.52 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.25/5.52 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.25/5.52 | ( ( ord_less_eq_nat @ C @ A )
% 5.25/5.52 & ( ord_less_eq_nat @ B @ D )
% 5.25/5.52 & ( ( ord_less_nat @ C @ A )
% 5.25/5.52 | ( ord_less_nat @ B @ D ) ) ) )
% 5.25/5.52 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastatMost_psubset_iff
% 5.25/5.52 thf(fact_4943_atLeastatMost__psubset__iff,axiom,
% 5.25/5.52 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.52 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.25/5.52 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.25/5.52 | ( ( ord_less_eq_int @ C @ A )
% 5.25/5.52 & ( ord_less_eq_int @ B @ D )
% 5.25/5.52 & ( ( ord_less_int @ C @ A )
% 5.25/5.52 | ( ord_less_int @ B @ D ) ) ) )
% 5.25/5.52 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastatMost_psubset_iff
% 5.25/5.52 thf(fact_4944_atLeastatMost__psubset__iff,axiom,
% 5.25/5.52 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.52 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.25/5.52 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 5.25/5.52 | ( ( ord_less_eq_real @ C @ A )
% 5.25/5.52 & ( ord_less_eq_real @ B @ D )
% 5.25/5.52 & ( ( ord_less_real @ C @ A )
% 5.25/5.52 | ( ord_less_real @ B @ D ) ) ) )
% 5.25/5.52 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % atLeastatMost_psubset_iff
% 5.25/5.52 thf(fact_4945_Diff__mono,axiom,
% 5.25/5.52 ! [A2: set_nat,C5: set_nat,D4: set_nat,B3: set_nat] :
% 5.25/5.52 ( ( ord_less_eq_set_nat @ A2 @ C5 )
% 5.25/5.52 => ( ( ord_less_eq_set_nat @ D4 @ B3 )
% 5.25/5.52 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ ( minus_minus_set_nat @ C5 @ D4 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Diff_mono
% 5.25/5.52 thf(fact_4946_Diff__mono,axiom,
% 5.25/5.52 ! [A2: set_int,C5: set_int,D4: set_int,B3: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ A2 @ C5 )
% 5.25/5.52 => ( ( ord_less_eq_set_int @ D4 @ B3 )
% 5.25/5.52 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ ( minus_minus_set_int @ C5 @ D4 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Diff_mono
% 5.25/5.52 thf(fact_4947_Diff__subset,axiom,
% 5.25/5.52 ! [A2: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ A2 ) ).
% 5.25/5.52
% 5.25/5.52 % Diff_subset
% 5.25/5.52 thf(fact_4948_Diff__subset,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ A2 ) ).
% 5.25/5.52
% 5.25/5.52 % Diff_subset
% 5.25/5.52 thf(fact_4949_double__diff,axiom,
% 5.25/5.52 ! [A2: set_nat,B3: set_nat,C5: set_nat] :
% 5.25/5.52 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.25/5.52 => ( ( ord_less_eq_set_nat @ B3 @ C5 )
% 5.25/5.52 => ( ( minus_minus_set_nat @ B3 @ ( minus_minus_set_nat @ C5 @ A2 ) )
% 5.25/5.52 = A2 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % double_diff
% 5.25/5.52 thf(fact_4950_double__diff,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int,C5: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.52 => ( ( ord_less_eq_set_int @ B3 @ C5 )
% 5.25/5.52 => ( ( minus_minus_set_int @ B3 @ ( minus_minus_set_int @ C5 @ A2 ) )
% 5.25/5.52 = A2 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % double_diff
% 5.25/5.52 thf(fact_4951_in__mono,axiom,
% 5.25/5.52 ! [A2: set_nat,B3: set_nat,X3: nat] :
% 5.25/5.52 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.25/5.52 => ( ( member_nat @ X3 @ A2 )
% 5.25/5.52 => ( member_nat @ X3 @ B3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % in_mono
% 5.25/5.52 thf(fact_4952_in__mono,axiom,
% 5.25/5.52 ! [A2: set_real,B3: set_real,X3: real] :
% 5.25/5.52 ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.25/5.52 => ( ( member_real @ X3 @ A2 )
% 5.25/5.52 => ( member_real @ X3 @ B3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % in_mono
% 5.25/5.52 thf(fact_4953_in__mono,axiom,
% 5.25/5.52 ! [A2: set_complex,B3: set_complex,X3: complex] :
% 5.25/5.52 ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.25/5.52 => ( ( member_complex @ X3 @ A2 )
% 5.25/5.52 => ( member_complex @ X3 @ B3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % in_mono
% 5.25/5.52 thf(fact_4954_in__mono,axiom,
% 5.25/5.52 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,X3: product_prod_nat_nat] :
% 5.25/5.52 ( ( ord_le3146513528884898305at_nat @ A2 @ B3 )
% 5.25/5.52 => ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 5.25/5.52 => ( member8440522571783428010at_nat @ X3 @ B3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % in_mono
% 5.25/5.52 thf(fact_4955_in__mono,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int,X3: int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.52 => ( ( member_int @ X3 @ A2 )
% 5.25/5.52 => ( member_int @ X3 @ B3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % in_mono
% 5.25/5.52 thf(fact_4956_subsetD,axiom,
% 5.25/5.52 ! [A2: set_nat,B3: set_nat,C: nat] :
% 5.25/5.52 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.25/5.52 => ( ( member_nat @ C @ A2 )
% 5.25/5.52 => ( member_nat @ C @ B3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subsetD
% 5.25/5.52 thf(fact_4957_subsetD,axiom,
% 5.25/5.52 ! [A2: set_real,B3: set_real,C: real] :
% 5.25/5.52 ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.25/5.52 => ( ( member_real @ C @ A2 )
% 5.25/5.52 => ( member_real @ C @ B3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subsetD
% 5.25/5.52 thf(fact_4958_subsetD,axiom,
% 5.25/5.52 ! [A2: set_complex,B3: set_complex,C: complex] :
% 5.25/5.52 ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.25/5.52 => ( ( member_complex @ C @ A2 )
% 5.25/5.52 => ( member_complex @ C @ B3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subsetD
% 5.25/5.52 thf(fact_4959_subsetD,axiom,
% 5.25/5.52 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 5.25/5.52 ( ( ord_le3146513528884898305at_nat @ A2 @ B3 )
% 5.25/5.52 => ( ( member8440522571783428010at_nat @ C @ A2 )
% 5.25/5.52 => ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subsetD
% 5.25/5.52 thf(fact_4960_subsetD,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int,C: int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.52 => ( ( member_int @ C @ A2 )
% 5.25/5.52 => ( member_int @ C @ B3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subsetD
% 5.25/5.52 thf(fact_4961_equalityE,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int] :
% 5.25/5.52 ( ( A2 = B3 )
% 5.25/5.52 => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.52 => ~ ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % equalityE
% 5.25/5.52 thf(fact_4962_subset__eq,axiom,
% 5.25/5.52 ( ord_less_eq_set_nat
% 5.25/5.52 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.25/5.52 ! [X2: nat] :
% 5.25/5.52 ( ( member_nat @ X2 @ A6 )
% 5.25/5.52 => ( member_nat @ X2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_eq
% 5.25/5.52 thf(fact_4963_subset__eq,axiom,
% 5.25/5.52 ( ord_less_eq_set_real
% 5.25/5.52 = ( ^ [A6: set_real,B7: set_real] :
% 5.25/5.52 ! [X2: real] :
% 5.25/5.52 ( ( member_real @ X2 @ A6 )
% 5.25/5.52 => ( member_real @ X2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_eq
% 5.25/5.52 thf(fact_4964_subset__eq,axiom,
% 5.25/5.52 ( ord_le211207098394363844omplex
% 5.25/5.52 = ( ^ [A6: set_complex,B7: set_complex] :
% 5.25/5.52 ! [X2: complex] :
% 5.25/5.52 ( ( member_complex @ X2 @ A6 )
% 5.25/5.52 => ( member_complex @ X2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_eq
% 5.25/5.52 thf(fact_4965_subset__eq,axiom,
% 5.25/5.52 ( ord_le3146513528884898305at_nat
% 5.25/5.52 = ( ^ [A6: set_Pr1261947904930325089at_nat,B7: set_Pr1261947904930325089at_nat] :
% 5.25/5.52 ! [X2: product_prod_nat_nat] :
% 5.25/5.52 ( ( member8440522571783428010at_nat @ X2 @ A6 )
% 5.25/5.52 => ( member8440522571783428010at_nat @ X2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_eq
% 5.25/5.52 thf(fact_4966_subset__eq,axiom,
% 5.25/5.52 ( ord_less_eq_set_int
% 5.25/5.52 = ( ^ [A6: set_int,B7: set_int] :
% 5.25/5.52 ! [X2: int] :
% 5.25/5.52 ( ( member_int @ X2 @ A6 )
% 5.25/5.52 => ( member_int @ X2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_eq
% 5.25/5.52 thf(fact_4967_equalityD1,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int] :
% 5.25/5.52 ( ( A2 = B3 )
% 5.25/5.52 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.25/5.52
% 5.25/5.52 % equalityD1
% 5.25/5.52 thf(fact_4968_equalityD2,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int] :
% 5.25/5.52 ( ( A2 = B3 )
% 5.25/5.52 => ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 5.25/5.52
% 5.25/5.52 % equalityD2
% 5.25/5.52 thf(fact_4969_subset__iff,axiom,
% 5.25/5.52 ( ord_less_eq_set_nat
% 5.25/5.52 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.25/5.52 ! [T2: nat] :
% 5.25/5.52 ( ( member_nat @ T2 @ A6 )
% 5.25/5.52 => ( member_nat @ T2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_iff
% 5.25/5.52 thf(fact_4970_subset__iff,axiom,
% 5.25/5.52 ( ord_less_eq_set_real
% 5.25/5.52 = ( ^ [A6: set_real,B7: set_real] :
% 5.25/5.52 ! [T2: real] :
% 5.25/5.52 ( ( member_real @ T2 @ A6 )
% 5.25/5.52 => ( member_real @ T2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_iff
% 5.25/5.52 thf(fact_4971_subset__iff,axiom,
% 5.25/5.52 ( ord_le211207098394363844omplex
% 5.25/5.52 = ( ^ [A6: set_complex,B7: set_complex] :
% 5.25/5.52 ! [T2: complex] :
% 5.25/5.52 ( ( member_complex @ T2 @ A6 )
% 5.25/5.52 => ( member_complex @ T2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_iff
% 5.25/5.52 thf(fact_4972_subset__iff,axiom,
% 5.25/5.52 ( ord_le3146513528884898305at_nat
% 5.25/5.52 = ( ^ [A6: set_Pr1261947904930325089at_nat,B7: set_Pr1261947904930325089at_nat] :
% 5.25/5.52 ! [T2: product_prod_nat_nat] :
% 5.25/5.52 ( ( member8440522571783428010at_nat @ T2 @ A6 )
% 5.25/5.52 => ( member8440522571783428010at_nat @ T2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_iff
% 5.25/5.52 thf(fact_4973_subset__iff,axiom,
% 5.25/5.52 ( ord_less_eq_set_int
% 5.25/5.52 = ( ^ [A6: set_int,B7: set_int] :
% 5.25/5.52 ! [T2: int] :
% 5.25/5.52 ( ( member_int @ T2 @ A6 )
% 5.25/5.52 => ( member_int @ T2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_iff
% 5.25/5.52 thf(fact_4974_subset__refl,axiom,
% 5.25/5.52 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 5.25/5.52
% 5.25/5.52 % subset_refl
% 5.25/5.52 thf(fact_4975_Collect__mono,axiom,
% 5.25/5.52 ! [P: complex > $o,Q: complex > $o] :
% 5.25/5.52 ( ! [X5: complex] :
% 5.25/5.52 ( ( P @ X5 )
% 5.25/5.52 => ( Q @ X5 ) )
% 5.25/5.52 => ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_mono
% 5.25/5.52 thf(fact_4976_Collect__mono,axiom,
% 5.25/5.52 ! [P: real > $o,Q: real > $o] :
% 5.25/5.52 ( ! [X5: real] :
% 5.25/5.52 ( ( P @ X5 )
% 5.25/5.52 => ( Q @ X5 ) )
% 5.25/5.52 => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_mono
% 5.25/5.52 thf(fact_4977_Collect__mono,axiom,
% 5.25/5.52 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.25/5.52 ( ! [X5: list_nat] :
% 5.25/5.52 ( ( P @ X5 )
% 5.25/5.52 => ( Q @ X5 ) )
% 5.25/5.52 => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_mono
% 5.25/5.52 thf(fact_4978_Collect__mono,axiom,
% 5.25/5.52 ! [P: nat > $o,Q: nat > $o] :
% 5.25/5.52 ( ! [X5: nat] :
% 5.25/5.52 ( ( P @ X5 )
% 5.25/5.52 => ( Q @ X5 ) )
% 5.25/5.52 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_mono
% 5.25/5.52 thf(fact_4979_Collect__mono,axiom,
% 5.25/5.52 ! [P: int > $o,Q: int > $o] :
% 5.25/5.52 ( ! [X5: int] :
% 5.25/5.52 ( ( P @ X5 )
% 5.25/5.52 => ( Q @ X5 ) )
% 5.25/5.52 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_mono
% 5.25/5.52 thf(fact_4980_subset__trans,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int,C5: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.52 => ( ( ord_less_eq_set_int @ B3 @ C5 )
% 5.25/5.52 => ( ord_less_eq_set_int @ A2 @ C5 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_trans
% 5.25/5.52 thf(fact_4981_set__eq__subset,axiom,
% 5.25/5.52 ( ( ^ [Y5: set_int,Z3: set_int] : ( Y5 = Z3 ) )
% 5.25/5.52 = ( ^ [A6: set_int,B7: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ A6 @ B7 )
% 5.25/5.52 & ( ord_less_eq_set_int @ B7 @ A6 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % set_eq_subset
% 5.25/5.52 thf(fact_4982_Collect__mono__iff,axiom,
% 5.25/5.52 ! [P: complex > $o,Q: complex > $o] :
% 5.25/5.52 ( ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) )
% 5.25/5.52 = ( ! [X2: complex] :
% 5.25/5.52 ( ( P @ X2 )
% 5.25/5.52 => ( Q @ X2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_mono_iff
% 5.25/5.52 thf(fact_4983_Collect__mono__iff,axiom,
% 5.25/5.52 ! [P: real > $o,Q: real > $o] :
% 5.25/5.52 ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 5.25/5.52 = ( ! [X2: real] :
% 5.25/5.52 ( ( P @ X2 )
% 5.25/5.52 => ( Q @ X2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_mono_iff
% 5.25/5.52 thf(fact_4984_Collect__mono__iff,axiom,
% 5.25/5.52 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.25/5.52 ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) )
% 5.25/5.52 = ( ! [X2: list_nat] :
% 5.25/5.52 ( ( P @ X2 )
% 5.25/5.52 => ( Q @ X2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_mono_iff
% 5.25/5.52 thf(fact_4985_Collect__mono__iff,axiom,
% 5.25/5.52 ! [P: nat > $o,Q: nat > $o] :
% 5.25/5.52 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 5.25/5.52 = ( ! [X2: nat] :
% 5.25/5.52 ( ( P @ X2 )
% 5.25/5.52 => ( Q @ X2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_mono_iff
% 5.25/5.52 thf(fact_4986_Collect__mono__iff,axiom,
% 5.25/5.52 ! [P: int > $o,Q: int > $o] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 5.25/5.52 = ( ! [X2: int] :
% 5.25/5.52 ( ( P @ X2 )
% 5.25/5.52 => ( Q @ X2 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_mono_iff
% 5.25/5.52 thf(fact_4987_Collect__subset,axiom,
% 5.25/5.52 ! [A2: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 5.25/5.52 ( ord_le3146513528884898305at_nat
% 5.25/5.52 @ ( collec3392354462482085612at_nat
% 5.25/5.52 @ ^ [X2: product_prod_nat_nat] :
% 5.25/5.52 ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 5.25/5.52 & ( P @ X2 ) ) )
% 5.25/5.52 @ A2 ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_subset
% 5.25/5.52 thf(fact_4988_Collect__subset,axiom,
% 5.25/5.52 ! [A2: set_complex,P: complex > $o] :
% 5.25/5.52 ( ord_le211207098394363844omplex
% 5.25/5.52 @ ( collect_complex
% 5.25/5.52 @ ^ [X2: complex] :
% 5.25/5.52 ( ( member_complex @ X2 @ A2 )
% 5.25/5.52 & ( P @ X2 ) ) )
% 5.25/5.52 @ A2 ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_subset
% 5.25/5.52 thf(fact_4989_Collect__subset,axiom,
% 5.25/5.52 ! [A2: set_real,P: real > $o] :
% 5.25/5.52 ( ord_less_eq_set_real
% 5.25/5.52 @ ( collect_real
% 5.25/5.52 @ ^ [X2: real] :
% 5.25/5.52 ( ( member_real @ X2 @ A2 )
% 5.25/5.52 & ( P @ X2 ) ) )
% 5.25/5.52 @ A2 ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_subset
% 5.25/5.52 thf(fact_4990_Collect__subset,axiom,
% 5.25/5.52 ! [A2: set_list_nat,P: list_nat > $o] :
% 5.25/5.52 ( ord_le6045566169113846134st_nat
% 5.25/5.52 @ ( collect_list_nat
% 5.25/5.52 @ ^ [X2: list_nat] :
% 5.25/5.52 ( ( member_list_nat @ X2 @ A2 )
% 5.25/5.52 & ( P @ X2 ) ) )
% 5.25/5.52 @ A2 ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_subset
% 5.25/5.52 thf(fact_4991_Collect__subset,axiom,
% 5.25/5.52 ! [A2: set_nat,P: nat > $o] :
% 5.25/5.52 ( ord_less_eq_set_nat
% 5.25/5.52 @ ( collect_nat
% 5.25/5.52 @ ^ [X2: nat] :
% 5.25/5.52 ( ( member_nat @ X2 @ A2 )
% 5.25/5.52 & ( P @ X2 ) ) )
% 5.25/5.52 @ A2 ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_subset
% 5.25/5.52 thf(fact_4992_Collect__subset,axiom,
% 5.25/5.52 ! [A2: set_int,P: int > $o] :
% 5.25/5.52 ( ord_less_eq_set_int
% 5.25/5.52 @ ( collect_int
% 5.25/5.52 @ ^ [X2: int] :
% 5.25/5.52 ( ( member_int @ X2 @ A2 )
% 5.25/5.52 & ( P @ X2 ) ) )
% 5.25/5.52 @ A2 ) ).
% 5.25/5.52
% 5.25/5.52 % Collect_subset
% 5.25/5.52 thf(fact_4993_less__eq__set__def,axiom,
% 5.25/5.52 ( ord_less_eq_set_nat
% 5.25/5.52 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.25/5.52 ( ord_less_eq_nat_o
% 5.25/5.52 @ ^ [X2: nat] : ( member_nat @ X2 @ A6 )
% 5.25/5.52 @ ^ [X2: nat] : ( member_nat @ X2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_eq_set_def
% 5.25/5.52 thf(fact_4994_less__eq__set__def,axiom,
% 5.25/5.52 ( ord_less_eq_set_real
% 5.25/5.52 = ( ^ [A6: set_real,B7: set_real] :
% 5.25/5.52 ( ord_less_eq_real_o
% 5.25/5.52 @ ^ [X2: real] : ( member_real @ X2 @ A6 )
% 5.25/5.52 @ ^ [X2: real] : ( member_real @ X2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_eq_set_def
% 5.25/5.52 thf(fact_4995_less__eq__set__def,axiom,
% 5.25/5.52 ( ord_le211207098394363844omplex
% 5.25/5.52 = ( ^ [A6: set_complex,B7: set_complex] :
% 5.25/5.52 ( ord_le4573692005234683329plex_o
% 5.25/5.52 @ ^ [X2: complex] : ( member_complex @ X2 @ A6 )
% 5.25/5.52 @ ^ [X2: complex] : ( member_complex @ X2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_eq_set_def
% 5.25/5.52 thf(fact_4996_less__eq__set__def,axiom,
% 5.25/5.52 ( ord_le3146513528884898305at_nat
% 5.25/5.52 = ( ^ [A6: set_Pr1261947904930325089at_nat,B7: set_Pr1261947904930325089at_nat] :
% 5.25/5.52 ( ord_le704812498762024988_nat_o
% 5.25/5.52 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A6 )
% 5.25/5.52 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_eq_set_def
% 5.25/5.52 thf(fact_4997_less__eq__set__def,axiom,
% 5.25/5.52 ( ord_less_eq_set_int
% 5.25/5.52 = ( ^ [A6: set_int,B7: set_int] :
% 5.25/5.52 ( ord_less_eq_int_o
% 5.25/5.52 @ ^ [X2: int] : ( member_int @ X2 @ A6 )
% 5.25/5.52 @ ^ [X2: int] : ( member_int @ X2 @ B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % less_eq_set_def
% 5.25/5.52 thf(fact_4998_compl__le__swap2,axiom,
% 5.25/5.52 ! [Y: set_int,X3: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X3 )
% 5.25/5.52 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X3 ) @ Y ) ) ).
% 5.25/5.52
% 5.25/5.52 % compl_le_swap2
% 5.25/5.52 thf(fact_4999_compl__le__swap1,axiom,
% 5.25/5.52 ! [Y: set_int,X3: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X3 ) )
% 5.25/5.52 => ( ord_less_eq_set_int @ X3 @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % compl_le_swap1
% 5.25/5.52 thf(fact_5000_compl__mono,axiom,
% 5.25/5.52 ! [X3: set_int,Y: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ X3 @ Y )
% 5.25/5.52 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X3 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % compl_mono
% 5.25/5.52 thf(fact_5001_psubsetE,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int] :
% 5.25/5.52 ( ( ord_less_set_int @ A2 @ B3 )
% 5.25/5.52 => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.52 => ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % psubsetE
% 5.25/5.52 thf(fact_5002_psubset__eq,axiom,
% 5.25/5.52 ( ord_less_set_int
% 5.25/5.52 = ( ^ [A6: set_int,B7: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ A6 @ B7 )
% 5.25/5.52 & ( A6 != B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % psubset_eq
% 5.25/5.52 thf(fact_5003_psubset__imp__subset,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int] :
% 5.25/5.52 ( ( ord_less_set_int @ A2 @ B3 )
% 5.25/5.52 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.25/5.52
% 5.25/5.52 % psubset_imp_subset
% 5.25/5.52 thf(fact_5004_psubset__subset__trans,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int,C5: set_int] :
% 5.25/5.52 ( ( ord_less_set_int @ A2 @ B3 )
% 5.25/5.52 => ( ( ord_less_eq_set_int @ B3 @ C5 )
% 5.25/5.52 => ( ord_less_set_int @ A2 @ C5 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % psubset_subset_trans
% 5.25/5.52 thf(fact_5005_subset__not__subset__eq,axiom,
% 5.25/5.52 ( ord_less_set_int
% 5.25/5.52 = ( ^ [A6: set_int,B7: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ A6 @ B7 )
% 5.25/5.52 & ~ ( ord_less_eq_set_int @ B7 @ A6 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_not_subset_eq
% 5.25/5.52 thf(fact_5006_subset__psubset__trans,axiom,
% 5.25/5.52 ! [A2: set_int,B3: set_int,C5: set_int] :
% 5.25/5.52 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.52 => ( ( ord_less_set_int @ B3 @ C5 )
% 5.25/5.52 => ( ord_less_set_int @ A2 @ C5 ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_psubset_trans
% 5.25/5.52 thf(fact_5007_subset__iff__psubset__eq,axiom,
% 5.25/5.52 ( ord_less_eq_set_int
% 5.25/5.52 = ( ^ [A6: set_int,B7: set_int] :
% 5.25/5.52 ( ( ord_less_set_int @ A6 @ B7 )
% 5.25/5.52 | ( A6 = B7 ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % subset_iff_psubset_eq
% 5.25/5.52 thf(fact_5008_Bolzano,axiom,
% 5.25/5.52 ! [A: real,B: real,P: real > real > $o] :
% 5.25/5.52 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.52 => ( ! [A5: real,B5: real,C3: real] :
% 5.25/5.52 ( ( P @ A5 @ B5 )
% 5.25/5.52 => ( ( P @ B5 @ C3 )
% 5.25/5.52 => ( ( ord_less_eq_real @ A5 @ B5 )
% 5.25/5.52 => ( ( ord_less_eq_real @ B5 @ C3 )
% 5.25/5.52 => ( P @ A5 @ C3 ) ) ) ) )
% 5.25/5.52 => ( ! [X5: real] :
% 5.25/5.52 ( ( ord_less_eq_real @ A @ X5 )
% 5.25/5.52 => ( ( ord_less_eq_real @ X5 @ B )
% 5.25/5.52 => ? [D5: real] :
% 5.25/5.52 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.25/5.52 & ! [A5: real,B5: real] :
% 5.25/5.52 ( ( ( ord_less_eq_real @ A5 @ X5 )
% 5.25/5.52 & ( ord_less_eq_real @ X5 @ B5 )
% 5.25/5.52 & ( ord_less_real @ ( minus_minus_real @ B5 @ A5 ) @ D5 ) )
% 5.25/5.52 => ( P @ A5 @ B5 ) ) ) ) )
% 5.25/5.52 => ( P @ A @ B ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % Bolzano
% 5.25/5.52 thf(fact_5009_dbl__dec__simps_I4_J,axiom,
% 5.25/5.52 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.52 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(4)
% 5.25/5.52 thf(fact_5010_dbl__dec__simps_I4_J,axiom,
% 5.25/5.52 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.52 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(4)
% 5.25/5.52 thf(fact_5011_dbl__dec__simps_I4_J,axiom,
% 5.25/5.52 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(4)
% 5.25/5.52 thf(fact_5012_dbl__dec__simps_I4_J,axiom,
% 5.25/5.52 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.52 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(4)
% 5.25/5.52 thf(fact_5013_dbl__dec__simps_I4_J,axiom,
% 5.25/5.52 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.52 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(4)
% 5.25/5.52 thf(fact_5014_divmod__algorithm__code_I7_J,axiom,
% 5.25/5.52 ! [M: num,N: num] :
% 5.25/5.52 ( ( ( ord_less_eq_num @ M @ N )
% 5.25/5.52 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.25/5.52 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.25/5.52 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.25/5.52 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.25/5.52 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(7)
% 5.25/5.52 thf(fact_5015_divmod__algorithm__code_I7_J,axiom,
% 5.25/5.52 ! [M: num,N: num] :
% 5.25/5.52 ( ( ( ord_less_eq_num @ M @ N )
% 5.25/5.52 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.25/5.52 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.25/5.52 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.25/5.52 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.25/5.52 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(7)
% 5.25/5.52 thf(fact_5016_divmod__algorithm__code_I7_J,axiom,
% 5.25/5.52 ! [M: num,N: num] :
% 5.25/5.52 ( ( ( ord_less_eq_num @ M @ N )
% 5.25/5.52 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.25/5.52 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.25/5.52 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.25/5.52 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.25/5.52 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(7)
% 5.25/5.52 thf(fact_5017_divmod__algorithm__code_I8_J,axiom,
% 5.25/5.52 ! [M: num,N: num] :
% 5.25/5.52 ( ( ( ord_less_num @ M @ N )
% 5.25/5.52 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.25/5.52 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.25/5.52 & ( ~ ( ord_less_num @ M @ N )
% 5.25/5.52 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.25/5.52 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(8)
% 5.25/5.52 thf(fact_5018_divmod__algorithm__code_I8_J,axiom,
% 5.25/5.52 ! [M: num,N: num] :
% 5.25/5.52 ( ( ( ord_less_num @ M @ N )
% 5.25/5.52 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.25/5.52 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.25/5.52 & ( ~ ( ord_less_num @ M @ N )
% 5.25/5.52 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.25/5.52 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(8)
% 5.25/5.52 thf(fact_5019_divmod__algorithm__code_I8_J,axiom,
% 5.25/5.52 ! [M: num,N: num] :
% 5.25/5.52 ( ( ( ord_less_num @ M @ N )
% 5.25/5.52 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.25/5.52 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.25/5.52 & ( ~ ( ord_less_num @ M @ N )
% 5.25/5.52 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.25/5.52 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(8)
% 5.25/5.52 thf(fact_5020_triangle__def,axiom,
% 5.25/5.52 ( nat_triangle
% 5.25/5.52 = ( ^ [N2: nat] : ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % triangle_def
% 5.25/5.52 thf(fact_5021_vebt__buildup_Opelims,axiom,
% 5.25/5.52 ! [X3: nat,Y: vEBT_VEBT] :
% 5.25/5.52 ( ( ( vEBT_vebt_buildup @ X3 )
% 5.25/5.52 = Y )
% 5.25/5.52 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X3 )
% 5.25/5.52 => ( ( ( X3 = zero_zero_nat )
% 5.25/5.52 => ( ( Y
% 5.25/5.52 = ( vEBT_Leaf @ $false @ $false ) )
% 5.25/5.52 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.25/5.52 => ( ( ( X3
% 5.25/5.52 = ( suc @ zero_zero_nat ) )
% 5.25/5.52 => ( ( Y
% 5.25/5.52 = ( vEBT_Leaf @ $false @ $false ) )
% 5.25/5.52 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.25/5.52 => ~ ! [Va: nat] :
% 5.25/5.52 ( ( X3
% 5.25/5.52 = ( suc @ ( suc @ Va ) ) )
% 5.25/5.52 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.25/5.52 => ( Y
% 5.25/5.52 = ( 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 ) ) ) ) ) ) )
% 5.25/5.52 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.25/5.52 => ( Y
% 5.25/5.52 = ( 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 ) ) ) ) ) ) ) ) )
% 5.25/5.52 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % vebt_buildup.pelims
% 5.25/5.52 thf(fact_5022_dbl__dec__simps_I3_J,axiom,
% 5.25/5.52 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.25/5.52 = one_one_complex ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(3)
% 5.25/5.52 thf(fact_5023_dbl__dec__simps_I3_J,axiom,
% 5.25/5.52 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.25/5.52 = one_one_real ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(3)
% 5.25/5.52 thf(fact_5024_dbl__dec__simps_I3_J,axiom,
% 5.25/5.52 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 5.25/5.52 = one_one_rat ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(3)
% 5.25/5.52 thf(fact_5025_dbl__dec__simps_I3_J,axiom,
% 5.25/5.52 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.25/5.52 = one_one_int ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(3)
% 5.25/5.52 thf(fact_5026_triangle__Suc,axiom,
% 5.25/5.52 ! [N: nat] :
% 5.25/5.52 ( ( nat_triangle @ ( suc @ N ) )
% 5.25/5.52 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % triangle_Suc
% 5.25/5.52 thf(fact_5027_dbl__dec__simps_I2_J,axiom,
% 5.25/5.52 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.25/5.52 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(2)
% 5.25/5.52 thf(fact_5028_dbl__dec__simps_I2_J,axiom,
% 5.25/5.52 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.25/5.52 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(2)
% 5.25/5.52 thf(fact_5029_dbl__dec__simps_I2_J,axiom,
% 5.25/5.52 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(2)
% 5.25/5.52 thf(fact_5030_dbl__dec__simps_I2_J,axiom,
% 5.25/5.52 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.25/5.52 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(2)
% 5.25/5.52 thf(fact_5031_dbl__dec__simps_I2_J,axiom,
% 5.25/5.52 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.25/5.52 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(2)
% 5.25/5.52 thf(fact_5032_dbl__inc__simps_I1_J,axiom,
% 5.25/5.52 ! [K: num] :
% 5.25/5.52 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.25/5.52 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_inc_simps(1)
% 5.25/5.52 thf(fact_5033_dbl__inc__simps_I1_J,axiom,
% 5.25/5.52 ! [K: num] :
% 5.25/5.52 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.25/5.52 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_inc_simps(1)
% 5.25/5.52 thf(fact_5034_dbl__inc__simps_I1_J,axiom,
% 5.25/5.52 ! [K: num] :
% 5.25/5.52 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_inc_simps(1)
% 5.25/5.52 thf(fact_5035_dbl__inc__simps_I1_J,axiom,
% 5.25/5.52 ! [K: num] :
% 5.25/5.52 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.25/5.52 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_inc_simps(1)
% 5.25/5.52 thf(fact_5036_dbl__inc__simps_I1_J,axiom,
% 5.25/5.52 ! [K: num] :
% 5.25/5.52 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.25/5.52 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_inc_simps(1)
% 5.25/5.52 thf(fact_5037_dbl__dec__simps_I1_J,axiom,
% 5.25/5.52 ! [K: num] :
% 5.25/5.52 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.25/5.52 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(1)
% 5.25/5.52 thf(fact_5038_dbl__dec__simps_I1_J,axiom,
% 5.25/5.52 ! [K: num] :
% 5.25/5.52 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.25/5.52 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(1)
% 5.25/5.52 thf(fact_5039_dbl__dec__simps_I1_J,axiom,
% 5.25/5.52 ! [K: num] :
% 5.25/5.52 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.25/5.52 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(1)
% 5.25/5.52 thf(fact_5040_dbl__dec__simps_I1_J,axiom,
% 5.25/5.52 ! [K: num] :
% 5.25/5.52 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.25/5.52 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(1)
% 5.25/5.52 thf(fact_5041_dbl__dec__simps_I1_J,axiom,
% 5.25/5.52 ! [K: num] :
% 5.25/5.52 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.25/5.52 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_simps(1)
% 5.25/5.52 thf(fact_5042_dvd__numeral__simp,axiom,
% 5.25/5.52 ! [M: num,N: num] :
% 5.25/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.52 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dvd_numeral_simp
% 5.25/5.52 thf(fact_5043_dvd__numeral__simp,axiom,
% 5.25/5.52 ! [M: num,N: num] :
% 5.25/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.52 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dvd_numeral_simp
% 5.25/5.52 thf(fact_5044_dvd__numeral__simp,axiom,
% 5.25/5.52 ! [M: num,N: num] :
% 5.25/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 5.25/5.52 = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dvd_numeral_simp
% 5.25/5.52 thf(fact_5045_divmod__algorithm__code_I2_J,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ( ( unique5052692396658037445od_int @ M @ one )
% 5.25/5.52 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(2)
% 5.25/5.52 thf(fact_5046_divmod__algorithm__code_I2_J,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.25/5.52 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(2)
% 5.25/5.52 thf(fact_5047_divmod__algorithm__code_I2_J,axiom,
% 5.25/5.52 ! [M: num] :
% 5.25/5.52 ( ( unique3479559517661332726nteger @ M @ one )
% 5.25/5.52 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(2)
% 5.25/5.52 thf(fact_5048_divmod__algorithm__code_I3_J,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 5.25/5.52 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(3)
% 5.25/5.52 thf(fact_5049_divmod__algorithm__code_I3_J,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 5.25/5.52 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(3)
% 5.25/5.52 thf(fact_5050_divmod__algorithm__code_I3_J,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 5.25/5.52 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(3)
% 5.25/5.52 thf(fact_5051_divmod__algorithm__code_I4_J,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 5.25/5.52 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(4)
% 5.25/5.52 thf(fact_5052_divmod__algorithm__code_I4_J,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 5.25/5.52 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(4)
% 5.25/5.52 thf(fact_5053_divmod__algorithm__code_I4_J,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 5.25/5.52 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_algorithm_code(4)
% 5.25/5.52 thf(fact_5054_bset_I1_J,axiom,
% 5.25/5.52 ! [D4: int,B3: set_int,P: int > $o,Q: int > $o] :
% 5.25/5.52 ( ! [X5: int] :
% 5.25/5.52 ( ! [Xa: int] :
% 5.25/5.52 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb: int] :
% 5.25/5.52 ( ( member_int @ Xb @ B3 )
% 5.25/5.52 => ( X5
% 5.25/5.52 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.25/5.52 => ( ( P @ X5 )
% 5.25/5.52 => ( P @ ( minus_minus_int @ X5 @ D4 ) ) ) )
% 5.25/5.52 => ( ! [X5: int] :
% 5.25/5.52 ( ! [Xa: int] :
% 5.25/5.52 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb: int] :
% 5.25/5.52 ( ( member_int @ Xb @ B3 )
% 5.25/5.52 => ( X5
% 5.25/5.52 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.25/5.52 => ( ( Q @ X5 )
% 5.25/5.52 => ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ B3 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( ( P @ X )
% 5.25/5.52 & ( Q @ X ) )
% 5.25/5.52 => ( ( P @ ( minus_minus_int @ X @ D4 ) )
% 5.25/5.52 & ( Q @ ( minus_minus_int @ X @ D4 ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % bset(1)
% 5.25/5.52 thf(fact_5055_bset_I2_J,axiom,
% 5.25/5.52 ! [D4: int,B3: set_int,P: int > $o,Q: int > $o] :
% 5.25/5.52 ( ! [X5: int] :
% 5.25/5.52 ( ! [Xa: int] :
% 5.25/5.52 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb: int] :
% 5.25/5.52 ( ( member_int @ Xb @ B3 )
% 5.25/5.52 => ( X5
% 5.25/5.52 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.25/5.52 => ( ( P @ X5 )
% 5.25/5.52 => ( P @ ( minus_minus_int @ X5 @ D4 ) ) ) )
% 5.25/5.52 => ( ! [X5: int] :
% 5.25/5.52 ( ! [Xa: int] :
% 5.25/5.52 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb: int] :
% 5.25/5.52 ( ( member_int @ Xb @ B3 )
% 5.25/5.52 => ( X5
% 5.25/5.52 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.25/5.52 => ( ( Q @ X5 )
% 5.25/5.52 => ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ B3 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( ( P @ X )
% 5.25/5.52 | ( Q @ X ) )
% 5.25/5.52 => ( ( P @ ( minus_minus_int @ X @ D4 ) )
% 5.25/5.52 | ( Q @ ( minus_minus_int @ X @ D4 ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % bset(2)
% 5.25/5.52 thf(fact_5056_aset_I1_J,axiom,
% 5.25/5.52 ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.25/5.52 ( ! [X5: int] :
% 5.25/5.52 ( ! [Xa: int] :
% 5.25/5.52 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb: int] :
% 5.25/5.52 ( ( member_int @ Xb @ A2 )
% 5.25/5.52 => ( X5
% 5.25/5.52 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.25/5.52 => ( ( P @ X5 )
% 5.25/5.52 => ( P @ ( plus_plus_int @ X5 @ D4 ) ) ) )
% 5.25/5.52 => ( ! [X5: int] :
% 5.25/5.52 ( ! [Xa: int] :
% 5.25/5.52 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb: int] :
% 5.25/5.52 ( ( member_int @ Xb @ A2 )
% 5.25/5.52 => ( X5
% 5.25/5.52 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.25/5.52 => ( ( Q @ X5 )
% 5.25/5.52 => ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ A2 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( ( P @ X )
% 5.25/5.52 & ( Q @ X ) )
% 5.25/5.52 => ( ( P @ ( plus_plus_int @ X @ D4 ) )
% 5.25/5.52 & ( Q @ ( plus_plus_int @ X @ D4 ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % aset(1)
% 5.25/5.52 thf(fact_5057_aset_I2_J,axiom,
% 5.25/5.52 ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.25/5.52 ( ! [X5: int] :
% 5.25/5.52 ( ! [Xa: int] :
% 5.25/5.52 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb: int] :
% 5.25/5.52 ( ( member_int @ Xb @ A2 )
% 5.25/5.52 => ( X5
% 5.25/5.52 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.25/5.52 => ( ( P @ X5 )
% 5.25/5.52 => ( P @ ( plus_plus_int @ X5 @ D4 ) ) ) )
% 5.25/5.52 => ( ! [X5: int] :
% 5.25/5.52 ( ! [Xa: int] :
% 5.25/5.52 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb: int] :
% 5.25/5.52 ( ( member_int @ Xb @ A2 )
% 5.25/5.52 => ( X5
% 5.25/5.52 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.25/5.52 => ( ( Q @ X5 )
% 5.25/5.52 => ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ A2 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( ( P @ X )
% 5.25/5.52 | ( Q @ X ) )
% 5.25/5.52 => ( ( P @ ( plus_plus_int @ X @ D4 ) )
% 5.25/5.52 | ( Q @ ( plus_plus_int @ X @ D4 ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % aset(2)
% 5.25/5.52 thf(fact_5058_bset_I9_J,axiom,
% 5.25/5.52 ! [D: int,D4: int,B3: set_int,T: int] :
% 5.25/5.52 ( ( dvd_dvd_int @ D @ D4 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ B3 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) )
% 5.25/5.52 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X @ D4 ) @ T ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % bset(9)
% 5.25/5.52 thf(fact_5059_bset_I10_J,axiom,
% 5.25/5.52 ! [D: int,D4: int,B3: set_int,T: int] :
% 5.25/5.52 ( ( dvd_dvd_int @ D @ D4 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ B3 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) )
% 5.25/5.52 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X @ D4 ) @ T ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % bset(10)
% 5.25/5.52 thf(fact_5060_aset_I9_J,axiom,
% 5.25/5.52 ! [D: int,D4: int,A2: set_int,T: int] :
% 5.25/5.52 ( ( dvd_dvd_int @ D @ D4 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ A2 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) )
% 5.25/5.52 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X @ D4 ) @ T ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % aset(9)
% 5.25/5.52 thf(fact_5061_aset_I10_J,axiom,
% 5.25/5.52 ! [D: int,D4: int,A2: set_int,T: int] :
% 5.25/5.52 ( ( dvd_dvd_int @ D @ D4 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ A2 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) )
% 5.25/5.52 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X @ D4 ) @ T ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % aset(10)
% 5.25/5.52 thf(fact_5062_periodic__finite__ex,axiom,
% 5.25/5.52 ! [D: int,P: int > $o] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D )
% 5.25/5.52 => ( ! [X5: int,K2: int] :
% 5.25/5.52 ( ( P @ X5 )
% 5.25/5.52 = ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.25/5.52 => ( ( ? [X4: int] : ( P @ X4 ) )
% 5.25/5.52 = ( ? [X2: int] :
% 5.25/5.52 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.25/5.52 & ( P @ X2 ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % periodic_finite_ex
% 5.25/5.52 thf(fact_5063_bset_I3_J,axiom,
% 5.25/5.52 ! [D4: int,T: int,B3: set_int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.25/5.52 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B3 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ B3 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( X = T )
% 5.25/5.52 => ( ( minus_minus_int @ X @ D4 )
% 5.25/5.52 = T ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % bset(3)
% 5.25/5.52 thf(fact_5064_bset_I4_J,axiom,
% 5.25/5.52 ! [D4: int,T: int,B3: set_int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.25/5.52 => ( ( member_int @ T @ B3 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ B3 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( X != T )
% 5.25/5.52 => ( ( minus_minus_int @ X @ D4 )
% 5.25/5.52 != T ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % bset(4)
% 5.25/5.52 thf(fact_5065_bset_I5_J,axiom,
% 5.25/5.52 ! [D4: int,B3: set_int,T: int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ B3 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( ord_less_int @ X @ T )
% 5.25/5.52 => ( ord_less_int @ ( minus_minus_int @ X @ D4 ) @ T ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % bset(5)
% 5.25/5.52 thf(fact_5066_bset_I7_J,axiom,
% 5.25/5.52 ! [D4: int,T: int,B3: set_int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.25/5.52 => ( ( member_int @ T @ B3 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ B3 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( ord_less_int @ T @ X )
% 5.25/5.52 => ( ord_less_int @ T @ ( minus_minus_int @ X @ D4 ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % bset(7)
% 5.25/5.52 thf(fact_5067_aset_I3_J,axiom,
% 5.25/5.52 ! [D4: int,T: int,A2: set_int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.25/5.52 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ A2 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( X = T )
% 5.25/5.52 => ( ( plus_plus_int @ X @ D4 )
% 5.25/5.52 = T ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % aset(3)
% 5.25/5.52 thf(fact_5068_aset_I4_J,axiom,
% 5.25/5.52 ! [D4: int,T: int,A2: set_int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.25/5.52 => ( ( member_int @ T @ A2 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ A2 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( X != T )
% 5.25/5.52 => ( ( plus_plus_int @ X @ D4 )
% 5.25/5.52 != T ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % aset(4)
% 5.25/5.52 thf(fact_5069_aset_I5_J,axiom,
% 5.25/5.52 ! [D4: int,T: int,A2: set_int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.25/5.52 => ( ( member_int @ T @ A2 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ A2 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( ord_less_int @ X @ T )
% 5.25/5.52 => ( ord_less_int @ ( plus_plus_int @ X @ D4 ) @ T ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % aset(5)
% 5.25/5.52 thf(fact_5070_aset_I7_J,axiom,
% 5.25/5.52 ! [D4: int,A2: set_int,T: int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ A2 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( ord_less_int @ T @ X )
% 5.25/5.52 => ( ord_less_int @ T @ ( plus_plus_int @ X @ D4 ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % aset(7)
% 5.25/5.52 thf(fact_5071_divmod__int__def,axiom,
% 5.25/5.52 ( unique5052692396658037445od_int
% 5.25/5.52 = ( ^ [M6: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_int_def
% 5.25/5.52 thf(fact_5072_divmod__def,axiom,
% 5.25/5.52 ( unique5052692396658037445od_int
% 5.25/5.52 = ( ^ [M6: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_def
% 5.25/5.52 thf(fact_5073_divmod__def,axiom,
% 5.25/5.52 ( unique5055182867167087721od_nat
% 5.25/5.52 = ( ^ [M6: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_def
% 5.25/5.52 thf(fact_5074_divmod__def,axiom,
% 5.25/5.52 ( unique3479559517661332726nteger
% 5.25/5.52 = ( ^ [M6: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_def
% 5.25/5.52 thf(fact_5075_divmod_H__nat__def,axiom,
% 5.25/5.52 ( unique5055182867167087721od_nat
% 5.25/5.52 = ( ^ [M6: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod'_nat_def
% 5.25/5.52 thf(fact_5076_bset_I6_J,axiom,
% 5.25/5.52 ! [D4: int,B3: set_int,T: int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ B3 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( ord_less_eq_int @ X @ T )
% 5.25/5.52 => ( ord_less_eq_int @ ( minus_minus_int @ X @ D4 ) @ T ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % bset(6)
% 5.25/5.52 thf(fact_5077_bset_I8_J,axiom,
% 5.25/5.52 ! [D4: int,T: int,B3: set_int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.25/5.52 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B3 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ B3 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( ord_less_eq_int @ T @ X )
% 5.25/5.52 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X @ D4 ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % bset(8)
% 5.25/5.52 thf(fact_5078_aset_I6_J,axiom,
% 5.25/5.52 ! [D4: int,T: int,A2: set_int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.25/5.52 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ A2 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( ord_less_eq_int @ X @ T )
% 5.25/5.52 => ( ord_less_eq_int @ ( plus_plus_int @ X @ D4 ) @ T ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % aset(6)
% 5.25/5.52 thf(fact_5079_aset_I8_J,axiom,
% 5.25/5.52 ! [D4: int,A2: set_int,T: int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.25/5.52 => ! [X: int] :
% 5.25/5.52 ( ! [Xa3: int] :
% 5.25/5.52 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb2: int] :
% 5.25/5.52 ( ( member_int @ Xb2 @ A2 )
% 5.25/5.52 => ( X
% 5.25/5.52 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.25/5.52 => ( ( ord_less_eq_int @ T @ X )
% 5.25/5.52 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X @ D4 ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % aset(8)
% 5.25/5.52 thf(fact_5080_cppi,axiom,
% 5.25/5.52 ! [D4: int,P: int > $o,P3: int > $o,A2: set_int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.25/5.52 => ( ? [Z4: int] :
% 5.25/5.52 ! [X5: int] :
% 5.25/5.52 ( ( ord_less_int @ Z4 @ X5 )
% 5.25/5.52 => ( ( P @ X5 )
% 5.25/5.52 = ( P3 @ X5 ) ) )
% 5.25/5.52 => ( ! [X5: int] :
% 5.25/5.52 ( ! [Xa: int] :
% 5.25/5.52 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb: int] :
% 5.25/5.52 ( ( member_int @ Xb @ A2 )
% 5.25/5.52 => ( X5
% 5.25/5.52 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.25/5.52 => ( ( P @ X5 )
% 5.25/5.52 => ( P @ ( plus_plus_int @ X5 @ D4 ) ) ) )
% 5.25/5.52 => ( ! [X5: int,K2: int] :
% 5.25/5.52 ( ( P3 @ X5 )
% 5.25/5.52 = ( P3 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.25/5.52 => ( ( ? [X4: int] : ( P @ X4 ) )
% 5.25/5.52 = ( ? [X2: int] :
% 5.25/5.52 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 & ( P3 @ X2 ) )
% 5.25/5.52 | ? [X2: int] :
% 5.25/5.52 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 & ? [Y6: int] :
% 5.25/5.52 ( ( member_int @ Y6 @ A2 )
% 5.25/5.52 & ( P @ ( minus_minus_int @ Y6 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % cppi
% 5.25/5.52 thf(fact_5081_cpmi,axiom,
% 5.25/5.52 ! [D4: int,P: int > $o,P3: int > $o,B3: set_int] :
% 5.25/5.52 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.25/5.52 => ( ? [Z4: int] :
% 5.25/5.52 ! [X5: int] :
% 5.25/5.52 ( ( ord_less_int @ X5 @ Z4 )
% 5.25/5.52 => ( ( P @ X5 )
% 5.25/5.52 = ( P3 @ X5 ) ) )
% 5.25/5.52 => ( ! [X5: int] :
% 5.25/5.52 ( ! [Xa: int] :
% 5.25/5.52 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 => ! [Xb: int] :
% 5.25/5.52 ( ( member_int @ Xb @ B3 )
% 5.25/5.52 => ( X5
% 5.25/5.52 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.25/5.52 => ( ( P @ X5 )
% 5.25/5.52 => ( P @ ( minus_minus_int @ X5 @ D4 ) ) ) )
% 5.25/5.52 => ( ! [X5: int,K2: int] :
% 5.25/5.52 ( ( P3 @ X5 )
% 5.25/5.52 = ( P3 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.25/5.52 => ( ( ? [X4: int] : ( P @ X4 ) )
% 5.25/5.52 = ( ? [X2: int] :
% 5.25/5.52 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 & ( P3 @ X2 ) )
% 5.25/5.52 | ? [X2: int] :
% 5.25/5.52 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.25/5.52 & ? [Y6: int] :
% 5.25/5.52 ( ( member_int @ Y6 @ B3 )
% 5.25/5.52 & ( P @ ( plus_plus_int @ Y6 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % cpmi
% 5.25/5.52 thf(fact_5082_dbl__dec__def,axiom,
% 5.25/5.52 ( neg_nu6511756317524482435omplex
% 5.25/5.52 = ( ^ [X2: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_def
% 5.25/5.52 thf(fact_5083_dbl__dec__def,axiom,
% 5.25/5.52 ( neg_nu6075765906172075777c_real
% 5.25/5.52 = ( ^ [X2: real] : ( minus_minus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_def
% 5.25/5.52 thf(fact_5084_dbl__dec__def,axiom,
% 5.25/5.52 ( neg_nu3179335615603231917ec_rat
% 5.25/5.52 = ( ^ [X2: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_def
% 5.25/5.52 thf(fact_5085_dbl__dec__def,axiom,
% 5.25/5.52 ( neg_nu3811975205180677377ec_int
% 5.25/5.52 = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % dbl_dec_def
% 5.25/5.52 thf(fact_5086_divmod__divmod__step,axiom,
% 5.25/5.52 ( unique5055182867167087721od_nat
% 5.25/5.52 = ( ^ [M6: num,N2: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M6 @ N2 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M6 ) ) @ ( unique5026877609467782581ep_nat @ N2 @ ( unique5055182867167087721od_nat @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_divmod_step
% 5.25/5.52 thf(fact_5087_divmod__divmod__step,axiom,
% 5.25/5.52 ( unique5052692396658037445od_int
% 5.25/5.52 = ( ^ [M6: num,N2: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M6 @ N2 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M6 ) ) @ ( unique5024387138958732305ep_int @ N2 @ ( unique5052692396658037445od_int @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_divmod_step
% 5.25/5.52 thf(fact_5088_divmod__divmod__step,axiom,
% 5.25/5.52 ( unique3479559517661332726nteger
% 5.25/5.52 = ( ^ [M6: num,N2: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M6 @ N2 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M6 ) ) @ ( unique4921790084139445826nteger @ N2 @ ( unique3479559517661332726nteger @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % divmod_divmod_step
% 5.25/5.52 thf(fact_5089_minus__one__div__numeral,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.52 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_one_div_numeral
% 5.25/5.52 thf(fact_5090_one__div__minus__numeral,axiom,
% 5.25/5.52 ! [N: num] :
% 5.25/5.52 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.52 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % one_div_minus_numeral
% 5.25/5.52 thf(fact_5091_numeral__div__minus__numeral,axiom,
% 5.25/5.52 ! [M: num,N: num] :
% 5.25/5.52 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.52 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % numeral_div_minus_numeral
% 5.25/5.52 thf(fact_5092_minus__numeral__div__numeral,axiom,
% 5.25/5.52 ! [M: num,N: num] :
% 5.25/5.52 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.52 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % minus_numeral_div_numeral
% 5.25/5.52 thf(fact_5093_option_Osize__gen_I2_J,axiom,
% 5.25/5.52 ! [X3: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 5.25/5.52 ( ( size_o8335143837870341156at_nat @ X3 @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.25/5.52 = ( plus_plus_nat @ ( X3 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % option.size_gen(2)
% 5.25/5.52 thf(fact_5094_option_Osize__gen_I2_J,axiom,
% 5.25/5.52 ! [X3: num > nat,X22: num] :
% 5.25/5.52 ( ( size_option_num @ X3 @ ( some_num @ X22 ) )
% 5.25/5.52 = ( plus_plus_nat @ ( X3 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % option.size_gen(2)
% 5.25/5.52 thf(fact_5095_of__int__code__if,axiom,
% 5.25/5.52 ( ring_1_of_int_int
% 5.25/5.52 = ( ^ [K3: int] :
% 5.25/5.52 ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 5.25/5.52 @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.25/5.52 @ ( if_int
% 5.25/5.52 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.52 = zero_zero_int )
% 5.25/5.52 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.25/5.52 @ ( 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 ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_code_if
% 5.25/5.52 thf(fact_5096_of__int__code__if,axiom,
% 5.25/5.52 ( ring_1_of_int_real
% 5.25/5.52 = ( ^ [K3: int] :
% 5.25/5.52 ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 5.25/5.52 @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 5.25/5.52 @ ( if_real
% 5.25/5.52 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.52 = zero_zero_int )
% 5.25/5.52 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.25/5.52 @ ( 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 ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_code_if
% 5.25/5.52 thf(fact_5097_of__int__code__if,axiom,
% 5.25/5.52 ( ring_17405671764205052669omplex
% 5.25/5.52 = ( ^ [K3: int] :
% 5.25/5.52 ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 5.25/5.52 @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 5.25/5.52 @ ( if_complex
% 5.25/5.52 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.52 = zero_zero_int )
% 5.25/5.52 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.25/5.52 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_code_if
% 5.25/5.52 thf(fact_5098_of__int__code__if,axiom,
% 5.25/5.52 ( ring_18347121197199848620nteger
% 5.25/5.52 = ( ^ [K3: int] :
% 5.25/5.52 ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.25/5.52 @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 5.25/5.52 @ ( if_Code_integer
% 5.25/5.52 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.52 = zero_zero_int )
% 5.25/5.52 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.25/5.52 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_code_if
% 5.25/5.52 thf(fact_5099_of__int__code__if,axiom,
% 5.25/5.52 ( ring_1_of_int_rat
% 5.25/5.52 = ( ^ [K3: int] :
% 5.25/5.52 ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 5.25/5.52 @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 5.25/5.52 @ ( if_rat
% 5.25/5.52 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.52 = zero_zero_int )
% 5.25/5.52 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.25/5.52 @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_code_if
% 5.25/5.52 thf(fact_5100_order__refl,axiom,
% 5.25/5.52 ! [X3: set_int] : ( ord_less_eq_set_int @ X3 @ X3 ) ).
% 5.25/5.52
% 5.25/5.52 % order_refl
% 5.25/5.52 thf(fact_5101_order__refl,axiom,
% 5.25/5.52 ! [X3: rat] : ( ord_less_eq_rat @ X3 @ X3 ) ).
% 5.25/5.52
% 5.25/5.52 % order_refl
% 5.25/5.52 thf(fact_5102_order__refl,axiom,
% 5.25/5.52 ! [X3: num] : ( ord_less_eq_num @ X3 @ X3 ) ).
% 5.25/5.52
% 5.25/5.52 % order_refl
% 5.25/5.52 thf(fact_5103_order__refl,axiom,
% 5.25/5.52 ! [X3: nat] : ( ord_less_eq_nat @ X3 @ X3 ) ).
% 5.25/5.52
% 5.25/5.52 % order_refl
% 5.25/5.52 thf(fact_5104_order__refl,axiom,
% 5.25/5.52 ! [X3: int] : ( ord_less_eq_int @ X3 @ X3 ) ).
% 5.25/5.52
% 5.25/5.52 % order_refl
% 5.25/5.52 thf(fact_5105_dual__order_Orefl,axiom,
% 5.25/5.52 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.25/5.52
% 5.25/5.52 % dual_order.refl
% 5.25/5.52 thf(fact_5106_dual__order_Orefl,axiom,
% 5.25/5.52 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.25/5.52
% 5.25/5.52 % dual_order.refl
% 5.25/5.52 thf(fact_5107_dual__order_Orefl,axiom,
% 5.25/5.52 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.25/5.52
% 5.25/5.52 % dual_order.refl
% 5.25/5.52 thf(fact_5108_dual__order_Orefl,axiom,
% 5.25/5.52 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.25/5.52
% 5.25/5.52 % dual_order.refl
% 5.25/5.52 thf(fact_5109_dual__order_Orefl,axiom,
% 5.25/5.52 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.25/5.52
% 5.25/5.52 % dual_order.refl
% 5.25/5.52 thf(fact_5110_of__int__le__iff,axiom,
% 5.25/5.52 ! [W: int,Z: int] :
% 5.25/5.52 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.25/5.52 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_le_iff
% 5.25/5.52 thf(fact_5111_of__int__le__iff,axiom,
% 5.25/5.52 ! [W: int,Z: int] :
% 5.25/5.52 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.25/5.52 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_le_iff
% 5.25/5.52 thf(fact_5112_of__int__le__iff,axiom,
% 5.25/5.52 ! [W: int,Z: int] :
% 5.25/5.52 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.25/5.52 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_le_iff
% 5.25/5.52 thf(fact_5113_of__int__numeral,axiom,
% 5.25/5.52 ! [K: num] :
% 5.25/5.52 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.25/5.52 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_numeral
% 5.25/5.52 thf(fact_5114_of__int__numeral,axiom,
% 5.25/5.52 ! [K: num] :
% 5.25/5.52 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.25/5.52 = ( numeral_numeral_real @ K ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_numeral
% 5.25/5.52 thf(fact_5115_of__int__numeral,axiom,
% 5.25/5.52 ! [K: num] :
% 5.25/5.52 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.25/5.52 = ( numeral_numeral_rat @ K ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_numeral
% 5.25/5.52 thf(fact_5116_of__int__numeral,axiom,
% 5.25/5.52 ! [K: num] :
% 5.25/5.52 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.25/5.52 = ( numeral_numeral_int @ K ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_numeral
% 5.25/5.52 thf(fact_5117_of__int__eq__numeral__iff,axiom,
% 5.25/5.52 ! [Z: int,N: num] :
% 5.25/5.52 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.25/5.52 = ( numera6690914467698888265omplex @ N ) )
% 5.25/5.52 = ( Z
% 5.25/5.52 = ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_eq_numeral_iff
% 5.25/5.52 thf(fact_5118_of__int__eq__numeral__iff,axiom,
% 5.25/5.52 ! [Z: int,N: num] :
% 5.25/5.52 ( ( ( ring_1_of_int_real @ Z )
% 5.25/5.52 = ( numeral_numeral_real @ N ) )
% 5.25/5.52 = ( Z
% 5.25/5.52 = ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_eq_numeral_iff
% 5.25/5.52 thf(fact_5119_of__int__eq__numeral__iff,axiom,
% 5.25/5.52 ! [Z: int,N: num] :
% 5.25/5.52 ( ( ( ring_1_of_int_rat @ Z )
% 5.25/5.52 = ( numeral_numeral_rat @ N ) )
% 5.25/5.52 = ( Z
% 5.25/5.52 = ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_eq_numeral_iff
% 5.25/5.52 thf(fact_5120_of__int__eq__numeral__iff,axiom,
% 5.25/5.52 ! [Z: int,N: num] :
% 5.25/5.52 ( ( ( ring_1_of_int_int @ Z )
% 5.25/5.52 = ( numeral_numeral_int @ N ) )
% 5.25/5.52 = ( Z
% 5.25/5.52 = ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_eq_numeral_iff
% 5.25/5.52 thf(fact_5121_of__int__less__iff,axiom,
% 5.25/5.52 ! [W: int,Z: int] :
% 5.25/5.52 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.25/5.52 = ( ord_less_int @ W @ Z ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_less_iff
% 5.25/5.52 thf(fact_5122_of__int__less__iff,axiom,
% 5.25/5.52 ! [W: int,Z: int] :
% 5.25/5.52 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.25/5.52 = ( ord_less_int @ W @ Z ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_less_iff
% 5.25/5.52 thf(fact_5123_of__int__less__iff,axiom,
% 5.25/5.52 ! [W: int,Z: int] :
% 5.25/5.52 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.25/5.52 = ( ord_less_int @ W @ Z ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_less_iff
% 5.25/5.52 thf(fact_5124_of__int__1,axiom,
% 5.25/5.52 ( ( ring_17405671764205052669omplex @ one_one_int )
% 5.25/5.52 = one_one_complex ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_1
% 5.25/5.52 thf(fact_5125_of__int__1,axiom,
% 5.25/5.52 ( ( ring_1_of_int_int @ one_one_int )
% 5.25/5.52 = one_one_int ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_1
% 5.25/5.52 thf(fact_5126_of__int__1,axiom,
% 5.25/5.52 ( ( ring_1_of_int_real @ one_one_int )
% 5.25/5.52 = one_one_real ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_1
% 5.25/5.52 thf(fact_5127_of__int__1,axiom,
% 5.25/5.52 ( ( ring_1_of_int_rat @ one_one_int )
% 5.25/5.52 = one_one_rat ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_1
% 5.25/5.52 thf(fact_5128_of__int__eq__1__iff,axiom,
% 5.25/5.52 ! [Z: int] :
% 5.25/5.52 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.25/5.52 = one_one_complex )
% 5.25/5.52 = ( Z = one_one_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_eq_1_iff
% 5.25/5.52 thf(fact_5129_of__int__eq__1__iff,axiom,
% 5.25/5.52 ! [Z: int] :
% 5.25/5.52 ( ( ( ring_1_of_int_int @ Z )
% 5.25/5.52 = one_one_int )
% 5.25/5.52 = ( Z = one_one_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_eq_1_iff
% 5.25/5.52 thf(fact_5130_of__int__eq__1__iff,axiom,
% 5.25/5.52 ! [Z: int] :
% 5.25/5.52 ( ( ( ring_1_of_int_real @ Z )
% 5.25/5.52 = one_one_real )
% 5.25/5.52 = ( Z = one_one_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_eq_1_iff
% 5.25/5.52 thf(fact_5131_of__int__eq__1__iff,axiom,
% 5.25/5.52 ! [Z: int] :
% 5.25/5.52 ( ( ( ring_1_of_int_rat @ Z )
% 5.25/5.52 = one_one_rat )
% 5.25/5.52 = ( Z = one_one_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_eq_1_iff
% 5.25/5.52 thf(fact_5132_of__int__mult,axiom,
% 5.25/5.52 ! [W: int,Z: int] :
% 5.25/5.52 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 5.25/5.52 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_mult
% 5.25/5.52 thf(fact_5133_of__int__mult,axiom,
% 5.25/5.52 ! [W: int,Z: int] :
% 5.25/5.52 ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 5.25/5.52 = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_mult
% 5.25/5.52 thf(fact_5134_of__int__mult,axiom,
% 5.25/5.52 ! [W: int,Z: int] :
% 5.25/5.52 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 5.25/5.52 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_mult
% 5.25/5.52 thf(fact_5135_of__int__add,axiom,
% 5.25/5.52 ! [W: int,Z: int] :
% 5.25/5.52 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 5.25/5.52 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_add
% 5.25/5.52 thf(fact_5136_of__int__add,axiom,
% 5.25/5.52 ! [W: int,Z: int] :
% 5.25/5.52 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 5.25/5.52 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_add
% 5.25/5.52 thf(fact_5137_of__int__add,axiom,
% 5.25/5.52 ! [W: int,Z: int] :
% 5.25/5.52 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 5.25/5.52 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_add
% 5.25/5.52 thf(fact_5138_of__int__power,axiom,
% 5.25/5.52 ! [Z: int,N: nat] :
% 5.25/5.52 ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N ) )
% 5.25/5.52 = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_power
% 5.25/5.52 thf(fact_5139_of__int__power,axiom,
% 5.25/5.52 ! [Z: int,N: nat] :
% 5.25/5.52 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 5.25/5.52 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_power
% 5.25/5.52 thf(fact_5140_of__int__power,axiom,
% 5.25/5.52 ! [Z: int,N: nat] :
% 5.25/5.52 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 5.25/5.52 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_power
% 5.25/5.52 thf(fact_5141_of__int__power,axiom,
% 5.25/5.52 ! [Z: int,N: nat] :
% 5.25/5.52 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 5.25/5.52 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_power
% 5.25/5.52 thf(fact_5142_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.25/5.52 ! [B: int,W: nat,X3: int] :
% 5.25/5.52 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 5.25/5.52 = ( ring_1_of_int_rat @ X3 ) )
% 5.25/5.52 = ( ( power_power_int @ B @ W )
% 5.25/5.52 = X3 ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_eq_of_int_power_cancel_iff
% 5.25/5.52 thf(fact_5143_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.25/5.52 ! [B: int,W: nat,X3: int] :
% 5.25/5.52 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 5.25/5.52 = ( ring_1_of_int_real @ X3 ) )
% 5.25/5.52 = ( ( power_power_int @ B @ W )
% 5.25/5.52 = X3 ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_eq_of_int_power_cancel_iff
% 5.25/5.52 thf(fact_5144_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.25/5.52 ! [B: int,W: nat,X3: int] :
% 5.25/5.52 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 5.25/5.52 = ( ring_1_of_int_int @ X3 ) )
% 5.25/5.52 = ( ( power_power_int @ B @ W )
% 5.25/5.52 = X3 ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_eq_of_int_power_cancel_iff
% 5.25/5.52 thf(fact_5145_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.25/5.52 ! [B: int,W: nat,X3: int] :
% 5.25/5.52 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 5.25/5.52 = ( ring_17405671764205052669omplex @ X3 ) )
% 5.25/5.52 = ( ( power_power_int @ B @ W )
% 5.25/5.52 = X3 ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_eq_of_int_power_cancel_iff
% 5.25/5.52 thf(fact_5146_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.25/5.52 ! [X3: int,B: int,W: nat] :
% 5.25/5.52 ( ( ( ring_1_of_int_rat @ X3 )
% 5.25/5.52 = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.25/5.52 = ( X3
% 5.25/5.52 = ( power_power_int @ B @ W ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_power_eq_of_int_cancel_iff
% 5.25/5.52 thf(fact_5147_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.25/5.52 ! [X3: int,B: int,W: nat] :
% 5.25/5.52 ( ( ( ring_1_of_int_real @ X3 )
% 5.25/5.52 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.25/5.52 = ( X3
% 5.25/5.52 = ( power_power_int @ B @ W ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_power_eq_of_int_cancel_iff
% 5.25/5.52 thf(fact_5148_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.25/5.52 ! [X3: int,B: int,W: nat] :
% 5.25/5.52 ( ( ( ring_1_of_int_int @ X3 )
% 5.25/5.52 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.25/5.52 = ( X3
% 5.25/5.52 = ( power_power_int @ B @ W ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_power_eq_of_int_cancel_iff
% 5.25/5.52 thf(fact_5149_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.25/5.52 ! [X3: int,B: int,W: nat] :
% 5.25/5.52 ( ( ( ring_17405671764205052669omplex @ X3 )
% 5.25/5.52 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 5.25/5.52 = ( X3
% 5.25/5.52 = ( power_power_int @ B @ W ) ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_power_eq_of_int_cancel_iff
% 5.25/5.52 thf(fact_5150_of__int__0__le__iff,axiom,
% 5.25/5.52 ! [Z: int] :
% 5.25/5.52 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.25/5.52 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_0_le_iff
% 5.25/5.52 thf(fact_5151_of__int__0__le__iff,axiom,
% 5.25/5.52 ! [Z: int] :
% 5.25/5.52 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.25/5.52 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_0_le_iff
% 5.25/5.52 thf(fact_5152_of__int__0__le__iff,axiom,
% 5.25/5.52 ! [Z: int] :
% 5.25/5.52 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.25/5.52 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_0_le_iff
% 5.25/5.52 thf(fact_5153_of__int__le__0__iff,axiom,
% 5.25/5.52 ! [Z: int] :
% 5.25/5.52 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.25/5.52 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_le_0_iff
% 5.25/5.52 thf(fact_5154_of__int__le__0__iff,axiom,
% 5.25/5.52 ! [Z: int] :
% 5.25/5.52 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.25/5.52 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_le_0_iff
% 5.25/5.52 thf(fact_5155_of__int__le__0__iff,axiom,
% 5.25/5.52 ! [Z: int] :
% 5.25/5.52 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.25/5.52 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.25/5.52
% 5.25/5.52 % of_int_le_0_iff
% 5.25/5.52 thf(fact_5156_of__int__less__0__iff,axiom,
% 5.25/5.52 ! [Z: int] :
% 5.25/5.52 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.25/5.53 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_0_iff
% 5.25/5.53 thf(fact_5157_of__int__less__0__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.25/5.53 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_0_iff
% 5.25/5.53 thf(fact_5158_of__int__less__0__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.25/5.53 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_0_iff
% 5.25/5.53 thf(fact_5159_of__int__0__less__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.25/5.53 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_0_less_iff
% 5.25/5.53 thf(fact_5160_of__int__0__less__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.25/5.53 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_0_less_iff
% 5.25/5.53 thf(fact_5161_of__int__0__less__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.25/5.53 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_0_less_iff
% 5.25/5.53 thf(fact_5162_of__int__le__numeral__iff,axiom,
% 5.25/5.53 ! [Z: int,N: num] :
% 5.25/5.53 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.25/5.53 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_numeral_iff
% 5.25/5.53 thf(fact_5163_of__int__le__numeral__iff,axiom,
% 5.25/5.53 ! [Z: int,N: num] :
% 5.25/5.53 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.25/5.53 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_numeral_iff
% 5.25/5.53 thf(fact_5164_of__int__le__numeral__iff,axiom,
% 5.25/5.53 ! [Z: int,N: num] :
% 5.25/5.53 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.53 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_numeral_iff
% 5.25/5.53 thf(fact_5165_of__int__numeral__le__iff,axiom,
% 5.25/5.53 ! [N: num,Z: int] :
% 5.25/5.53 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.25/5.53 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_numeral_le_iff
% 5.25/5.53 thf(fact_5166_of__int__numeral__le__iff,axiom,
% 5.25/5.53 ! [N: num,Z: int] :
% 5.25/5.53 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.25/5.53 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_numeral_le_iff
% 5.25/5.53 thf(fact_5167_of__int__numeral__le__iff,axiom,
% 5.25/5.53 ! [N: num,Z: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.25/5.53 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_numeral_le_iff
% 5.25/5.53 thf(fact_5168_of__int__less__numeral__iff,axiom,
% 5.25/5.53 ! [Z: int,N: num] :
% 5.25/5.53 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.25/5.53 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_numeral_iff
% 5.25/5.53 thf(fact_5169_of__int__less__numeral__iff,axiom,
% 5.25/5.53 ! [Z: int,N: num] :
% 5.25/5.53 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.25/5.53 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_numeral_iff
% 5.25/5.53 thf(fact_5170_of__int__less__numeral__iff,axiom,
% 5.25/5.53 ! [Z: int,N: num] :
% 5.25/5.53 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.53 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_numeral_iff
% 5.25/5.53 thf(fact_5171_of__int__numeral__less__iff,axiom,
% 5.25/5.53 ! [N: num,Z: int] :
% 5.25/5.53 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.25/5.53 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_numeral_less_iff
% 5.25/5.53 thf(fact_5172_of__int__numeral__less__iff,axiom,
% 5.25/5.53 ! [N: num,Z: int] :
% 5.25/5.53 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.25/5.53 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_numeral_less_iff
% 5.25/5.53 thf(fact_5173_of__int__numeral__less__iff,axiom,
% 5.25/5.53 ! [N: num,Z: int] :
% 5.25/5.53 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.25/5.53 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_numeral_less_iff
% 5.25/5.53 thf(fact_5174_of__int__1__le__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.25/5.53 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_1_le_iff
% 5.25/5.53 thf(fact_5175_of__int__1__le__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.25/5.53 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_1_le_iff
% 5.25/5.53 thf(fact_5176_of__int__1__le__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.25/5.53 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_1_le_iff
% 5.25/5.53 thf(fact_5177_of__int__le__1__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.25/5.53 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_1_iff
% 5.25/5.53 thf(fact_5178_of__int__le__1__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.25/5.53 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_1_iff
% 5.25/5.53 thf(fact_5179_of__int__le__1__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.25/5.53 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_1_iff
% 5.25/5.53 thf(fact_5180_of__int__1__less__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.25/5.53 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_1_less_iff
% 5.25/5.53 thf(fact_5181_of__int__1__less__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.25/5.53 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_1_less_iff
% 5.25/5.53 thf(fact_5182_of__int__1__less__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.25/5.53 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_1_less_iff
% 5.25/5.53 thf(fact_5183_of__int__less__1__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.25/5.53 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_1_iff
% 5.25/5.53 thf(fact_5184_of__int__less__1__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.25/5.53 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_1_iff
% 5.25/5.53 thf(fact_5185_of__int__less__1__iff,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.25/5.53 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_1_iff
% 5.25/5.53 thf(fact_5186_of__int__le__of__int__power__cancel__iff,axiom,
% 5.25/5.53 ! [B: int,W: nat,X3: int] :
% 5.25/5.53 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X3 ) )
% 5.25/5.53 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_of_int_power_cancel_iff
% 5.25/5.53 thf(fact_5187_of__int__le__of__int__power__cancel__iff,axiom,
% 5.25/5.53 ! [B: int,W: nat,X3: int] :
% 5.25/5.53 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X3 ) )
% 5.25/5.53 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_of_int_power_cancel_iff
% 5.25/5.53 thf(fact_5188_of__int__le__of__int__power__cancel__iff,axiom,
% 5.25/5.53 ! [B: int,W: nat,X3: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X3 ) )
% 5.25/5.53 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_of_int_power_cancel_iff
% 5.25/5.53 thf(fact_5189_of__int__power__le__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: int,B: int,W: nat] :
% 5.25/5.53 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.25/5.53 = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_power_le_of_int_cancel_iff
% 5.25/5.53 thf(fact_5190_of__int__power__le__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: int,B: int,W: nat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.25/5.53 = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_power_le_of_int_cancel_iff
% 5.25/5.53 thf(fact_5191_of__int__power__le__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: int,B: int,W: nat] :
% 5.25/5.53 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X3 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.25/5.53 = ( ord_less_eq_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_power_le_of_int_cancel_iff
% 5.25/5.53 thf(fact_5192_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,Y: int] :
% 5.25/5.53 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N )
% 5.25/5.53 = ( ring_17405671764205052669omplex @ Y ) )
% 5.25/5.53 = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % numeral_power_eq_of_int_cancel_iff
% 5.25/5.53 thf(fact_5193_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,Y: int] :
% 5.25/5.53 ( ( ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N )
% 5.25/5.53 = ( ring_1_of_int_real @ Y ) )
% 5.25/5.53 = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % numeral_power_eq_of_int_cancel_iff
% 5.25/5.53 thf(fact_5194_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,Y: int] :
% 5.25/5.53 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N )
% 5.25/5.53 = ( ring_1_of_int_rat @ Y ) )
% 5.25/5.53 = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % numeral_power_eq_of_int_cancel_iff
% 5.25/5.53 thf(fact_5195_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,Y: int] :
% 5.25/5.53 ( ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 5.25/5.53 = ( ring_1_of_int_int @ Y ) )
% 5.25/5.53 = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % numeral_power_eq_of_int_cancel_iff
% 5.25/5.53 thf(fact_5196_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [Y: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.25/5.53 = ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N ) )
% 5.25/5.53 = ( Y
% 5.25/5.53 = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_eq_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5197_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [Y: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ( ring_1_of_int_real @ Y )
% 5.25/5.53 = ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 5.25/5.53 = ( Y
% 5.25/5.53 = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_eq_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5198_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [Y: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ( ring_1_of_int_rat @ Y )
% 5.25/5.53 = ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 5.25/5.53 = ( Y
% 5.25/5.53 = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_eq_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5199_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [Y: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ( ring_1_of_int_int @ Y )
% 5.25/5.53 = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) )
% 5.25/5.53 = ( Y
% 5.25/5.53 = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_eq_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5200_of__int__less__of__int__power__cancel__iff,axiom,
% 5.25/5.53 ! [B: int,W: nat,X3: int] :
% 5.25/5.53 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X3 ) )
% 5.25/5.53 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_of_int_power_cancel_iff
% 5.25/5.53 thf(fact_5201_of__int__less__of__int__power__cancel__iff,axiom,
% 5.25/5.53 ! [B: int,W: nat,X3: int] :
% 5.25/5.53 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X3 ) )
% 5.25/5.53 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_of_int_power_cancel_iff
% 5.25/5.53 thf(fact_5202_of__int__less__of__int__power__cancel__iff,axiom,
% 5.25/5.53 ! [B: int,W: nat,X3: int] :
% 5.25/5.53 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X3 ) )
% 5.25/5.53 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_of_int_power_cancel_iff
% 5.25/5.53 thf(fact_5203_of__int__power__less__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: int,B: int,W: nat] :
% 5.25/5.53 ( ( ord_less_real @ ( ring_1_of_int_real @ X3 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.25/5.53 = ( ord_less_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_power_less_of_int_cancel_iff
% 5.25/5.53 thf(fact_5204_of__int__power__less__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: int,B: int,W: nat] :
% 5.25/5.53 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X3 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.25/5.53 = ( ord_less_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_power_less_of_int_cancel_iff
% 5.25/5.53 thf(fact_5205_of__int__power__less__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: int,B: int,W: nat] :
% 5.25/5.53 ( ( ord_less_int @ ( ring_1_of_int_int @ X3 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.25/5.53 = ( ord_less_int @ X3 @ ( power_power_int @ B @ W ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_power_less_of_int_cancel_iff
% 5.25/5.53 thf(fact_5206_numeral__power__le__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,A: int] :
% 5.25/5.53 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.25/5.53 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % numeral_power_le_of_int_cancel_iff
% 5.25/5.53 thf(fact_5207_numeral__power__le__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,A: int] :
% 5.25/5.53 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.25/5.53 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % numeral_power_le_of_int_cancel_iff
% 5.25/5.53 thf(fact_5208_numeral__power__le__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,A: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.25/5.53 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % numeral_power_le_of_int_cancel_iff
% 5.25/5.53 thf(fact_5209_of__int__le__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [A: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 5.25/5.53 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5210_of__int__le__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [A: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 5.25/5.53 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5211_of__int__le__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [A: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) )
% 5.25/5.53 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5212_numeral__power__less__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,A: int] :
% 5.25/5.53 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.25/5.53 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % numeral_power_less_of_int_cancel_iff
% 5.25/5.53 thf(fact_5213_numeral__power__less__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,A: int] :
% 5.25/5.53 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.25/5.53 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % numeral_power_less_of_int_cancel_iff
% 5.25/5.53 thf(fact_5214_numeral__power__less__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,A: int] :
% 5.25/5.53 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.25/5.53 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % numeral_power_less_of_int_cancel_iff
% 5.25/5.53 thf(fact_5215_of__int__less__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [A: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 5.25/5.53 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5216_of__int__less__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [A: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 5.25/5.53 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5217_of__int__less__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [A: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) )
% 5.25/5.53 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5218_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,Y: int] :
% 5.25/5.53 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 5.25/5.53 = ( ring_1_of_int_int @ Y ) )
% 5.25/5.53 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % neg_numeral_power_eq_of_int_cancel_iff
% 5.25/5.53 thf(fact_5219_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,Y: int] :
% 5.25/5.53 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N )
% 5.25/5.53 = ( ring_1_of_int_real @ Y ) )
% 5.25/5.53 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % neg_numeral_power_eq_of_int_cancel_iff
% 5.25/5.53 thf(fact_5220_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,Y: int] :
% 5.25/5.53 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X3 ) ) @ N )
% 5.25/5.53 = ( ring_17405671764205052669omplex @ Y ) )
% 5.25/5.53 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % neg_numeral_power_eq_of_int_cancel_iff
% 5.25/5.53 thf(fact_5221_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,Y: int] :
% 5.25/5.53 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N )
% 5.25/5.53 = ( ring_18347121197199848620nteger @ Y ) )
% 5.25/5.53 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % neg_numeral_power_eq_of_int_cancel_iff
% 5.25/5.53 thf(fact_5222_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,Y: int] :
% 5.25/5.53 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N )
% 5.25/5.53 = ( ring_1_of_int_rat @ Y ) )
% 5.25/5.53 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % neg_numeral_power_eq_of_int_cancel_iff
% 5.25/5.53 thf(fact_5223_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [Y: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ( ring_1_of_int_int @ Y )
% 5.25/5.53 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) )
% 5.25/5.53 = ( Y
% 5.25/5.53 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_eq_neg_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5224_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [Y: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ( ring_1_of_int_real @ Y )
% 5.25/5.53 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) )
% 5.25/5.53 = ( Y
% 5.25/5.53 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_eq_neg_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5225_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [Y: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.25/5.53 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X3 ) ) @ N ) )
% 5.25/5.53 = ( Y
% 5.25/5.53 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_eq_neg_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5226_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [Y: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ( ring_18347121197199848620nteger @ Y )
% 5.25/5.53 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) )
% 5.25/5.53 = ( Y
% 5.25/5.53 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_eq_neg_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5227_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [Y: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ( ring_1_of_int_rat @ Y )
% 5.25/5.53 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) )
% 5.25/5.53 = ( Y
% 5.25/5.53 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_eq_neg_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5228_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,A: int] :
% 5.25/5.53 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.25/5.53 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % neg_numeral_power_le_of_int_cancel_iff
% 5.25/5.53 thf(fact_5229_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,A: int] :
% 5.25/5.53 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.25/5.53 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % neg_numeral_power_le_of_int_cancel_iff
% 5.25/5.53 thf(fact_5230_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,A: int] :
% 5.25/5.53 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.25/5.53 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % neg_numeral_power_le_of_int_cancel_iff
% 5.25/5.53 thf(fact_5231_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,A: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.25/5.53 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % neg_numeral_power_le_of_int_cancel_iff
% 5.25/5.53 thf(fact_5232_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [A: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) )
% 5.25/5.53 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_neg_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5233_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [A: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) )
% 5.25/5.53 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_neg_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5234_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [A: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) )
% 5.25/5.53 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_neg_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5235_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [A: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) )
% 5.25/5.53 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_le_neg_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5236_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,A: int] :
% 5.25/5.53 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.25/5.53 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % neg_numeral_power_less_of_int_cancel_iff
% 5.25/5.53 thf(fact_5237_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,A: int] :
% 5.25/5.53 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.25/5.53 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % neg_numeral_power_less_of_int_cancel_iff
% 5.25/5.53 thf(fact_5238_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,A: int] :
% 5.25/5.53 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.25/5.53 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % neg_numeral_power_less_of_int_cancel_iff
% 5.25/5.53 thf(fact_5239_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.25/5.53 ! [X3: num,N: nat,A: int] :
% 5.25/5.53 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.25/5.53 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % neg_numeral_power_less_of_int_cancel_iff
% 5.25/5.53 thf(fact_5240_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [A: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) )
% 5.25/5.53 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_neg_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5241_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [A: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X3 ) ) @ N ) )
% 5.25/5.53 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_neg_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5242_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [A: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X3 ) ) @ N ) )
% 5.25/5.53 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_neg_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5243_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.25/5.53 ! [A: int,X3: num,N: nat] :
% 5.25/5.53 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X3 ) ) @ N ) )
% 5.25/5.53 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X3 ) ) @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_less_neg_numeral_power_cancel_iff
% 5.25/5.53 thf(fact_5244_mult__of__int__commute,axiom,
% 5.25/5.53 ! [X3: int,Y: real] :
% 5.25/5.53 ( ( times_times_real @ ( ring_1_of_int_real @ X3 ) @ Y )
% 5.25/5.53 = ( times_times_real @ Y @ ( ring_1_of_int_real @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % mult_of_int_commute
% 5.25/5.53 thf(fact_5245_mult__of__int__commute,axiom,
% 5.25/5.53 ! [X3: int,Y: rat] :
% 5.25/5.53 ( ( times_times_rat @ ( ring_1_of_int_rat @ X3 ) @ Y )
% 5.25/5.53 = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % mult_of_int_commute
% 5.25/5.53 thf(fact_5246_mult__of__int__commute,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( times_times_int @ ( ring_1_of_int_int @ X3 ) @ Y )
% 5.25/5.53 = ( times_times_int @ Y @ ( ring_1_of_int_int @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % mult_of_int_commute
% 5.25/5.53 thf(fact_5247_real__of__int__div4,axiom,
% 5.25/5.53 ! [N: int,X3: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X3 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % real_of_int_div4
% 5.25/5.53 thf(fact_5248_real__of__int__div,axiom,
% 5.25/5.53 ! [D: int,N: int] :
% 5.25/5.53 ( ( dvd_dvd_int @ D @ N )
% 5.25/5.53 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D ) )
% 5.25/5.53 = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % real_of_int_div
% 5.25/5.53 thf(fact_5249_nle__le,axiom,
% 5.25/5.53 ! [A: rat,B: rat] :
% 5.25/5.53 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 5.25/5.53 = ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.53 & ( B != A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % nle_le
% 5.25/5.53 thf(fact_5250_nle__le,axiom,
% 5.25/5.53 ! [A: num,B: num] :
% 5.25/5.53 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 5.25/5.53 = ( ( ord_less_eq_num @ B @ A )
% 5.25/5.53 & ( B != A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % nle_le
% 5.25/5.53 thf(fact_5251_nle__le,axiom,
% 5.25/5.53 ! [A: nat,B: nat] :
% 5.25/5.53 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 5.25/5.53 = ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.53 & ( B != A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % nle_le
% 5.25/5.53 thf(fact_5252_nle__le,axiom,
% 5.25/5.53 ! [A: int,B: int] :
% 5.25/5.53 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 5.25/5.53 = ( ( ord_less_eq_int @ B @ A )
% 5.25/5.53 & ( B != A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % nle_le
% 5.25/5.53 thf(fact_5253_le__cases3,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat,Z: rat] :
% 5.25/5.53 ( ( ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 5.25/5.53 => ( ( ( ord_less_eq_rat @ Y @ X3 )
% 5.25/5.53 => ~ ( ord_less_eq_rat @ X3 @ Z ) )
% 5.25/5.53 => ( ( ( ord_less_eq_rat @ X3 @ Z )
% 5.25/5.53 => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 5.25/5.53 => ( ( ( ord_less_eq_rat @ Z @ Y )
% 5.25/5.53 => ~ ( ord_less_eq_rat @ Y @ X3 ) )
% 5.25/5.53 => ( ( ( ord_less_eq_rat @ Y @ Z )
% 5.25/5.53 => ~ ( ord_less_eq_rat @ Z @ X3 ) )
% 5.25/5.53 => ~ ( ( ord_less_eq_rat @ Z @ X3 )
% 5.25/5.53 => ~ ( ord_less_eq_rat @ X3 @ Y ) ) ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % le_cases3
% 5.25/5.53 thf(fact_5254_le__cases3,axiom,
% 5.25/5.53 ! [X3: num,Y: num,Z: num] :
% 5.25/5.53 ( ( ( ord_less_eq_num @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_eq_num @ Y @ Z ) )
% 5.25/5.53 => ( ( ( ord_less_eq_num @ Y @ X3 )
% 5.25/5.53 => ~ ( ord_less_eq_num @ X3 @ Z ) )
% 5.25/5.53 => ( ( ( ord_less_eq_num @ X3 @ Z )
% 5.25/5.53 => ~ ( ord_less_eq_num @ Z @ Y ) )
% 5.25/5.53 => ( ( ( ord_less_eq_num @ Z @ Y )
% 5.25/5.53 => ~ ( ord_less_eq_num @ Y @ X3 ) )
% 5.25/5.53 => ( ( ( ord_less_eq_num @ Y @ Z )
% 5.25/5.53 => ~ ( ord_less_eq_num @ Z @ X3 ) )
% 5.25/5.53 => ~ ( ( ord_less_eq_num @ Z @ X3 )
% 5.25/5.53 => ~ ( ord_less_eq_num @ X3 @ Y ) ) ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % le_cases3
% 5.25/5.53 thf(fact_5255_le__cases3,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat,Z: nat] :
% 5.25/5.53 ( ( ( ord_less_eq_nat @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 5.25/5.53 => ( ( ( ord_less_eq_nat @ Y @ X3 )
% 5.25/5.53 => ~ ( ord_less_eq_nat @ X3 @ Z ) )
% 5.25/5.53 => ( ( ( ord_less_eq_nat @ X3 @ Z )
% 5.25/5.53 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 5.25/5.53 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 5.25/5.53 => ~ ( ord_less_eq_nat @ Y @ X3 ) )
% 5.25/5.53 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 5.25/5.53 => ~ ( ord_less_eq_nat @ Z @ X3 ) )
% 5.25/5.53 => ~ ( ( ord_less_eq_nat @ Z @ X3 )
% 5.25/5.53 => ~ ( ord_less_eq_nat @ X3 @ Y ) ) ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % le_cases3
% 5.25/5.53 thf(fact_5256_le__cases3,axiom,
% 5.25/5.53 ! [X3: int,Y: int,Z: int] :
% 5.25/5.53 ( ( ( ord_less_eq_int @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_eq_int @ Y @ Z ) )
% 5.25/5.53 => ( ( ( ord_less_eq_int @ Y @ X3 )
% 5.25/5.53 => ~ ( ord_less_eq_int @ X3 @ Z ) )
% 5.25/5.53 => ( ( ( ord_less_eq_int @ X3 @ Z )
% 5.25/5.53 => ~ ( ord_less_eq_int @ Z @ Y ) )
% 5.25/5.53 => ( ( ( ord_less_eq_int @ Z @ Y )
% 5.25/5.53 => ~ ( ord_less_eq_int @ Y @ X3 ) )
% 5.25/5.53 => ( ( ( ord_less_eq_int @ Y @ Z )
% 5.25/5.53 => ~ ( ord_less_eq_int @ Z @ X3 ) )
% 5.25/5.53 => ~ ( ( ord_less_eq_int @ Z @ X3 )
% 5.25/5.53 => ~ ( ord_less_eq_int @ X3 @ Y ) ) ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % le_cases3
% 5.25/5.53 thf(fact_5257_order__class_Oorder__eq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: set_int,Z3: set_int] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [X2: set_int,Y6: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ X2 @ Y6 )
% 5.25/5.53 & ( ord_less_eq_set_int @ Y6 @ X2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_class.order_eq_iff
% 5.25/5.53 thf(fact_5258_order__class_Oorder__eq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: rat,Z3: rat] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [X2: rat,Y6: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X2 @ Y6 )
% 5.25/5.53 & ( ord_less_eq_rat @ Y6 @ X2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_class.order_eq_iff
% 5.25/5.53 thf(fact_5259_order__class_Oorder__eq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: num,Z3: num] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [X2: num,Y6: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X2 @ Y6 )
% 5.25/5.53 & ( ord_less_eq_num @ Y6 @ X2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_class.order_eq_iff
% 5.25/5.53 thf(fact_5260_order__class_Oorder__eq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: nat,Z3: nat] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [X2: nat,Y6: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X2 @ Y6 )
% 5.25/5.53 & ( ord_less_eq_nat @ Y6 @ X2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_class.order_eq_iff
% 5.25/5.53 thf(fact_5261_order__class_Oorder__eq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: int,Z3: int] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [X2: int,Y6: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ X2 @ Y6 )
% 5.25/5.53 & ( ord_less_eq_int @ Y6 @ X2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_class.order_eq_iff
% 5.25/5.53 thf(fact_5262_ord__eq__le__trans,axiom,
% 5.25/5.53 ! [A: set_int,B: set_int,C: set_int] :
% 5.25/5.53 ( ( A = B )
% 5.25/5.53 => ( ( ord_less_eq_set_int @ B @ C )
% 5.25/5.53 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_trans
% 5.25/5.53 thf(fact_5263_ord__eq__le__trans,axiom,
% 5.25/5.53 ! [A: rat,B: rat,C: rat] :
% 5.25/5.53 ( ( A = B )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_trans
% 5.25/5.53 thf(fact_5264_ord__eq__le__trans,axiom,
% 5.25/5.53 ! [A: num,B: num,C: num] :
% 5.25/5.53 ( ( A = B )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_trans
% 5.25/5.53 thf(fact_5265_ord__eq__le__trans,axiom,
% 5.25/5.53 ! [A: nat,B: nat,C: nat] :
% 5.25/5.53 ( ( A = B )
% 5.25/5.53 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.53 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_trans
% 5.25/5.53 thf(fact_5266_ord__eq__le__trans,axiom,
% 5.25/5.53 ! [A: int,B: int,C: int] :
% 5.25/5.53 ( ( A = B )
% 5.25/5.53 => ( ( ord_less_eq_int @ B @ C )
% 5.25/5.53 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_trans
% 5.25/5.53 thf(fact_5267_ord__le__eq__trans,axiom,
% 5.25/5.53 ! [A: set_int,B: set_int,C: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ A @ B )
% 5.25/5.53 => ( ( B = C )
% 5.25/5.53 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_trans
% 5.25/5.53 thf(fact_5268_ord__le__eq__trans,axiom,
% 5.25/5.53 ! [A: rat,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( B = C )
% 5.25/5.53 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_trans
% 5.25/5.53 thf(fact_5269_ord__le__eq__trans,axiom,
% 5.25/5.53 ! [A: num,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( B = C )
% 5.25/5.53 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_trans
% 5.25/5.53 thf(fact_5270_ord__le__eq__trans,axiom,
% 5.25/5.53 ! [A: nat,B: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.53 => ( ( B = C )
% 5.25/5.53 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_trans
% 5.25/5.53 thf(fact_5271_ord__le__eq__trans,axiom,
% 5.25/5.53 ! [A: int,B: int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.53 => ( ( B = C )
% 5.25/5.53 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_trans
% 5.25/5.53 thf(fact_5272_order__antisym,axiom,
% 5.25/5.53 ! [X3: set_int,Y: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_set_int @ Y @ X3 )
% 5.25/5.53 => ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_antisym
% 5.25/5.53 thf(fact_5273_order__antisym,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_rat @ Y @ X3 )
% 5.25/5.53 => ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_antisym
% 5.25/5.53 thf(fact_5274_order__antisym,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_num @ Y @ X3 )
% 5.25/5.53 => ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_antisym
% 5.25/5.53 thf(fact_5275_order__antisym,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_nat @ Y @ X3 )
% 5.25/5.53 => ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_antisym
% 5.25/5.53 thf(fact_5276_order__antisym,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_int @ Y @ X3 )
% 5.25/5.53 => ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_antisym
% 5.25/5.53 thf(fact_5277_order_Otrans,axiom,
% 5.25/5.53 ! [A: set_int,B: set_int,C: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_set_int @ B @ C )
% 5.25/5.53 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.trans
% 5.25/5.53 thf(fact_5278_order_Otrans,axiom,
% 5.25/5.53 ! [A: rat,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.trans
% 5.25/5.53 thf(fact_5279_order_Otrans,axiom,
% 5.25/5.53 ! [A: num,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.trans
% 5.25/5.53 thf(fact_5280_order_Otrans,axiom,
% 5.25/5.53 ! [A: nat,B: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.53 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.trans
% 5.25/5.53 thf(fact_5281_order_Otrans,axiom,
% 5.25/5.53 ! [A: int,B: int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_int @ B @ C )
% 5.25/5.53 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.trans
% 5.25/5.53 thf(fact_5282_order__trans,axiom,
% 5.25/5.53 ! [X3: set_int,Y: set_int,Z: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_set_int @ Y @ Z )
% 5.25/5.53 => ( ord_less_eq_set_int @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_trans
% 5.25/5.53 thf(fact_5283_order__trans,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat,Z: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_rat @ Y @ Z )
% 5.25/5.53 => ( ord_less_eq_rat @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_trans
% 5.25/5.53 thf(fact_5284_order__trans,axiom,
% 5.25/5.53 ! [X3: num,Y: num,Z: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_num @ Y @ Z )
% 5.25/5.53 => ( ord_less_eq_num @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_trans
% 5.25/5.53 thf(fact_5285_order__trans,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat,Z: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.25/5.53 => ( ord_less_eq_nat @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_trans
% 5.25/5.53 thf(fact_5286_order__trans,axiom,
% 5.25/5.53 ! [X3: int,Y: int,Z: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_int @ Y @ Z )
% 5.25/5.53 => ( ord_less_eq_int @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_trans
% 5.25/5.53 thf(fact_5287_linorder__wlog,axiom,
% 5.25/5.53 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.25/5.53 ( ! [A5: rat,B5: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A5 @ B5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( ! [A5: rat,B5: rat] :
% 5.25/5.53 ( ( P @ B5 @ A5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( P @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_wlog
% 5.25/5.53 thf(fact_5288_linorder__wlog,axiom,
% 5.25/5.53 ! [P: num > num > $o,A: num,B: num] :
% 5.25/5.53 ( ! [A5: num,B5: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ A5 @ B5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( ! [A5: num,B5: num] :
% 5.25/5.53 ( ( P @ B5 @ A5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( P @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_wlog
% 5.25/5.53 thf(fact_5289_linorder__wlog,axiom,
% 5.25/5.53 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.25/5.53 ( ! [A5: nat,B5: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A5 @ B5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( ! [A5: nat,B5: nat] :
% 5.25/5.53 ( ( P @ B5 @ A5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( P @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_wlog
% 5.25/5.53 thf(fact_5290_linorder__wlog,axiom,
% 5.25/5.53 ! [P: int > int > $o,A: int,B: int] :
% 5.25/5.53 ( ! [A5: int,B5: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ A5 @ B5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( ! [A5: int,B5: int] :
% 5.25/5.53 ( ( P @ B5 @ A5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( P @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_wlog
% 5.25/5.53 thf(fact_5291_dual__order_Oeq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: set_int,Z3: set_int] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [A3: set_int,B2: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.25/5.53 & ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.eq_iff
% 5.25/5.53 thf(fact_5292_dual__order_Oeq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: rat,Z3: rat] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [A3: rat,B2: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ B2 @ A3 )
% 5.25/5.53 & ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.eq_iff
% 5.25/5.53 thf(fact_5293_dual__order_Oeq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: num,Z3: num] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [A3: num,B2: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ B2 @ A3 )
% 5.25/5.53 & ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.eq_iff
% 5.25/5.53 thf(fact_5294_dual__order_Oeq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: nat,Z3: nat] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ B2 @ A3 )
% 5.25/5.53 & ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.eq_iff
% 5.25/5.53 thf(fact_5295_dual__order_Oeq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: int,Z3: int] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [A3: int,B2: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ B2 @ A3 )
% 5.25/5.53 & ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.eq_iff
% 5.25/5.53 thf(fact_5296_dual__order_Oantisym,axiom,
% 5.25/5.53 ! [B: set_int,A: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_set_int @ A @ B )
% 5.25/5.53 => ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.antisym
% 5.25/5.53 thf(fact_5297_dual__order_Oantisym,axiom,
% 5.25/5.53 ! [B: rat,A: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.antisym
% 5.25/5.53 thf(fact_5298_dual__order_Oantisym,axiom,
% 5.25/5.53 ! [B: num,A: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.antisym
% 5.25/5.53 thf(fact_5299_dual__order_Oantisym,axiom,
% 5.25/5.53 ! [B: nat,A: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.53 => ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.antisym
% 5.25/5.53 thf(fact_5300_dual__order_Oantisym,axiom,
% 5.25/5.53 ! [B: int,A: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_int @ A @ B )
% 5.25/5.53 => ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.antisym
% 5.25/5.53 thf(fact_5301_dual__order_Otrans,axiom,
% 5.25/5.53 ! [B: set_int,A: set_int,C: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_set_int @ C @ B )
% 5.25/5.53 => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.trans
% 5.25/5.53 thf(fact_5302_dual__order_Otrans,axiom,
% 5.25/5.53 ! [B: rat,A: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_rat @ C @ B )
% 5.25/5.53 => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.trans
% 5.25/5.53 thf(fact_5303_dual__order_Otrans,axiom,
% 5.25/5.53 ! [B: num,A: num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_num @ C @ B )
% 5.25/5.53 => ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.trans
% 5.25/5.53 thf(fact_5304_dual__order_Otrans,axiom,
% 5.25/5.53 ! [B: nat,A: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_nat @ C @ B )
% 5.25/5.53 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.trans
% 5.25/5.53 thf(fact_5305_dual__order_Otrans,axiom,
% 5.25/5.53 ! [B: int,A: int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_int @ C @ B )
% 5.25/5.53 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.trans
% 5.25/5.53 thf(fact_5306_antisym,axiom,
% 5.25/5.53 ! [A: set_int,B: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_set_int @ B @ A )
% 5.25/5.53 => ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym
% 5.25/5.53 thf(fact_5307_antisym,axiom,
% 5.25/5.53 ! [A: rat,B: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.53 => ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym
% 5.25/5.53 thf(fact_5308_antisym,axiom,
% 5.25/5.53 ! [A: num,B: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ A )
% 5.25/5.53 => ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym
% 5.25/5.53 thf(fact_5309_antisym,axiom,
% 5.25/5.53 ! [A: nat,B: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.53 => ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym
% 5.25/5.53 thf(fact_5310_antisym,axiom,
% 5.25/5.53 ! [A: int,B: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_int @ B @ A )
% 5.25/5.53 => ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym
% 5.25/5.53 thf(fact_5311_Orderings_Oorder__eq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: set_int,Z3: set_int] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [A3: set_int,B2: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.25/5.53 & ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % Orderings.order_eq_iff
% 5.25/5.53 thf(fact_5312_Orderings_Oorder__eq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: rat,Z3: rat] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [A3: rat,B2: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.25/5.53 & ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % Orderings.order_eq_iff
% 5.25/5.53 thf(fact_5313_Orderings_Oorder__eq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: num,Z3: num] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [A3: num,B2: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.25/5.53 & ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % Orderings.order_eq_iff
% 5.25/5.53 thf(fact_5314_Orderings_Oorder__eq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: nat,Z3: nat] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.25/5.53 & ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % Orderings.order_eq_iff
% 5.25/5.53 thf(fact_5315_Orderings_Oorder__eq__iff,axiom,
% 5.25/5.53 ( ( ^ [Y5: int,Z3: int] : ( Y5 = Z3 ) )
% 5.25/5.53 = ( ^ [A3: int,B2: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.25/5.53 & ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % Orderings.order_eq_iff
% 5.25/5.53 thf(fact_5316_order__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst1
% 5.25/5.53 thf(fact_5317_order__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst1
% 5.25/5.53 thf(fact_5318_order__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.53 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst1
% 5.25/5.53 thf(fact_5319_order__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_int @ B @ C )
% 5.25/5.53 => ( ! [X5: int,Y3: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst1
% 5.25/5.53 thf(fact_5320_order__subst1,axiom,
% 5.25/5.53 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst1
% 5.25/5.53 thf(fact_5321_order__subst1,axiom,
% 5.25/5.53 ! [A: num,F: num > num,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst1
% 5.25/5.53 thf(fact_5322_order__subst1,axiom,
% 5.25/5.53 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.53 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst1
% 5.25/5.53 thf(fact_5323_order__subst1,axiom,
% 5.25/5.53 ! [A: num,F: int > num,B: int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_int @ B @ C )
% 5.25/5.53 => ( ! [X5: int,Y3: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst1
% 5.25/5.53 thf(fact_5324_order__subst1,axiom,
% 5.25/5.53 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst1
% 5.25/5.53 thf(fact_5325_order__subst1,axiom,
% 5.25/5.53 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst1
% 5.25/5.53 thf(fact_5326_order__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst2
% 5.25/5.53 thf(fact_5327_order__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst2
% 5.25/5.53 thf(fact_5328_order__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst2
% 5.25/5.53 thf(fact_5329_order__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst2
% 5.25/5.53 thf(fact_5330_order__subst2,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst2
% 5.25/5.53 thf(fact_5331_order__subst2,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst2
% 5.25/5.53 thf(fact_5332_order__subst2,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst2
% 5.25/5.53 thf(fact_5333_order__subst2,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst2
% 5.25/5.53 thf(fact_5334_order__subst2,axiom,
% 5.25/5.53 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst2
% 5.25/5.53 thf(fact_5335_order__subst2,axiom,
% 5.25/5.53 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_subst2
% 5.25/5.53 thf(fact_5336_order__eq__refl,axiom,
% 5.25/5.53 ! [X3: set_int,Y: set_int] :
% 5.25/5.53 ( ( X3 = Y )
% 5.25/5.53 => ( ord_less_eq_set_int @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_eq_refl
% 5.25/5.53 thf(fact_5337_order__eq__refl,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( X3 = Y )
% 5.25/5.53 => ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_eq_refl
% 5.25/5.53 thf(fact_5338_order__eq__refl,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( X3 = Y )
% 5.25/5.53 => ( ord_less_eq_num @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_eq_refl
% 5.25/5.53 thf(fact_5339_order__eq__refl,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( X3 = Y )
% 5.25/5.53 => ( ord_less_eq_nat @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_eq_refl
% 5.25/5.53 thf(fact_5340_order__eq__refl,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( X3 = Y )
% 5.25/5.53 => ( ord_less_eq_int @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_eq_refl
% 5.25/5.53 thf(fact_5341_linorder__linear,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.53 | ( ord_less_eq_rat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_linear
% 5.25/5.53 thf(fact_5342_linorder__linear,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X3 @ Y )
% 5.25/5.53 | ( ord_less_eq_num @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_linear
% 5.25/5.53 thf(fact_5343_linorder__linear,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X3 @ Y )
% 5.25/5.53 | ( ord_less_eq_nat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_linear
% 5.25/5.53 thf(fact_5344_linorder__linear,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ X3 @ Y )
% 5.25/5.53 | ( ord_less_eq_int @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_linear
% 5.25/5.53 thf(fact_5345_ord__eq__le__subst,axiom,
% 5.25/5.53 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_subst
% 5.25/5.53 thf(fact_5346_ord__eq__le__subst,axiom,
% 5.25/5.53 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_subst
% 5.25/5.53 thf(fact_5347_ord__eq__le__subst,axiom,
% 5.25/5.53 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_subst
% 5.25/5.53 thf(fact_5348_ord__eq__le__subst,axiom,
% 5.25/5.53 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_subst
% 5.25/5.53 thf(fact_5349_ord__eq__le__subst,axiom,
% 5.25/5.53 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_subst
% 5.25/5.53 thf(fact_5350_ord__eq__le__subst,axiom,
% 5.25/5.53 ! [A: num,F: num > num,B: num,C: num] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_subst
% 5.25/5.53 thf(fact_5351_ord__eq__le__subst,axiom,
% 5.25/5.53 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_subst
% 5.25/5.53 thf(fact_5352_ord__eq__le__subst,axiom,
% 5.25/5.53 ! [A: int,F: num > int,B: num,C: num] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_subst
% 5.25/5.53 thf(fact_5353_ord__eq__le__subst,axiom,
% 5.25/5.53 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.53 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_subst
% 5.25/5.53 thf(fact_5354_ord__eq__le__subst,axiom,
% 5.25/5.53 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.53 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_le_subst
% 5.25/5.53 thf(fact_5355_ord__le__eq__subst,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_subst
% 5.25/5.53 thf(fact_5356_ord__le__eq__subst,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_subst
% 5.25/5.53 thf(fact_5357_ord__le__eq__subst,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_subst
% 5.25/5.53 thf(fact_5358_ord__le__eq__subst,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_subst
% 5.25/5.53 thf(fact_5359_ord__le__eq__subst,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_subst
% 5.25/5.53 thf(fact_5360_ord__le__eq__subst,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_subst
% 5.25/5.53 thf(fact_5361_ord__le__eq__subst,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_subst
% 5.25/5.53 thf(fact_5362_ord__le__eq__subst,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_subst
% 5.25/5.53 thf(fact_5363_ord__le__eq__subst,axiom,
% 5.25/5.53 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_subst
% 5.25/5.53 thf(fact_5364_ord__le__eq__subst,axiom,
% 5.25/5.53 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_le_eq_subst
% 5.25/5.53 thf(fact_5365_linorder__le__cases,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ~ ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_rat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_le_cases
% 5.25/5.53 thf(fact_5366_linorder__le__cases,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ~ ( ord_less_eq_num @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_num @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_le_cases
% 5.25/5.53 thf(fact_5367_linorder__le__cases,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ~ ( ord_less_eq_nat @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_nat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_le_cases
% 5.25/5.53 thf(fact_5368_linorder__le__cases,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ~ ( ord_less_eq_int @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_int @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_le_cases
% 5.25/5.53 thf(fact_5369_order__antisym__conv,axiom,
% 5.25/5.53 ! [Y: set_int,X3: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ Y @ X3 )
% 5.25/5.53 => ( ( ord_less_eq_set_int @ X3 @ Y )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_antisym_conv
% 5.25/5.53 thf(fact_5370_order__antisym__conv,axiom,
% 5.25/5.53 ! [Y: rat,X3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ Y @ X3 )
% 5.25/5.53 => ( ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_antisym_conv
% 5.25/5.53 thf(fact_5371_order__antisym__conv,axiom,
% 5.25/5.53 ! [Y: num,X3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ Y @ X3 )
% 5.25/5.53 => ( ( ord_less_eq_num @ X3 @ Y )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_antisym_conv
% 5.25/5.53 thf(fact_5372_order__antisym__conv,axiom,
% 5.25/5.53 ! [Y: nat,X3: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ Y @ X3 )
% 5.25/5.53 => ( ( ord_less_eq_nat @ X3 @ Y )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_antisym_conv
% 5.25/5.53 thf(fact_5373_order__antisym__conv,axiom,
% 5.25/5.53 ! [Y: int,X3: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ Y @ X3 )
% 5.25/5.53 => ( ( ord_less_eq_int @ X3 @ Y )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_antisym_conv
% 5.25/5.53 thf(fact_5374_lt__ex,axiom,
% 5.25/5.53 ! [X3: real] :
% 5.25/5.53 ? [Y3: real] : ( ord_less_real @ Y3 @ X3 ) ).
% 5.25/5.53
% 5.25/5.53 % lt_ex
% 5.25/5.53 thf(fact_5375_lt__ex,axiom,
% 5.25/5.53 ! [X3: rat] :
% 5.25/5.53 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X3 ) ).
% 5.25/5.53
% 5.25/5.53 % lt_ex
% 5.25/5.53 thf(fact_5376_lt__ex,axiom,
% 5.25/5.53 ! [X3: int] :
% 5.25/5.53 ? [Y3: int] : ( ord_less_int @ Y3 @ X3 ) ).
% 5.25/5.53
% 5.25/5.53 % lt_ex
% 5.25/5.53 thf(fact_5377_gt__ex,axiom,
% 5.25/5.53 ! [X3: real] :
% 5.25/5.53 ? [X_12: real] : ( ord_less_real @ X3 @ X_12 ) ).
% 5.25/5.53
% 5.25/5.53 % gt_ex
% 5.25/5.53 thf(fact_5378_gt__ex,axiom,
% 5.25/5.53 ! [X3: rat] :
% 5.25/5.53 ? [X_12: rat] : ( ord_less_rat @ X3 @ X_12 ) ).
% 5.25/5.53
% 5.25/5.53 % gt_ex
% 5.25/5.53 thf(fact_5379_gt__ex,axiom,
% 5.25/5.53 ! [X3: nat] :
% 5.25/5.53 ? [X_12: nat] : ( ord_less_nat @ X3 @ X_12 ) ).
% 5.25/5.53
% 5.25/5.53 % gt_ex
% 5.25/5.53 thf(fact_5380_gt__ex,axiom,
% 5.25/5.53 ! [X3: int] :
% 5.25/5.53 ? [X_12: int] : ( ord_less_int @ X3 @ X_12 ) ).
% 5.25/5.53
% 5.25/5.53 % gt_ex
% 5.25/5.53 thf(fact_5381_dense,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ? [Z2: real] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ Z2 )
% 5.25/5.53 & ( ord_less_real @ Z2 @ Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dense
% 5.25/5.53 thf(fact_5382_dense,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ? [Z2: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ Z2 )
% 5.25/5.53 & ( ord_less_rat @ Z2 @ Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dense
% 5.25/5.53 thf(fact_5383_less__imp__neq,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ( X3 != Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % less_imp_neq
% 5.25/5.53 thf(fact_5384_less__imp__neq,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ( X3 != Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % less_imp_neq
% 5.25/5.53 thf(fact_5385_less__imp__neq,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ord_less_num @ X3 @ Y )
% 5.25/5.53 => ( X3 != Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % less_imp_neq
% 5.25/5.53 thf(fact_5386_less__imp__neq,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 => ( X3 != Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % less_imp_neq
% 5.25/5.53 thf(fact_5387_less__imp__neq,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ord_less_int @ X3 @ Y )
% 5.25/5.53 => ( X3 != Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % less_imp_neq
% 5.25/5.53 thf(fact_5388_order_Oasym,axiom,
% 5.25/5.53 ! [A: real,B: real] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.asym
% 5.25/5.53 thf(fact_5389_order_Oasym,axiom,
% 5.25/5.53 ! [A: rat,B: rat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.asym
% 5.25/5.53 thf(fact_5390_order_Oasym,axiom,
% 5.25/5.53 ! [A: num,B: num] :
% 5.25/5.53 ( ( ord_less_num @ A @ B )
% 5.25/5.53 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.asym
% 5.25/5.53 thf(fact_5391_order_Oasym,axiom,
% 5.25/5.53 ! [A: nat,B: nat] :
% 5.25/5.53 ( ( ord_less_nat @ A @ B )
% 5.25/5.53 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.asym
% 5.25/5.53 thf(fact_5392_order_Oasym,axiom,
% 5.25/5.53 ! [A: int,B: int] :
% 5.25/5.53 ( ( ord_less_int @ A @ B )
% 5.25/5.53 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.asym
% 5.25/5.53 thf(fact_5393_ord__eq__less__trans,axiom,
% 5.25/5.53 ! [A: real,B: real,C: real] :
% 5.25/5.53 ( ( A = B )
% 5.25/5.53 => ( ( ord_less_real @ B @ C )
% 5.25/5.53 => ( ord_less_real @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_trans
% 5.25/5.53 thf(fact_5394_ord__eq__less__trans,axiom,
% 5.25/5.53 ! [A: rat,B: rat,C: rat] :
% 5.25/5.53 ( ( A = B )
% 5.25/5.53 => ( ( ord_less_rat @ B @ C )
% 5.25/5.53 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_trans
% 5.25/5.53 thf(fact_5395_ord__eq__less__trans,axiom,
% 5.25/5.53 ! [A: num,B: num,C: num] :
% 5.25/5.53 ( ( A = B )
% 5.25/5.53 => ( ( ord_less_num @ B @ C )
% 5.25/5.53 => ( ord_less_num @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_trans
% 5.25/5.53 thf(fact_5396_ord__eq__less__trans,axiom,
% 5.25/5.53 ! [A: nat,B: nat,C: nat] :
% 5.25/5.53 ( ( A = B )
% 5.25/5.53 => ( ( ord_less_nat @ B @ C )
% 5.25/5.53 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_trans
% 5.25/5.53 thf(fact_5397_ord__eq__less__trans,axiom,
% 5.25/5.53 ! [A: int,B: int,C: int] :
% 5.25/5.53 ( ( A = B )
% 5.25/5.53 => ( ( ord_less_int @ B @ C )
% 5.25/5.53 => ( ord_less_int @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_trans
% 5.25/5.53 thf(fact_5398_ord__less__eq__trans,axiom,
% 5.25/5.53 ! [A: real,B: real,C: real] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( B = C )
% 5.25/5.53 => ( ord_less_real @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_trans
% 5.25/5.53 thf(fact_5399_ord__less__eq__trans,axiom,
% 5.25/5.53 ! [A: rat,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( B = C )
% 5.25/5.53 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_trans
% 5.25/5.53 thf(fact_5400_ord__less__eq__trans,axiom,
% 5.25/5.53 ! [A: num,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_num @ A @ B )
% 5.25/5.53 => ( ( B = C )
% 5.25/5.53 => ( ord_less_num @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_trans
% 5.25/5.53 thf(fact_5401_ord__less__eq__trans,axiom,
% 5.25/5.53 ! [A: nat,B: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_nat @ A @ B )
% 5.25/5.53 => ( ( B = C )
% 5.25/5.53 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_trans
% 5.25/5.53 thf(fact_5402_ord__less__eq__trans,axiom,
% 5.25/5.53 ! [A: int,B: int,C: int] :
% 5.25/5.53 ( ( ord_less_int @ A @ B )
% 5.25/5.53 => ( ( B = C )
% 5.25/5.53 => ( ord_less_int @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_trans
% 5.25/5.53 thf(fact_5403_less__induct,axiom,
% 5.25/5.53 ! [P: nat > $o,A: nat] :
% 5.25/5.53 ( ! [X5: nat] :
% 5.25/5.53 ( ! [Y4: nat] :
% 5.25/5.53 ( ( ord_less_nat @ Y4 @ X5 )
% 5.25/5.53 => ( P @ Y4 ) )
% 5.25/5.53 => ( P @ X5 ) )
% 5.25/5.53 => ( P @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % less_induct
% 5.25/5.53 thf(fact_5404_antisym__conv3,axiom,
% 5.25/5.53 ! [Y: real,X3: real] :
% 5.25/5.53 ( ~ ( ord_less_real @ Y @ X3 )
% 5.25/5.53 => ( ( ~ ( ord_less_real @ X3 @ Y ) )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv3
% 5.25/5.53 thf(fact_5405_antisym__conv3,axiom,
% 5.25/5.53 ! [Y: rat,X3: rat] :
% 5.25/5.53 ( ~ ( ord_less_rat @ Y @ X3 )
% 5.25/5.53 => ( ( ~ ( ord_less_rat @ X3 @ Y ) )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv3
% 5.25/5.53 thf(fact_5406_antisym__conv3,axiom,
% 5.25/5.53 ! [Y: num,X3: num] :
% 5.25/5.53 ( ~ ( ord_less_num @ Y @ X3 )
% 5.25/5.53 => ( ( ~ ( ord_less_num @ X3 @ Y ) )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv3
% 5.25/5.53 thf(fact_5407_antisym__conv3,axiom,
% 5.25/5.53 ! [Y: nat,X3: nat] :
% 5.25/5.53 ( ~ ( ord_less_nat @ Y @ X3 )
% 5.25/5.53 => ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv3
% 5.25/5.53 thf(fact_5408_antisym__conv3,axiom,
% 5.25/5.53 ! [Y: int,X3: int] :
% 5.25/5.53 ( ~ ( ord_less_int @ Y @ X3 )
% 5.25/5.53 => ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv3
% 5.25/5.53 thf(fact_5409_linorder__cases,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ~ ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ( ( X3 != Y )
% 5.25/5.53 => ( ord_less_real @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_cases
% 5.25/5.53 thf(fact_5410_linorder__cases,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ~ ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ( ( X3 != Y )
% 5.25/5.53 => ( ord_less_rat @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_cases
% 5.25/5.53 thf(fact_5411_linorder__cases,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ~ ( ord_less_num @ X3 @ Y )
% 5.25/5.53 => ( ( X3 != Y )
% 5.25/5.53 => ( ord_less_num @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_cases
% 5.25/5.53 thf(fact_5412_linorder__cases,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ~ ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 => ( ( X3 != Y )
% 5.25/5.53 => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_cases
% 5.25/5.53 thf(fact_5413_linorder__cases,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ~ ( ord_less_int @ X3 @ Y )
% 5.25/5.53 => ( ( X3 != Y )
% 5.25/5.53 => ( ord_less_int @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_cases
% 5.25/5.53 thf(fact_5414_dual__order_Oasym,axiom,
% 5.25/5.53 ! [B: real,A: real] :
% 5.25/5.53 ( ( ord_less_real @ B @ A )
% 5.25/5.53 => ~ ( ord_less_real @ A @ B ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.asym
% 5.25/5.53 thf(fact_5415_dual__order_Oasym,axiom,
% 5.25/5.53 ! [B: rat,A: rat] :
% 5.25/5.53 ( ( ord_less_rat @ B @ A )
% 5.25/5.53 => ~ ( ord_less_rat @ A @ B ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.asym
% 5.25/5.53 thf(fact_5416_dual__order_Oasym,axiom,
% 5.25/5.53 ! [B: num,A: num] :
% 5.25/5.53 ( ( ord_less_num @ B @ A )
% 5.25/5.53 => ~ ( ord_less_num @ A @ B ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.asym
% 5.25/5.53 thf(fact_5417_dual__order_Oasym,axiom,
% 5.25/5.53 ! [B: nat,A: nat] :
% 5.25/5.53 ( ( ord_less_nat @ B @ A )
% 5.25/5.53 => ~ ( ord_less_nat @ A @ B ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.asym
% 5.25/5.53 thf(fact_5418_dual__order_Oasym,axiom,
% 5.25/5.53 ! [B: int,A: int] :
% 5.25/5.53 ( ( ord_less_int @ B @ A )
% 5.25/5.53 => ~ ( ord_less_int @ A @ B ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.asym
% 5.25/5.53 thf(fact_5419_dual__order_Oirrefl,axiom,
% 5.25/5.53 ! [A: real] :
% 5.25/5.53 ~ ( ord_less_real @ A @ A ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.irrefl
% 5.25/5.53 thf(fact_5420_dual__order_Oirrefl,axiom,
% 5.25/5.53 ! [A: rat] :
% 5.25/5.53 ~ ( ord_less_rat @ A @ A ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.irrefl
% 5.25/5.53 thf(fact_5421_dual__order_Oirrefl,axiom,
% 5.25/5.53 ! [A: num] :
% 5.25/5.53 ~ ( ord_less_num @ A @ A ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.irrefl
% 5.25/5.53 thf(fact_5422_dual__order_Oirrefl,axiom,
% 5.25/5.53 ! [A: nat] :
% 5.25/5.53 ~ ( ord_less_nat @ A @ A ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.irrefl
% 5.25/5.53 thf(fact_5423_dual__order_Oirrefl,axiom,
% 5.25/5.53 ! [A: int] :
% 5.25/5.53 ~ ( ord_less_int @ A @ A ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.irrefl
% 5.25/5.53 thf(fact_5424_exists__least__iff,axiom,
% 5.25/5.53 ( ( ^ [P5: nat > $o] :
% 5.25/5.53 ? [X7: nat] : ( P5 @ X7 ) )
% 5.25/5.53 = ( ^ [P6: nat > $o] :
% 5.25/5.53 ? [N2: nat] :
% 5.25/5.53 ( ( P6 @ N2 )
% 5.25/5.53 & ! [M6: nat] :
% 5.25/5.53 ( ( ord_less_nat @ M6 @ N2 )
% 5.25/5.53 => ~ ( P6 @ M6 ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % exists_least_iff
% 5.25/5.53 thf(fact_5425_linorder__less__wlog,axiom,
% 5.25/5.53 ! [P: real > real > $o,A: real,B: real] :
% 5.25/5.53 ( ! [A5: real,B5: real] :
% 5.25/5.53 ( ( ord_less_real @ A5 @ B5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( ! [A5: real] : ( P @ A5 @ A5 )
% 5.25/5.53 => ( ! [A5: real,B5: real] :
% 5.25/5.53 ( ( P @ B5 @ A5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( P @ A @ B ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_less_wlog
% 5.25/5.53 thf(fact_5426_linorder__less__wlog,axiom,
% 5.25/5.53 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.25/5.53 ( ! [A5: rat,B5: rat] :
% 5.25/5.53 ( ( ord_less_rat @ A5 @ B5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( ! [A5: rat] : ( P @ A5 @ A5 )
% 5.25/5.53 => ( ! [A5: rat,B5: rat] :
% 5.25/5.53 ( ( P @ B5 @ A5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( P @ A @ B ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_less_wlog
% 5.25/5.53 thf(fact_5427_linorder__less__wlog,axiom,
% 5.25/5.53 ! [P: num > num > $o,A: num,B: num] :
% 5.25/5.53 ( ! [A5: num,B5: num] :
% 5.25/5.53 ( ( ord_less_num @ A5 @ B5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( ! [A5: num] : ( P @ A5 @ A5 )
% 5.25/5.53 => ( ! [A5: num,B5: num] :
% 5.25/5.53 ( ( P @ B5 @ A5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( P @ A @ B ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_less_wlog
% 5.25/5.53 thf(fact_5428_linorder__less__wlog,axiom,
% 5.25/5.53 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.25/5.53 ( ! [A5: nat,B5: nat] :
% 5.25/5.53 ( ( ord_less_nat @ A5 @ B5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( ! [A5: nat] : ( P @ A5 @ A5 )
% 5.25/5.53 => ( ! [A5: nat,B5: nat] :
% 5.25/5.53 ( ( P @ B5 @ A5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( P @ A @ B ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_less_wlog
% 5.25/5.53 thf(fact_5429_linorder__less__wlog,axiom,
% 5.25/5.53 ! [P: int > int > $o,A: int,B: int] :
% 5.25/5.53 ( ! [A5: int,B5: int] :
% 5.25/5.53 ( ( ord_less_int @ A5 @ B5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( ! [A5: int] : ( P @ A5 @ A5 )
% 5.25/5.53 => ( ! [A5: int,B5: int] :
% 5.25/5.53 ( ( P @ B5 @ A5 )
% 5.25/5.53 => ( P @ A5 @ B5 ) )
% 5.25/5.53 => ( P @ A @ B ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_less_wlog
% 5.25/5.53 thf(fact_5430_order_Ostrict__trans,axiom,
% 5.25/5.53 ! [A: real,B: real,C: real] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( ord_less_real @ B @ C )
% 5.25/5.53 => ( ord_less_real @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans
% 5.25/5.53 thf(fact_5431_order_Ostrict__trans,axiom,
% 5.25/5.53 ! [A: rat,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_rat @ B @ C )
% 5.25/5.53 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans
% 5.25/5.53 thf(fact_5432_order_Ostrict__trans,axiom,
% 5.25/5.53 ! [A: num,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_num @ B @ C )
% 5.25/5.53 => ( ord_less_num @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans
% 5.25/5.53 thf(fact_5433_order_Ostrict__trans,axiom,
% 5.25/5.53 ! [A: nat,B: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_nat @ A @ B )
% 5.25/5.53 => ( ( ord_less_nat @ B @ C )
% 5.25/5.53 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans
% 5.25/5.53 thf(fact_5434_order_Ostrict__trans,axiom,
% 5.25/5.53 ! [A: int,B: int,C: int] :
% 5.25/5.53 ( ( ord_less_int @ A @ B )
% 5.25/5.53 => ( ( ord_less_int @ B @ C )
% 5.25/5.53 => ( ord_less_int @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans
% 5.25/5.53 thf(fact_5435_not__less__iff__gr__or__eq,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ~ ( ord_less_real @ X3 @ Y ) )
% 5.25/5.53 = ( ( ord_less_real @ Y @ X3 )
% 5.25/5.53 | ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % not_less_iff_gr_or_eq
% 5.25/5.53 thf(fact_5436_not__less__iff__gr__or__eq,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ~ ( ord_less_rat @ X3 @ Y ) )
% 5.25/5.53 = ( ( ord_less_rat @ Y @ X3 )
% 5.25/5.53 | ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % not_less_iff_gr_or_eq
% 5.25/5.53 thf(fact_5437_not__less__iff__gr__or__eq,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ~ ( ord_less_num @ X3 @ Y ) )
% 5.25/5.53 = ( ( ord_less_num @ Y @ X3 )
% 5.25/5.53 | ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % not_less_iff_gr_or_eq
% 5.25/5.53 thf(fact_5438_not__less__iff__gr__or__eq,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 5.25/5.53 = ( ( ord_less_nat @ Y @ X3 )
% 5.25/5.53 | ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % not_less_iff_gr_or_eq
% 5.25/5.53 thf(fact_5439_not__less__iff__gr__or__eq,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 5.25/5.53 = ( ( ord_less_int @ Y @ X3 )
% 5.25/5.53 | ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % not_less_iff_gr_or_eq
% 5.25/5.53 thf(fact_5440_dual__order_Ostrict__trans,axiom,
% 5.25/5.53 ! [B: real,A: real,C: real] :
% 5.25/5.53 ( ( ord_less_real @ B @ A )
% 5.25/5.53 => ( ( ord_less_real @ C @ B )
% 5.25/5.53 => ( ord_less_real @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans
% 5.25/5.53 thf(fact_5441_dual__order_Ostrict__trans,axiom,
% 5.25/5.53 ! [B: rat,A: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_rat @ B @ A )
% 5.25/5.53 => ( ( ord_less_rat @ C @ B )
% 5.25/5.53 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans
% 5.25/5.53 thf(fact_5442_dual__order_Ostrict__trans,axiom,
% 5.25/5.53 ! [B: num,A: num,C: num] :
% 5.25/5.53 ( ( ord_less_num @ B @ A )
% 5.25/5.53 => ( ( ord_less_num @ C @ B )
% 5.25/5.53 => ( ord_less_num @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans
% 5.25/5.53 thf(fact_5443_dual__order_Ostrict__trans,axiom,
% 5.25/5.53 ! [B: nat,A: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_nat @ B @ A )
% 5.25/5.53 => ( ( ord_less_nat @ C @ B )
% 5.25/5.53 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans
% 5.25/5.53 thf(fact_5444_dual__order_Ostrict__trans,axiom,
% 5.25/5.53 ! [B: int,A: int,C: int] :
% 5.25/5.53 ( ( ord_less_int @ B @ A )
% 5.25/5.53 => ( ( ord_less_int @ C @ B )
% 5.25/5.53 => ( ord_less_int @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans
% 5.25/5.53 thf(fact_5445_order_Ostrict__implies__not__eq,axiom,
% 5.25/5.53 ! [A: real,B: real] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( A != B ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_implies_not_eq
% 5.25/5.53 thf(fact_5446_order_Ostrict__implies__not__eq,axiom,
% 5.25/5.53 ! [A: rat,B: rat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( A != B ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_implies_not_eq
% 5.25/5.53 thf(fact_5447_order_Ostrict__implies__not__eq,axiom,
% 5.25/5.53 ! [A: num,B: num] :
% 5.25/5.53 ( ( ord_less_num @ A @ B )
% 5.25/5.53 => ( A != B ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_implies_not_eq
% 5.25/5.53 thf(fact_5448_order_Ostrict__implies__not__eq,axiom,
% 5.25/5.53 ! [A: nat,B: nat] :
% 5.25/5.53 ( ( ord_less_nat @ A @ B )
% 5.25/5.53 => ( A != B ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_implies_not_eq
% 5.25/5.53 thf(fact_5449_order_Ostrict__implies__not__eq,axiom,
% 5.25/5.53 ! [A: int,B: int] :
% 5.25/5.53 ( ( ord_less_int @ A @ B )
% 5.25/5.53 => ( A != B ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_implies_not_eq
% 5.25/5.53 thf(fact_5450_dual__order_Ostrict__implies__not__eq,axiom,
% 5.25/5.53 ! [B: real,A: real] :
% 5.25/5.53 ( ( ord_less_real @ B @ A )
% 5.25/5.53 => ( A != B ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_implies_not_eq
% 5.25/5.53 thf(fact_5451_dual__order_Ostrict__implies__not__eq,axiom,
% 5.25/5.53 ! [B: rat,A: rat] :
% 5.25/5.53 ( ( ord_less_rat @ B @ A )
% 5.25/5.53 => ( A != B ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_implies_not_eq
% 5.25/5.53 thf(fact_5452_dual__order_Ostrict__implies__not__eq,axiom,
% 5.25/5.53 ! [B: num,A: num] :
% 5.25/5.53 ( ( ord_less_num @ B @ A )
% 5.25/5.53 => ( A != B ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_implies_not_eq
% 5.25/5.53 thf(fact_5453_dual__order_Ostrict__implies__not__eq,axiom,
% 5.25/5.53 ! [B: nat,A: nat] :
% 5.25/5.53 ( ( ord_less_nat @ B @ A )
% 5.25/5.53 => ( A != B ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_implies_not_eq
% 5.25/5.53 thf(fact_5454_dual__order_Ostrict__implies__not__eq,axiom,
% 5.25/5.53 ! [B: int,A: int] :
% 5.25/5.53 ( ( ord_less_int @ B @ A )
% 5.25/5.53 => ( A != B ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_implies_not_eq
% 5.25/5.53 thf(fact_5455_linorder__neqE,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( X3 != Y )
% 5.25/5.53 => ( ~ ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ( ord_less_real @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_neqE
% 5.25/5.53 thf(fact_5456_linorder__neqE,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( X3 != Y )
% 5.25/5.53 => ( ~ ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ( ord_less_rat @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_neqE
% 5.25/5.53 thf(fact_5457_linorder__neqE,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( X3 != Y )
% 5.25/5.53 => ( ~ ( ord_less_num @ X3 @ Y )
% 5.25/5.53 => ( ord_less_num @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_neqE
% 5.25/5.53 thf(fact_5458_linorder__neqE,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( X3 != Y )
% 5.25/5.53 => ( ~ ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_neqE
% 5.25/5.53 thf(fact_5459_linorder__neqE,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( X3 != Y )
% 5.25/5.53 => ( ~ ( ord_less_int @ X3 @ Y )
% 5.25/5.53 => ( ord_less_int @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_neqE
% 5.25/5.53 thf(fact_5460_order__less__asym,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_real @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_asym
% 5.25/5.53 thf(fact_5461_order__less__asym,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_rat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_asym
% 5.25/5.53 thf(fact_5462_order__less__asym,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ord_less_num @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_num @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_asym
% 5.25/5.53 thf(fact_5463_order__less__asym,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_asym
% 5.25/5.53 thf(fact_5464_order__less__asym,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ord_less_int @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_asym
% 5.25/5.53 thf(fact_5465_linorder__neq__iff,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( X3 != Y )
% 5.25/5.53 = ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 | ( ord_less_real @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_neq_iff
% 5.25/5.53 thf(fact_5466_linorder__neq__iff,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( X3 != Y )
% 5.25/5.53 = ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 | ( ord_less_rat @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_neq_iff
% 5.25/5.53 thf(fact_5467_linorder__neq__iff,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( X3 != Y )
% 5.25/5.53 = ( ( ord_less_num @ X3 @ Y )
% 5.25/5.53 | ( ord_less_num @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_neq_iff
% 5.25/5.53 thf(fact_5468_linorder__neq__iff,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( X3 != Y )
% 5.25/5.53 = ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 | ( ord_less_nat @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_neq_iff
% 5.25/5.53 thf(fact_5469_linorder__neq__iff,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( X3 != Y )
% 5.25/5.53 = ( ( ord_less_int @ X3 @ Y )
% 5.25/5.53 | ( ord_less_int @ Y @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_neq_iff
% 5.25/5.53 thf(fact_5470_order__less__asym_H,axiom,
% 5.25/5.53 ! [A: real,B: real] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_asym'
% 5.25/5.53 thf(fact_5471_order__less__asym_H,axiom,
% 5.25/5.53 ! [A: rat,B: rat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_asym'
% 5.25/5.53 thf(fact_5472_order__less__asym_H,axiom,
% 5.25/5.53 ! [A: num,B: num] :
% 5.25/5.53 ( ( ord_less_num @ A @ B )
% 5.25/5.53 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_asym'
% 5.25/5.53 thf(fact_5473_order__less__asym_H,axiom,
% 5.25/5.53 ! [A: nat,B: nat] :
% 5.25/5.53 ( ( ord_less_nat @ A @ B )
% 5.25/5.53 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_asym'
% 5.25/5.53 thf(fact_5474_order__less__asym_H,axiom,
% 5.25/5.53 ! [A: int,B: int] :
% 5.25/5.53 ( ( ord_less_int @ A @ B )
% 5.25/5.53 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_asym'
% 5.25/5.53 thf(fact_5475_order__less__trans,axiom,
% 5.25/5.53 ! [X3: real,Y: real,Z: real] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_real @ Y @ Z )
% 5.25/5.53 => ( ord_less_real @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_trans
% 5.25/5.53 thf(fact_5476_order__less__trans,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat,Z: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_rat @ Y @ Z )
% 5.25/5.53 => ( ord_less_rat @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_trans
% 5.25/5.53 thf(fact_5477_order__less__trans,axiom,
% 5.25/5.53 ! [X3: num,Y: num,Z: num] :
% 5.25/5.53 ( ( ord_less_num @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_num @ Y @ Z )
% 5.25/5.53 => ( ord_less_num @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_trans
% 5.25/5.53 thf(fact_5478_order__less__trans,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat,Z: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_nat @ Y @ Z )
% 5.25/5.53 => ( ord_less_nat @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_trans
% 5.25/5.53 thf(fact_5479_order__less__trans,axiom,
% 5.25/5.53 ! [X3: int,Y: int,Z: int] :
% 5.25/5.53 ( ( ord_less_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_int @ Y @ Z )
% 5.25/5.53 => ( ord_less_int @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_trans
% 5.25/5.53 thf(fact_5480_ord__eq__less__subst,axiom,
% 5.25/5.53 ! [A: real,F: real > real,B: real,C: real] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_real @ B @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_subst
% 5.25/5.53 thf(fact_5481_ord__eq__less__subst,axiom,
% 5.25/5.53 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_real @ B @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_subst
% 5.25/5.53 thf(fact_5482_ord__eq__less__subst,axiom,
% 5.25/5.53 ! [A: num,F: real > num,B: real,C: real] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_real @ B @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_subst
% 5.25/5.53 thf(fact_5483_ord__eq__less__subst,axiom,
% 5.25/5.53 ! [A: nat,F: real > nat,B: real,C: real] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_real @ B @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_subst
% 5.25/5.53 thf(fact_5484_ord__eq__less__subst,axiom,
% 5.25/5.53 ! [A: int,F: real > int,B: real,C: real] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_real @ B @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_subst
% 5.25/5.53 thf(fact_5485_ord__eq__less__subst,axiom,
% 5.25/5.53 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_subst
% 5.25/5.53 thf(fact_5486_ord__eq__less__subst,axiom,
% 5.25/5.53 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_subst
% 5.25/5.53 thf(fact_5487_ord__eq__less__subst,axiom,
% 5.25/5.53 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_subst
% 5.25/5.53 thf(fact_5488_ord__eq__less__subst,axiom,
% 5.25/5.53 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_subst
% 5.25/5.53 thf(fact_5489_ord__eq__less__subst,axiom,
% 5.25/5.53 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.25/5.53 ( ( A
% 5.25/5.53 = ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_eq_less_subst
% 5.25/5.53 thf(fact_5490_ord__less__eq__subst,axiom,
% 5.25/5.53 ! [A: real,B: real,F: real > real,C: real] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_subst
% 5.25/5.53 thf(fact_5491_ord__less__eq__subst,axiom,
% 5.25/5.53 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_subst
% 5.25/5.53 thf(fact_5492_ord__less__eq__subst,axiom,
% 5.25/5.53 ! [A: real,B: real,F: real > num,C: num] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_subst
% 5.25/5.53 thf(fact_5493_ord__less__eq__subst,axiom,
% 5.25/5.53 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_subst
% 5.25/5.53 thf(fact_5494_ord__less__eq__subst,axiom,
% 5.25/5.53 ! [A: real,B: real,F: real > int,C: int] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_subst
% 5.25/5.53 thf(fact_5495_ord__less__eq__subst,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_subst
% 5.25/5.53 thf(fact_5496_ord__less__eq__subst,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_subst
% 5.25/5.53 thf(fact_5497_ord__less__eq__subst,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_subst
% 5.25/5.53 thf(fact_5498_ord__less__eq__subst,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_subst
% 5.25/5.53 thf(fact_5499_ord__less__eq__subst,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( ( F @ B )
% 5.25/5.53 = C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % ord_less_eq_subst
% 5.25/5.53 thf(fact_5500_order__less__irrefl,axiom,
% 5.25/5.53 ! [X3: real] :
% 5.25/5.53 ~ ( ord_less_real @ X3 @ X3 ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_irrefl
% 5.25/5.53 thf(fact_5501_order__less__irrefl,axiom,
% 5.25/5.53 ! [X3: rat] :
% 5.25/5.53 ~ ( ord_less_rat @ X3 @ X3 ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_irrefl
% 5.25/5.53 thf(fact_5502_order__less__irrefl,axiom,
% 5.25/5.53 ! [X3: num] :
% 5.25/5.53 ~ ( ord_less_num @ X3 @ X3 ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_irrefl
% 5.25/5.53 thf(fact_5503_order__less__irrefl,axiom,
% 5.25/5.53 ! [X3: nat] :
% 5.25/5.53 ~ ( ord_less_nat @ X3 @ X3 ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_irrefl
% 5.25/5.53 thf(fact_5504_order__less__irrefl,axiom,
% 5.25/5.53 ! [X3: int] :
% 5.25/5.53 ~ ( ord_less_int @ X3 @ X3 ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_irrefl
% 5.25/5.53 thf(fact_5505_order__less__subst1,axiom,
% 5.25/5.53 ! [A: real,F: real > real,B: real,C: real] :
% 5.25/5.53 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_real @ B @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst1
% 5.25/5.53 thf(fact_5506_order__less__subst1,axiom,
% 5.25/5.53 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst1
% 5.25/5.53 thf(fact_5507_order__less__subst1,axiom,
% 5.25/5.53 ! [A: real,F: num > real,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst1
% 5.25/5.53 thf(fact_5508_order__less__subst1,axiom,
% 5.25/5.53 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_nat @ B @ C )
% 5.25/5.53 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst1
% 5.25/5.53 thf(fact_5509_order__less__subst1,axiom,
% 5.25/5.53 ! [A: real,F: int > real,B: int,C: int] :
% 5.25/5.53 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_int @ B @ C )
% 5.25/5.53 => ( ! [X5: int,Y3: int] :
% 5.25/5.53 ( ( ord_less_int @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst1
% 5.25/5.53 thf(fact_5510_order__less__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.25/5.53 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_real @ B @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst1
% 5.25/5.53 thf(fact_5511_order__less__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst1
% 5.25/5.53 thf(fact_5512_order__less__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst1
% 5.25/5.53 thf(fact_5513_order__less__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_nat @ B @ C )
% 5.25/5.53 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst1
% 5.25/5.53 thf(fact_5514_order__less__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.25/5.53 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_int @ B @ C )
% 5.25/5.53 => ( ! [X5: int,Y3: int] :
% 5.25/5.53 ( ( ord_less_int @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst1
% 5.25/5.53 thf(fact_5515_order__less__subst2,axiom,
% 5.25/5.53 ! [A: real,B: real,F: real > real,C: real] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst2
% 5.25/5.53 thf(fact_5516_order__less__subst2,axiom,
% 5.25/5.53 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst2
% 5.25/5.53 thf(fact_5517_order__less__subst2,axiom,
% 5.25/5.53 ! [A: real,B: real,F: real > num,C: num] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst2
% 5.25/5.53 thf(fact_5518_order__less__subst2,axiom,
% 5.25/5.53 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst2
% 5.25/5.53 thf(fact_5519_order__less__subst2,axiom,
% 5.25/5.53 ! [A: real,B: real,F: real > int,C: int] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst2
% 5.25/5.53 thf(fact_5520_order__less__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst2
% 5.25/5.53 thf(fact_5521_order__less__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst2
% 5.25/5.53 thf(fact_5522_order__less__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst2
% 5.25/5.53 thf(fact_5523_order__less__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst2
% 5.25/5.53 thf(fact_5524_order__less__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_subst2
% 5.25/5.53 thf(fact_5525_order__less__not__sym,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_real @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_not_sym
% 5.25/5.53 thf(fact_5526_order__less__not__sym,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_rat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_not_sym
% 5.25/5.53 thf(fact_5527_order__less__not__sym,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ord_less_num @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_num @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_not_sym
% 5.25/5.53 thf(fact_5528_order__less__not__sym,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_not_sym
% 5.25/5.53 thf(fact_5529_order__less__not__sym,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ord_less_int @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_not_sym
% 5.25/5.53 thf(fact_5530_order__less__imp__triv,axiom,
% 5.25/5.53 ! [X3: real,Y: real,P: $o] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_real @ Y @ X3 )
% 5.25/5.53 => P ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_triv
% 5.25/5.53 thf(fact_5531_order__less__imp__triv,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat,P: $o] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_rat @ Y @ X3 )
% 5.25/5.53 => P ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_triv
% 5.25/5.53 thf(fact_5532_order__less__imp__triv,axiom,
% 5.25/5.53 ! [X3: num,Y: num,P: $o] :
% 5.25/5.53 ( ( ord_less_num @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_num @ Y @ X3 )
% 5.25/5.53 => P ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_triv
% 5.25/5.53 thf(fact_5533_order__less__imp__triv,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat,P: $o] :
% 5.25/5.53 ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_nat @ Y @ X3 )
% 5.25/5.53 => P ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_triv
% 5.25/5.53 thf(fact_5534_order__less__imp__triv,axiom,
% 5.25/5.53 ! [X3: int,Y: int,P: $o] :
% 5.25/5.53 ( ( ord_less_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_int @ Y @ X3 )
% 5.25/5.53 => P ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_triv
% 5.25/5.53 thf(fact_5535_linorder__less__linear,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 | ( X3 = Y )
% 5.25/5.53 | ( ord_less_real @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_less_linear
% 5.25/5.53 thf(fact_5536_linorder__less__linear,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 | ( X3 = Y )
% 5.25/5.53 | ( ord_less_rat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_less_linear
% 5.25/5.53 thf(fact_5537_linorder__less__linear,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ord_less_num @ X3 @ Y )
% 5.25/5.53 | ( X3 = Y )
% 5.25/5.53 | ( ord_less_num @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_less_linear
% 5.25/5.53 thf(fact_5538_linorder__less__linear,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 | ( X3 = Y )
% 5.25/5.53 | ( ord_less_nat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_less_linear
% 5.25/5.53 thf(fact_5539_linorder__less__linear,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ord_less_int @ X3 @ Y )
% 5.25/5.53 | ( X3 = Y )
% 5.25/5.53 | ( ord_less_int @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_less_linear
% 5.25/5.53 thf(fact_5540_order__less__imp__not__eq,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ( X3 != Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_eq
% 5.25/5.53 thf(fact_5541_order__less__imp__not__eq,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ( X3 != Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_eq
% 5.25/5.53 thf(fact_5542_order__less__imp__not__eq,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ord_less_num @ X3 @ Y )
% 5.25/5.53 => ( X3 != Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_eq
% 5.25/5.53 thf(fact_5543_order__less__imp__not__eq,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 => ( X3 != Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_eq
% 5.25/5.53 thf(fact_5544_order__less__imp__not__eq,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ord_less_int @ X3 @ Y )
% 5.25/5.53 => ( X3 != Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_eq
% 5.25/5.53 thf(fact_5545_order__less__imp__not__eq2,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ( Y != X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_eq2
% 5.25/5.53 thf(fact_5546_order__less__imp__not__eq2,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ( Y != X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_eq2
% 5.25/5.53 thf(fact_5547_order__less__imp__not__eq2,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ord_less_num @ X3 @ Y )
% 5.25/5.53 => ( Y != X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_eq2
% 5.25/5.53 thf(fact_5548_order__less__imp__not__eq2,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 => ( Y != X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_eq2
% 5.25/5.53 thf(fact_5549_order__less__imp__not__eq2,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ord_less_int @ X3 @ Y )
% 5.25/5.53 => ( Y != X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_eq2
% 5.25/5.53 thf(fact_5550_order__less__imp__not__less,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_real @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_less
% 5.25/5.53 thf(fact_5551_order__less__imp__not__less,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_rat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_less
% 5.25/5.53 thf(fact_5552_order__less__imp__not__less,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ord_less_num @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_num @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_less
% 5.25/5.53 thf(fact_5553_order__less__imp__not__less,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_less
% 5.25/5.53 thf(fact_5554_order__less__imp__not__less,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ord_less_int @ X3 @ Y )
% 5.25/5.53 => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_not_less
% 5.25/5.53 thf(fact_5555_of__int__nonneg,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.53 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_nonneg
% 5.25/5.53 thf(fact_5556_of__int__nonneg,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.53 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_nonneg
% 5.25/5.53 thf(fact_5557_of__int__nonneg,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.53 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_nonneg
% 5.25/5.53 thf(fact_5558_of__int__pos,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.25/5.53 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_pos
% 5.25/5.53 thf(fact_5559_of__int__pos,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.25/5.53 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_pos
% 5.25/5.53 thf(fact_5560_of__int__pos,axiom,
% 5.25/5.53 ! [Z: int] :
% 5.25/5.53 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.25/5.53 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_pos
% 5.25/5.53 thf(fact_5561_of__int__neg__numeral,axiom,
% 5.25/5.53 ! [K: num] :
% 5.25/5.53 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.25/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_neg_numeral
% 5.25/5.53 thf(fact_5562_of__int__neg__numeral,axiom,
% 5.25/5.53 ! [K: num] :
% 5.25/5.53 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.25/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_neg_numeral
% 5.25/5.53 thf(fact_5563_of__int__neg__numeral,axiom,
% 5.25/5.53 ! [K: num] :
% 5.25/5.53 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.25/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_neg_numeral
% 5.25/5.53 thf(fact_5564_of__int__neg__numeral,axiom,
% 5.25/5.53 ! [K: num] :
% 5.25/5.53 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.25/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_neg_numeral
% 5.25/5.53 thf(fact_5565_of__int__neg__numeral,axiom,
% 5.25/5.53 ! [K: num] :
% 5.25/5.53 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.25/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_int_neg_numeral
% 5.25/5.53 thf(fact_5566_int__le__real__less,axiom,
% 5.25/5.53 ( ord_less_eq_int
% 5.25/5.53 = ( ^ [N2: int,M6: int] : ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % int_le_real_less
% 5.25/5.53 thf(fact_5567_int__less__real__le,axiom,
% 5.25/5.53 ( ord_less_int
% 5.25/5.53 = ( ^ [N2: int,M6: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) @ ( ring_1_of_int_real @ M6 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % int_less_real_le
% 5.25/5.53 thf(fact_5568_real__of__int__div__aux,axiom,
% 5.25/5.53 ! [X3: int,D: int] :
% 5.25/5.53 ( ( divide_divide_real @ ( ring_1_of_int_real @ X3 ) @ ( ring_1_of_int_real @ D ) )
% 5.25/5.53 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X3 @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X3 @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % real_of_int_div_aux
% 5.25/5.53 thf(fact_5569_real__of__int__div2,axiom,
% 5.25/5.53 ! [N: int,X3: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X3 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X3 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % real_of_int_div2
% 5.25/5.53 thf(fact_5570_real__of__int__div3,axiom,
% 5.25/5.53 ! [N: int,X3: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X3 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X3 ) ) ) @ one_one_real ) ).
% 5.25/5.53
% 5.25/5.53 % real_of_int_div3
% 5.25/5.53 thf(fact_5571_even__of__int__iff,axiom,
% 5.25/5.53 ! [K: int] :
% 5.25/5.53 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 5.25/5.53 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.25/5.53
% 5.25/5.53 % even_of_int_iff
% 5.25/5.53 thf(fact_5572_even__of__int__iff,axiom,
% 5.25/5.53 ! [K: int] :
% 5.25/5.53 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.25/5.53 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.25/5.53
% 5.25/5.53 % even_of_int_iff
% 5.25/5.53 thf(fact_5573_leD,axiom,
% 5.25/5.53 ! [Y: real,X3: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ Y @ X3 )
% 5.25/5.53 => ~ ( ord_less_real @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % leD
% 5.25/5.53 thf(fact_5574_leD,axiom,
% 5.25/5.53 ! [Y: set_int,X3: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ Y @ X3 )
% 5.25/5.53 => ~ ( ord_less_set_int @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % leD
% 5.25/5.53 thf(fact_5575_leD,axiom,
% 5.25/5.53 ! [Y: rat,X3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ Y @ X3 )
% 5.25/5.53 => ~ ( ord_less_rat @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % leD
% 5.25/5.53 thf(fact_5576_leD,axiom,
% 5.25/5.53 ! [Y: num,X3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ Y @ X3 )
% 5.25/5.53 => ~ ( ord_less_num @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % leD
% 5.25/5.53 thf(fact_5577_leD,axiom,
% 5.25/5.53 ! [Y: nat,X3: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ Y @ X3 )
% 5.25/5.53 => ~ ( ord_less_nat @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % leD
% 5.25/5.53 thf(fact_5578_leD,axiom,
% 5.25/5.53 ! [Y: int,X3: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ Y @ X3 )
% 5.25/5.53 => ~ ( ord_less_int @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % leD
% 5.25/5.53 thf(fact_5579_leI,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ~ ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_real @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % leI
% 5.25/5.53 thf(fact_5580_leI,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ~ ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_rat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % leI
% 5.25/5.53 thf(fact_5581_leI,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ~ ( ord_less_num @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_num @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % leI
% 5.25/5.53 thf(fact_5582_leI,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ~ ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_nat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % leI
% 5.25/5.53 thf(fact_5583_leI,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ~ ( ord_less_int @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_int @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % leI
% 5.25/5.53 thf(fact_5584_nless__le,axiom,
% 5.25/5.53 ! [A: real,B: real] :
% 5.25/5.53 ( ( ~ ( ord_less_real @ A @ B ) )
% 5.25/5.53 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.25/5.53 | ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % nless_le
% 5.25/5.53 thf(fact_5585_nless__le,axiom,
% 5.25/5.53 ! [A: set_int,B: set_int] :
% 5.25/5.53 ( ( ~ ( ord_less_set_int @ A @ B ) )
% 5.25/5.53 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.25/5.53 | ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % nless_le
% 5.25/5.53 thf(fact_5586_nless__le,axiom,
% 5.25/5.53 ! [A: rat,B: rat] :
% 5.25/5.53 ( ( ~ ( ord_less_rat @ A @ B ) )
% 5.25/5.53 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 | ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % nless_le
% 5.25/5.53 thf(fact_5587_nless__le,axiom,
% 5.25/5.53 ! [A: num,B: num] :
% 5.25/5.53 ( ( ~ ( ord_less_num @ A @ B ) )
% 5.25/5.53 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.25/5.53 | ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % nless_le
% 5.25/5.53 thf(fact_5588_nless__le,axiom,
% 5.25/5.53 ! [A: nat,B: nat] :
% 5.25/5.53 ( ( ~ ( ord_less_nat @ A @ B ) )
% 5.25/5.53 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.25/5.53 | ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % nless_le
% 5.25/5.53 thf(fact_5589_nless__le,axiom,
% 5.25/5.53 ! [A: int,B: int] :
% 5.25/5.53 ( ( ~ ( ord_less_int @ A @ B ) )
% 5.25/5.53 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.25/5.53 | ( A = B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % nless_le
% 5.25/5.53 thf(fact_5590_antisym__conv1,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ~ ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv1
% 5.25/5.53 thf(fact_5591_antisym__conv1,axiom,
% 5.25/5.53 ! [X3: set_int,Y: set_int] :
% 5.25/5.53 ( ~ ( ord_less_set_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_set_int @ X3 @ Y )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv1
% 5.25/5.53 thf(fact_5592_antisym__conv1,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ~ ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv1
% 5.25/5.53 thf(fact_5593_antisym__conv1,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ~ ( ord_less_num @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_num @ X3 @ Y )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv1
% 5.25/5.53 thf(fact_5594_antisym__conv1,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ~ ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_nat @ X3 @ Y )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv1
% 5.25/5.53 thf(fact_5595_antisym__conv1,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ~ ( ord_less_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_int @ X3 @ Y )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv1
% 5.25/5.53 thf(fact_5596_antisym__conv2,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.53 => ( ( ~ ( ord_less_real @ X3 @ Y ) )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv2
% 5.25/5.53 thf(fact_5597_antisym__conv2,axiom,
% 5.25/5.53 ! [X3: set_int,Y: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ X3 @ Y )
% 5.25/5.53 => ( ( ~ ( ord_less_set_int @ X3 @ Y ) )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv2
% 5.25/5.53 thf(fact_5598_antisym__conv2,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.53 => ( ( ~ ( ord_less_rat @ X3 @ Y ) )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv2
% 5.25/5.53 thf(fact_5599_antisym__conv2,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X3 @ Y )
% 5.25/5.53 => ( ( ~ ( ord_less_num @ X3 @ Y ) )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv2
% 5.25/5.53 thf(fact_5600_antisym__conv2,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X3 @ Y )
% 5.25/5.53 => ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv2
% 5.25/5.53 thf(fact_5601_antisym__conv2,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ X3 @ Y )
% 5.25/5.53 => ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 5.25/5.53 = ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % antisym_conv2
% 5.25/5.53 thf(fact_5602_dense__ge,axiom,
% 5.25/5.53 ! [Z: real,Y: real] :
% 5.25/5.53 ( ! [X5: real] :
% 5.25/5.53 ( ( ord_less_real @ Z @ X5 )
% 5.25/5.53 => ( ord_less_eq_real @ Y @ X5 ) )
% 5.25/5.53 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % dense_ge
% 5.25/5.53 thf(fact_5603_dense__ge,axiom,
% 5.25/5.53 ! [Z: rat,Y: rat] :
% 5.25/5.53 ( ! [X5: rat] :
% 5.25/5.53 ( ( ord_less_rat @ Z @ X5 )
% 5.25/5.53 => ( ord_less_eq_rat @ Y @ X5 ) )
% 5.25/5.53 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % dense_ge
% 5.25/5.53 thf(fact_5604_dense__le,axiom,
% 5.25/5.53 ! [Y: real,Z: real] :
% 5.25/5.53 ( ! [X5: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y )
% 5.25/5.53 => ( ord_less_eq_real @ X5 @ Z ) )
% 5.25/5.53 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % dense_le
% 5.25/5.53 thf(fact_5605_dense__le,axiom,
% 5.25/5.53 ! [Y: rat,Z: rat] :
% 5.25/5.53 ( ! [X5: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y )
% 5.25/5.53 => ( ord_less_eq_rat @ X5 @ Z ) )
% 5.25/5.53 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 5.25/5.53
% 5.25/5.53 % dense_le
% 5.25/5.53 thf(fact_5606_less__le__not__le,axiom,
% 5.25/5.53 ( ord_less_real
% 5.25/5.53 = ( ^ [X2: real,Y6: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ X2 @ Y6 )
% 5.25/5.53 & ~ ( ord_less_eq_real @ Y6 @ X2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % less_le_not_le
% 5.25/5.53 thf(fact_5607_less__le__not__le,axiom,
% 5.25/5.53 ( ord_less_set_int
% 5.25/5.53 = ( ^ [X2: set_int,Y6: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ X2 @ Y6 )
% 5.25/5.53 & ~ ( ord_less_eq_set_int @ Y6 @ X2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % less_le_not_le
% 5.25/5.53 thf(fact_5608_less__le__not__le,axiom,
% 5.25/5.53 ( ord_less_rat
% 5.25/5.53 = ( ^ [X2: rat,Y6: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X2 @ Y6 )
% 5.25/5.53 & ~ ( ord_less_eq_rat @ Y6 @ X2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % less_le_not_le
% 5.25/5.53 thf(fact_5609_less__le__not__le,axiom,
% 5.25/5.53 ( ord_less_num
% 5.25/5.53 = ( ^ [X2: num,Y6: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X2 @ Y6 )
% 5.25/5.53 & ~ ( ord_less_eq_num @ Y6 @ X2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % less_le_not_le
% 5.25/5.53 thf(fact_5610_less__le__not__le,axiom,
% 5.25/5.53 ( ord_less_nat
% 5.25/5.53 = ( ^ [X2: nat,Y6: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X2 @ Y6 )
% 5.25/5.53 & ~ ( ord_less_eq_nat @ Y6 @ X2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % less_le_not_le
% 5.25/5.53 thf(fact_5611_less__le__not__le,axiom,
% 5.25/5.53 ( ord_less_int
% 5.25/5.53 = ( ^ [X2: int,Y6: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ X2 @ Y6 )
% 5.25/5.53 & ~ ( ord_less_eq_int @ Y6 @ X2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % less_le_not_le
% 5.25/5.53 thf(fact_5612_not__le__imp__less,axiom,
% 5.25/5.53 ! [Y: real,X3: real] :
% 5.25/5.53 ( ~ ( ord_less_eq_real @ Y @ X3 )
% 5.25/5.53 => ( ord_less_real @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % not_le_imp_less
% 5.25/5.53 thf(fact_5613_not__le__imp__less,axiom,
% 5.25/5.53 ! [Y: rat,X3: rat] :
% 5.25/5.53 ( ~ ( ord_less_eq_rat @ Y @ X3 )
% 5.25/5.53 => ( ord_less_rat @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % not_le_imp_less
% 5.25/5.53 thf(fact_5614_not__le__imp__less,axiom,
% 5.25/5.53 ! [Y: num,X3: num] :
% 5.25/5.53 ( ~ ( ord_less_eq_num @ Y @ X3 )
% 5.25/5.53 => ( ord_less_num @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % not_le_imp_less
% 5.25/5.53 thf(fact_5615_not__le__imp__less,axiom,
% 5.25/5.53 ! [Y: nat,X3: nat] :
% 5.25/5.53 ( ~ ( ord_less_eq_nat @ Y @ X3 )
% 5.25/5.53 => ( ord_less_nat @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % not_le_imp_less
% 5.25/5.53 thf(fact_5616_not__le__imp__less,axiom,
% 5.25/5.53 ! [Y: int,X3: int] :
% 5.25/5.53 ( ~ ( ord_less_eq_int @ Y @ X3 )
% 5.25/5.53 => ( ord_less_int @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % not_le_imp_less
% 5.25/5.53 thf(fact_5617_order_Oorder__iff__strict,axiom,
% 5.25/5.53 ( ord_less_eq_real
% 5.25/5.53 = ( ^ [A3: real,B2: real] :
% 5.25/5.53 ( ( ord_less_real @ A3 @ B2 )
% 5.25/5.53 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.order_iff_strict
% 5.25/5.53 thf(fact_5618_order_Oorder__iff__strict,axiom,
% 5.25/5.53 ( ord_less_eq_set_int
% 5.25/5.53 = ( ^ [A3: set_int,B2: set_int] :
% 5.25/5.53 ( ( ord_less_set_int @ A3 @ B2 )
% 5.25/5.53 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.order_iff_strict
% 5.25/5.53 thf(fact_5619_order_Oorder__iff__strict,axiom,
% 5.25/5.53 ( ord_less_eq_rat
% 5.25/5.53 = ( ^ [A3: rat,B2: rat] :
% 5.25/5.53 ( ( ord_less_rat @ A3 @ B2 )
% 5.25/5.53 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.order_iff_strict
% 5.25/5.53 thf(fact_5620_order_Oorder__iff__strict,axiom,
% 5.25/5.53 ( ord_less_eq_num
% 5.25/5.53 = ( ^ [A3: num,B2: num] :
% 5.25/5.53 ( ( ord_less_num @ A3 @ B2 )
% 5.25/5.53 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.order_iff_strict
% 5.25/5.53 thf(fact_5621_order_Oorder__iff__strict,axiom,
% 5.25/5.53 ( ord_less_eq_nat
% 5.25/5.53 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.53 ( ( ord_less_nat @ A3 @ B2 )
% 5.25/5.53 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.order_iff_strict
% 5.25/5.53 thf(fact_5622_order_Oorder__iff__strict,axiom,
% 5.25/5.53 ( ord_less_eq_int
% 5.25/5.53 = ( ^ [A3: int,B2: int] :
% 5.25/5.53 ( ( ord_less_int @ A3 @ B2 )
% 5.25/5.53 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.order_iff_strict
% 5.25/5.53 thf(fact_5623_order_Ostrict__iff__order,axiom,
% 5.25/5.53 ( ord_less_real
% 5.25/5.53 = ( ^ [A3: real,B2: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ A3 @ B2 )
% 5.25/5.53 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_iff_order
% 5.25/5.53 thf(fact_5624_order_Ostrict__iff__order,axiom,
% 5.25/5.53 ( ord_less_set_int
% 5.25/5.53 = ( ^ [A3: set_int,B2: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.25/5.53 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_iff_order
% 5.25/5.53 thf(fact_5625_order_Ostrict__iff__order,axiom,
% 5.25/5.53 ( ord_less_rat
% 5.25/5.53 = ( ^ [A3: rat,B2: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.25/5.53 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_iff_order
% 5.25/5.53 thf(fact_5626_order_Ostrict__iff__order,axiom,
% 5.25/5.53 ( ord_less_num
% 5.25/5.53 = ( ^ [A3: num,B2: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.25/5.53 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_iff_order
% 5.25/5.53 thf(fact_5627_order_Ostrict__iff__order,axiom,
% 5.25/5.53 ( ord_less_nat
% 5.25/5.53 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.25/5.53 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_iff_order
% 5.25/5.53 thf(fact_5628_order_Ostrict__iff__order,axiom,
% 5.25/5.53 ( ord_less_int
% 5.25/5.53 = ( ^ [A3: int,B2: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.25/5.53 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_iff_order
% 5.25/5.53 thf(fact_5629_order_Ostrict__trans1,axiom,
% 5.25/5.53 ! [A: real,B: real,C: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.53 => ( ( ord_less_real @ B @ C )
% 5.25/5.53 => ( ord_less_real @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans1
% 5.25/5.53 thf(fact_5630_order_Ostrict__trans1,axiom,
% 5.25/5.53 ! [A: set_int,B: set_int,C: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ A @ B )
% 5.25/5.53 => ( ( ord_less_set_int @ B @ C )
% 5.25/5.53 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans1
% 5.25/5.53 thf(fact_5631_order_Ostrict__trans1,axiom,
% 5.25/5.53 ! [A: rat,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_rat @ B @ C )
% 5.25/5.53 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans1
% 5.25/5.53 thf(fact_5632_order_Ostrict__trans1,axiom,
% 5.25/5.53 ! [A: num,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_num @ B @ C )
% 5.25/5.53 => ( ord_less_num @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans1
% 5.25/5.53 thf(fact_5633_order_Ostrict__trans1,axiom,
% 5.25/5.53 ! [A: nat,B: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.53 => ( ( ord_less_nat @ B @ C )
% 5.25/5.53 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans1
% 5.25/5.53 thf(fact_5634_order_Ostrict__trans1,axiom,
% 5.25/5.53 ! [A: int,B: int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.53 => ( ( ord_less_int @ B @ C )
% 5.25/5.53 => ( ord_less_int @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans1
% 5.25/5.53 thf(fact_5635_order_Ostrict__trans2,axiom,
% 5.25/5.53 ! [A: real,B: real,C: real] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_real @ B @ C )
% 5.25/5.53 => ( ord_less_real @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans2
% 5.25/5.53 thf(fact_5636_order_Ostrict__trans2,axiom,
% 5.25/5.53 ! [A: set_int,B: set_int,C: set_int] :
% 5.25/5.53 ( ( ord_less_set_int @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_set_int @ B @ C )
% 5.25/5.53 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans2
% 5.25/5.53 thf(fact_5637_order_Ostrict__trans2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans2
% 5.25/5.53 thf(fact_5638_order_Ostrict__trans2,axiom,
% 5.25/5.53 ! [A: num,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ord_less_num @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans2
% 5.25/5.53 thf(fact_5639_order_Ostrict__trans2,axiom,
% 5.25/5.53 ! [A: nat,B: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_nat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.53 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans2
% 5.25/5.53 thf(fact_5640_order_Ostrict__trans2,axiom,
% 5.25/5.53 ! [A: int,B: int,C: int] :
% 5.25/5.53 ( ( ord_less_int @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_int @ B @ C )
% 5.25/5.53 => ( ord_less_int @ A @ C ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_trans2
% 5.25/5.53 thf(fact_5641_order_Ostrict__iff__not,axiom,
% 5.25/5.53 ( ord_less_real
% 5.25/5.53 = ( ^ [A3: real,B2: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ A3 @ B2 )
% 5.25/5.53 & ~ ( ord_less_eq_real @ B2 @ A3 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_iff_not
% 5.25/5.53 thf(fact_5642_order_Ostrict__iff__not,axiom,
% 5.25/5.53 ( ord_less_set_int
% 5.25/5.53 = ( ^ [A3: set_int,B2: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.25/5.53 & ~ ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_iff_not
% 5.25/5.53 thf(fact_5643_order_Ostrict__iff__not,axiom,
% 5.25/5.53 ( ord_less_rat
% 5.25/5.53 = ( ^ [A3: rat,B2: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.25/5.53 & ~ ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_iff_not
% 5.25/5.53 thf(fact_5644_order_Ostrict__iff__not,axiom,
% 5.25/5.53 ( ord_less_num
% 5.25/5.53 = ( ^ [A3: num,B2: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.25/5.53 & ~ ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_iff_not
% 5.25/5.53 thf(fact_5645_order_Ostrict__iff__not,axiom,
% 5.25/5.53 ( ord_less_nat
% 5.25/5.53 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.25/5.53 & ~ ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_iff_not
% 5.25/5.53 thf(fact_5646_order_Ostrict__iff__not,axiom,
% 5.25/5.53 ( ord_less_int
% 5.25/5.53 = ( ^ [A3: int,B2: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.25/5.53 & ~ ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_iff_not
% 5.25/5.53 thf(fact_5647_dense__ge__bounded,axiom,
% 5.25/5.53 ! [Z: real,X3: real,Y: real] :
% 5.25/5.53 ( ( ord_less_real @ Z @ X3 )
% 5.25/5.53 => ( ! [W2: real] :
% 5.25/5.53 ( ( ord_less_real @ Z @ W2 )
% 5.25/5.53 => ( ( ord_less_real @ W2 @ X3 )
% 5.25/5.53 => ( ord_less_eq_real @ Y @ W2 ) ) )
% 5.25/5.53 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dense_ge_bounded
% 5.25/5.53 thf(fact_5648_dense__ge__bounded,axiom,
% 5.25/5.53 ! [Z: rat,X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_rat @ Z @ X3 )
% 5.25/5.53 => ( ! [W2: rat] :
% 5.25/5.53 ( ( ord_less_rat @ Z @ W2 )
% 5.25/5.53 => ( ( ord_less_rat @ W2 @ X3 )
% 5.25/5.53 => ( ord_less_eq_rat @ Y @ W2 ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dense_ge_bounded
% 5.25/5.53 thf(fact_5649_dense__le__bounded,axiom,
% 5.25/5.53 ! [X3: real,Y: real,Z: real] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ( ! [W2: real] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ W2 )
% 5.25/5.53 => ( ( ord_less_real @ W2 @ Y )
% 5.25/5.53 => ( ord_less_eq_real @ W2 @ Z ) ) )
% 5.25/5.53 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dense_le_bounded
% 5.25/5.53 thf(fact_5650_dense__le__bounded,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat,Z: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ( ! [W2: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ W2 )
% 5.25/5.53 => ( ( ord_less_rat @ W2 @ Y )
% 5.25/5.53 => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 5.25/5.53 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dense_le_bounded
% 5.25/5.53 thf(fact_5651_dual__order_Oorder__iff__strict,axiom,
% 5.25/5.53 ( ord_less_eq_real
% 5.25/5.53 = ( ^ [B2: real,A3: real] :
% 5.25/5.53 ( ( ord_less_real @ B2 @ A3 )
% 5.25/5.53 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.order_iff_strict
% 5.25/5.53 thf(fact_5652_dual__order_Oorder__iff__strict,axiom,
% 5.25/5.53 ( ord_less_eq_set_int
% 5.25/5.53 = ( ^ [B2: set_int,A3: set_int] :
% 5.25/5.53 ( ( ord_less_set_int @ B2 @ A3 )
% 5.25/5.53 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.order_iff_strict
% 5.25/5.53 thf(fact_5653_dual__order_Oorder__iff__strict,axiom,
% 5.25/5.53 ( ord_less_eq_rat
% 5.25/5.53 = ( ^ [B2: rat,A3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ B2 @ A3 )
% 5.25/5.53 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.order_iff_strict
% 5.25/5.53 thf(fact_5654_dual__order_Oorder__iff__strict,axiom,
% 5.25/5.53 ( ord_less_eq_num
% 5.25/5.53 = ( ^ [B2: num,A3: num] :
% 5.25/5.53 ( ( ord_less_num @ B2 @ A3 )
% 5.25/5.53 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.order_iff_strict
% 5.25/5.53 thf(fact_5655_dual__order_Oorder__iff__strict,axiom,
% 5.25/5.53 ( ord_less_eq_nat
% 5.25/5.53 = ( ^ [B2: nat,A3: nat] :
% 5.25/5.53 ( ( ord_less_nat @ B2 @ A3 )
% 5.25/5.53 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.order_iff_strict
% 5.25/5.53 thf(fact_5656_dual__order_Oorder__iff__strict,axiom,
% 5.25/5.53 ( ord_less_eq_int
% 5.25/5.53 = ( ^ [B2: int,A3: int] :
% 5.25/5.53 ( ( ord_less_int @ B2 @ A3 )
% 5.25/5.53 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.order_iff_strict
% 5.25/5.53 thf(fact_5657_dual__order_Ostrict__iff__order,axiom,
% 5.25/5.53 ( ord_less_real
% 5.25/5.53 = ( ^ [B2: real,A3: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ B2 @ A3 )
% 5.25/5.53 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_iff_order
% 5.25/5.53 thf(fact_5658_dual__order_Ostrict__iff__order,axiom,
% 5.25/5.53 ( ord_less_set_int
% 5.25/5.53 = ( ^ [B2: set_int,A3: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.25/5.53 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_iff_order
% 5.25/5.53 thf(fact_5659_dual__order_Ostrict__iff__order,axiom,
% 5.25/5.53 ( ord_less_rat
% 5.25/5.53 = ( ^ [B2: rat,A3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ B2 @ A3 )
% 5.25/5.53 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_iff_order
% 5.25/5.53 thf(fact_5660_dual__order_Ostrict__iff__order,axiom,
% 5.25/5.53 ( ord_less_num
% 5.25/5.53 = ( ^ [B2: num,A3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ B2 @ A3 )
% 5.25/5.53 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_iff_order
% 5.25/5.53 thf(fact_5661_dual__order_Ostrict__iff__order,axiom,
% 5.25/5.53 ( ord_less_nat
% 5.25/5.53 = ( ^ [B2: nat,A3: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ B2 @ A3 )
% 5.25/5.53 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_iff_order
% 5.25/5.53 thf(fact_5662_dual__order_Ostrict__iff__order,axiom,
% 5.25/5.53 ( ord_less_int
% 5.25/5.53 = ( ^ [B2: int,A3: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ B2 @ A3 )
% 5.25/5.53 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_iff_order
% 5.25/5.53 thf(fact_5663_dual__order_Ostrict__trans1,axiom,
% 5.25/5.53 ! [B: real,A: real,C: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ B @ A )
% 5.25/5.53 => ( ( ord_less_real @ C @ B )
% 5.25/5.53 => ( ord_less_real @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans1
% 5.25/5.53 thf(fact_5664_dual__order_Ostrict__trans1,axiom,
% 5.25/5.53 ! [B: set_int,A: set_int,C: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ B @ A )
% 5.25/5.53 => ( ( ord_less_set_int @ C @ B )
% 5.25/5.53 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans1
% 5.25/5.53 thf(fact_5665_dual__order_Ostrict__trans1,axiom,
% 5.25/5.53 ! [B: rat,A: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.53 => ( ( ord_less_rat @ C @ B )
% 5.25/5.53 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans1
% 5.25/5.53 thf(fact_5666_dual__order_Ostrict__trans1,axiom,
% 5.25/5.53 ! [B: num,A: num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ B @ A )
% 5.25/5.53 => ( ( ord_less_num @ C @ B )
% 5.25/5.53 => ( ord_less_num @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans1
% 5.25/5.53 thf(fact_5667_dual__order_Ostrict__trans1,axiom,
% 5.25/5.53 ! [B: nat,A: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.53 => ( ( ord_less_nat @ C @ B )
% 5.25/5.53 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans1
% 5.25/5.53 thf(fact_5668_dual__order_Ostrict__trans1,axiom,
% 5.25/5.53 ! [B: int,A: int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.53 => ( ( ord_less_int @ C @ B )
% 5.25/5.53 => ( ord_less_int @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans1
% 5.25/5.53 thf(fact_5669_dual__order_Ostrict__trans2,axiom,
% 5.25/5.53 ! [B: real,A: real,C: real] :
% 5.25/5.53 ( ( ord_less_real @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_real @ C @ B )
% 5.25/5.53 => ( ord_less_real @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans2
% 5.25/5.53 thf(fact_5670_dual__order_Ostrict__trans2,axiom,
% 5.25/5.53 ! [B: set_int,A: set_int,C: set_int] :
% 5.25/5.53 ( ( ord_less_set_int @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_set_int @ C @ B )
% 5.25/5.53 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans2
% 5.25/5.53 thf(fact_5671_dual__order_Ostrict__trans2,axiom,
% 5.25/5.53 ! [B: rat,A: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_rat @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_rat @ C @ B )
% 5.25/5.53 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans2
% 5.25/5.53 thf(fact_5672_dual__order_Ostrict__trans2,axiom,
% 5.25/5.53 ! [B: num,A: num,C: num] :
% 5.25/5.53 ( ( ord_less_num @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_num @ C @ B )
% 5.25/5.53 => ( ord_less_num @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans2
% 5.25/5.53 thf(fact_5673_dual__order_Ostrict__trans2,axiom,
% 5.25/5.53 ! [B: nat,A: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_nat @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_nat @ C @ B )
% 5.25/5.53 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans2
% 5.25/5.53 thf(fact_5674_dual__order_Ostrict__trans2,axiom,
% 5.25/5.53 ! [B: int,A: int,C: int] :
% 5.25/5.53 ( ( ord_less_int @ B @ A )
% 5.25/5.53 => ( ( ord_less_eq_int @ C @ B )
% 5.25/5.53 => ( ord_less_int @ C @ A ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_trans2
% 5.25/5.53 thf(fact_5675_dual__order_Ostrict__iff__not,axiom,
% 5.25/5.53 ( ord_less_real
% 5.25/5.53 = ( ^ [B2: real,A3: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ B2 @ A3 )
% 5.25/5.53 & ~ ( ord_less_eq_real @ A3 @ B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_iff_not
% 5.25/5.53 thf(fact_5676_dual__order_Ostrict__iff__not,axiom,
% 5.25/5.53 ( ord_less_set_int
% 5.25/5.53 = ( ^ [B2: set_int,A3: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.25/5.53 & ~ ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_iff_not
% 5.25/5.53 thf(fact_5677_dual__order_Ostrict__iff__not,axiom,
% 5.25/5.53 ( ord_less_rat
% 5.25/5.53 = ( ^ [B2: rat,A3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ B2 @ A3 )
% 5.25/5.53 & ~ ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_iff_not
% 5.25/5.53 thf(fact_5678_dual__order_Ostrict__iff__not,axiom,
% 5.25/5.53 ( ord_less_num
% 5.25/5.53 = ( ^ [B2: num,A3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ B2 @ A3 )
% 5.25/5.53 & ~ ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_iff_not
% 5.25/5.53 thf(fact_5679_dual__order_Ostrict__iff__not,axiom,
% 5.25/5.53 ( ord_less_nat
% 5.25/5.53 = ( ^ [B2: nat,A3: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ B2 @ A3 )
% 5.25/5.53 & ~ ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_iff_not
% 5.25/5.53 thf(fact_5680_dual__order_Ostrict__iff__not,axiom,
% 5.25/5.53 ( ord_less_int
% 5.25/5.53 = ( ^ [B2: int,A3: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ B2 @ A3 )
% 5.25/5.53 & ~ ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_iff_not
% 5.25/5.53 thf(fact_5681_order_Ostrict__implies__order,axiom,
% 5.25/5.53 ! [A: real,B: real] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_implies_order
% 5.25/5.53 thf(fact_5682_order_Ostrict__implies__order,axiom,
% 5.25/5.53 ! [A: set_int,B: set_int] :
% 5.25/5.53 ( ( ord_less_set_int @ A @ B )
% 5.25/5.53 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_implies_order
% 5.25/5.53 thf(fact_5683_order_Ostrict__implies__order,axiom,
% 5.25/5.53 ! [A: rat,B: rat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_implies_order
% 5.25/5.53 thf(fact_5684_order_Ostrict__implies__order,axiom,
% 5.25/5.53 ! [A: num,B: num] :
% 5.25/5.53 ( ( ord_less_num @ A @ B )
% 5.25/5.53 => ( ord_less_eq_num @ A @ B ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_implies_order
% 5.25/5.53 thf(fact_5685_order_Ostrict__implies__order,axiom,
% 5.25/5.53 ! [A: nat,B: nat] :
% 5.25/5.53 ( ( ord_less_nat @ A @ B )
% 5.25/5.53 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_implies_order
% 5.25/5.53 thf(fact_5686_order_Ostrict__implies__order,axiom,
% 5.25/5.53 ! [A: int,B: int] :
% 5.25/5.53 ( ( ord_less_int @ A @ B )
% 5.25/5.53 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.25/5.53
% 5.25/5.53 % order.strict_implies_order
% 5.25/5.53 thf(fact_5687_dual__order_Ostrict__implies__order,axiom,
% 5.25/5.53 ! [B: real,A: real] :
% 5.25/5.53 ( ( ord_less_real @ B @ A )
% 5.25/5.53 => ( ord_less_eq_real @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_implies_order
% 5.25/5.53 thf(fact_5688_dual__order_Ostrict__implies__order,axiom,
% 5.25/5.53 ! [B: set_int,A: set_int] :
% 5.25/5.53 ( ( ord_less_set_int @ B @ A )
% 5.25/5.53 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_implies_order
% 5.25/5.53 thf(fact_5689_dual__order_Ostrict__implies__order,axiom,
% 5.25/5.53 ! [B: rat,A: rat] :
% 5.25/5.53 ( ( ord_less_rat @ B @ A )
% 5.25/5.53 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_implies_order
% 5.25/5.53 thf(fact_5690_dual__order_Ostrict__implies__order,axiom,
% 5.25/5.53 ! [B: num,A: num] :
% 5.25/5.53 ( ( ord_less_num @ B @ A )
% 5.25/5.53 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_implies_order
% 5.25/5.53 thf(fact_5691_dual__order_Ostrict__implies__order,axiom,
% 5.25/5.53 ! [B: nat,A: nat] :
% 5.25/5.53 ( ( ord_less_nat @ B @ A )
% 5.25/5.53 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_implies_order
% 5.25/5.53 thf(fact_5692_dual__order_Ostrict__implies__order,axiom,
% 5.25/5.53 ! [B: int,A: int] :
% 5.25/5.53 ( ( ord_less_int @ B @ A )
% 5.25/5.53 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.25/5.53
% 5.25/5.53 % dual_order.strict_implies_order
% 5.25/5.53 thf(fact_5693_order__le__less,axiom,
% 5.25/5.53 ( ord_less_eq_real
% 5.25/5.53 = ( ^ [X2: real,Y6: real] :
% 5.25/5.53 ( ( ord_less_real @ X2 @ Y6 )
% 5.25/5.53 | ( X2 = Y6 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less
% 5.25/5.53 thf(fact_5694_order__le__less,axiom,
% 5.25/5.53 ( ord_less_eq_set_int
% 5.25/5.53 = ( ^ [X2: set_int,Y6: set_int] :
% 5.25/5.53 ( ( ord_less_set_int @ X2 @ Y6 )
% 5.25/5.53 | ( X2 = Y6 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less
% 5.25/5.53 thf(fact_5695_order__le__less,axiom,
% 5.25/5.53 ( ord_less_eq_rat
% 5.25/5.53 = ( ^ [X2: rat,Y6: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X2 @ Y6 )
% 5.25/5.53 | ( X2 = Y6 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less
% 5.25/5.53 thf(fact_5696_order__le__less,axiom,
% 5.25/5.53 ( ord_less_eq_num
% 5.25/5.53 = ( ^ [X2: num,Y6: num] :
% 5.25/5.53 ( ( ord_less_num @ X2 @ Y6 )
% 5.25/5.53 | ( X2 = Y6 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less
% 5.25/5.53 thf(fact_5697_order__le__less,axiom,
% 5.25/5.53 ( ord_less_eq_nat
% 5.25/5.53 = ( ^ [X2: nat,Y6: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X2 @ Y6 )
% 5.25/5.53 | ( X2 = Y6 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less
% 5.25/5.53 thf(fact_5698_order__le__less,axiom,
% 5.25/5.53 ( ord_less_eq_int
% 5.25/5.53 = ( ^ [X2: int,Y6: int] :
% 5.25/5.53 ( ( ord_less_int @ X2 @ Y6 )
% 5.25/5.53 | ( X2 = Y6 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less
% 5.25/5.53 thf(fact_5699_order__less__le,axiom,
% 5.25/5.53 ( ord_less_real
% 5.25/5.53 = ( ^ [X2: real,Y6: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ X2 @ Y6 )
% 5.25/5.53 & ( X2 != Y6 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le
% 5.25/5.53 thf(fact_5700_order__less__le,axiom,
% 5.25/5.53 ( ord_less_set_int
% 5.25/5.53 = ( ^ [X2: set_int,Y6: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ X2 @ Y6 )
% 5.25/5.53 & ( X2 != Y6 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le
% 5.25/5.53 thf(fact_5701_order__less__le,axiom,
% 5.25/5.53 ( ord_less_rat
% 5.25/5.53 = ( ^ [X2: rat,Y6: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X2 @ Y6 )
% 5.25/5.53 & ( X2 != Y6 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le
% 5.25/5.53 thf(fact_5702_order__less__le,axiom,
% 5.25/5.53 ( ord_less_num
% 5.25/5.53 = ( ^ [X2: num,Y6: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X2 @ Y6 )
% 5.25/5.53 & ( X2 != Y6 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le
% 5.25/5.53 thf(fact_5703_order__less__le,axiom,
% 5.25/5.53 ( ord_less_nat
% 5.25/5.53 = ( ^ [X2: nat,Y6: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X2 @ Y6 )
% 5.25/5.53 & ( X2 != Y6 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le
% 5.25/5.53 thf(fact_5704_order__less__le,axiom,
% 5.25/5.53 ( ord_less_int
% 5.25/5.53 = ( ^ [X2: int,Y6: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ X2 @ Y6 )
% 5.25/5.53 & ( X2 != Y6 ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le
% 5.25/5.53 thf(fact_5705_linorder__not__le,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ~ ( ord_less_eq_real @ X3 @ Y ) )
% 5.25/5.53 = ( ord_less_real @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_not_le
% 5.25/5.53 thf(fact_5706_linorder__not__le,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ~ ( ord_less_eq_rat @ X3 @ Y ) )
% 5.25/5.53 = ( ord_less_rat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_not_le
% 5.25/5.53 thf(fact_5707_linorder__not__le,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ~ ( ord_less_eq_num @ X3 @ Y ) )
% 5.25/5.53 = ( ord_less_num @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_not_le
% 5.25/5.53 thf(fact_5708_linorder__not__le,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ~ ( ord_less_eq_nat @ X3 @ Y ) )
% 5.25/5.53 = ( ord_less_nat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_not_le
% 5.25/5.53 thf(fact_5709_linorder__not__le,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ~ ( ord_less_eq_int @ X3 @ Y ) )
% 5.25/5.53 = ( ord_less_int @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_not_le
% 5.25/5.53 thf(fact_5710_linorder__not__less,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ~ ( ord_less_real @ X3 @ Y ) )
% 5.25/5.53 = ( ord_less_eq_real @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_not_less
% 5.25/5.53 thf(fact_5711_linorder__not__less,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ~ ( ord_less_rat @ X3 @ Y ) )
% 5.25/5.53 = ( ord_less_eq_rat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_not_less
% 5.25/5.53 thf(fact_5712_linorder__not__less,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ~ ( ord_less_num @ X3 @ Y ) )
% 5.25/5.53 = ( ord_less_eq_num @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_not_less
% 5.25/5.53 thf(fact_5713_linorder__not__less,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 5.25/5.53 = ( ord_less_eq_nat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_not_less
% 5.25/5.53 thf(fact_5714_linorder__not__less,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 5.25/5.53 = ( ord_less_eq_int @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_not_less
% 5.25/5.53 thf(fact_5715_order__less__imp__le,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_real @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_le
% 5.25/5.53 thf(fact_5716_order__less__imp__le,axiom,
% 5.25/5.53 ! [X3: set_int,Y: set_int] :
% 5.25/5.53 ( ( ord_less_set_int @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_set_int @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_le
% 5.25/5.53 thf(fact_5717_order__less__imp__le,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_le
% 5.25/5.53 thf(fact_5718_order__less__imp__le,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ord_less_num @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_num @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_le
% 5.25/5.53 thf(fact_5719_order__less__imp__le,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_nat @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_le
% 5.25/5.53 thf(fact_5720_order__less__imp__le,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ord_less_int @ X3 @ Y )
% 5.25/5.53 => ( ord_less_eq_int @ X3 @ Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_imp_le
% 5.25/5.53 thf(fact_5721_order__le__neq__trans,axiom,
% 5.25/5.53 ! [A: real,B: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.53 => ( ( A != B )
% 5.25/5.53 => ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_neq_trans
% 5.25/5.53 thf(fact_5722_order__le__neq__trans,axiom,
% 5.25/5.53 ! [A: set_int,B: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ A @ B )
% 5.25/5.53 => ( ( A != B )
% 5.25/5.53 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_neq_trans
% 5.25/5.53 thf(fact_5723_order__le__neq__trans,axiom,
% 5.25/5.53 ! [A: rat,B: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( A != B )
% 5.25/5.53 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_neq_trans
% 5.25/5.53 thf(fact_5724_order__le__neq__trans,axiom,
% 5.25/5.53 ! [A: num,B: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( A != B )
% 5.25/5.53 => ( ord_less_num @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_neq_trans
% 5.25/5.53 thf(fact_5725_order__le__neq__trans,axiom,
% 5.25/5.53 ! [A: nat,B: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.53 => ( ( A != B )
% 5.25/5.53 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_neq_trans
% 5.25/5.53 thf(fact_5726_order__le__neq__trans,axiom,
% 5.25/5.53 ! [A: int,B: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.53 => ( ( A != B )
% 5.25/5.53 => ( ord_less_int @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_neq_trans
% 5.25/5.53 thf(fact_5727_order__neq__le__trans,axiom,
% 5.25/5.53 ! [A: real,B: real] :
% 5.25/5.53 ( ( A != B )
% 5.25/5.53 => ( ( ord_less_eq_real @ A @ B )
% 5.25/5.53 => ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_neq_le_trans
% 5.25/5.53 thf(fact_5728_order__neq__le__trans,axiom,
% 5.25/5.53 ! [A: set_int,B: set_int] :
% 5.25/5.53 ( ( A != B )
% 5.25/5.53 => ( ( ord_less_eq_set_int @ A @ B )
% 5.25/5.53 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_neq_le_trans
% 5.25/5.53 thf(fact_5729_order__neq__le__trans,axiom,
% 5.25/5.53 ! [A: rat,B: rat] :
% 5.25/5.53 ( ( A != B )
% 5.25/5.53 => ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_neq_le_trans
% 5.25/5.53 thf(fact_5730_order__neq__le__trans,axiom,
% 5.25/5.53 ! [A: num,B: num] :
% 5.25/5.53 ( ( A != B )
% 5.25/5.53 => ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ord_less_num @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_neq_le_trans
% 5.25/5.53 thf(fact_5731_order__neq__le__trans,axiom,
% 5.25/5.53 ! [A: nat,B: nat] :
% 5.25/5.53 ( ( A != B )
% 5.25/5.53 => ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.53 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_neq_le_trans
% 5.25/5.53 thf(fact_5732_order__neq__le__trans,axiom,
% 5.25/5.53 ! [A: int,B: int] :
% 5.25/5.53 ( ( A != B )
% 5.25/5.53 => ( ( ord_less_eq_int @ A @ B )
% 5.25/5.53 => ( ord_less_int @ A @ B ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_neq_le_trans
% 5.25/5.53 thf(fact_5733_order__le__less__trans,axiom,
% 5.25/5.53 ! [X3: real,Y: real,Z: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_real @ Y @ Z )
% 5.25/5.53 => ( ord_less_real @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_trans
% 5.25/5.53 thf(fact_5734_order__le__less__trans,axiom,
% 5.25/5.53 ! [X3: set_int,Y: set_int,Z: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_set_int @ Y @ Z )
% 5.25/5.53 => ( ord_less_set_int @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_trans
% 5.25/5.53 thf(fact_5735_order__le__less__trans,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat,Z: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_rat @ Y @ Z )
% 5.25/5.53 => ( ord_less_rat @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_trans
% 5.25/5.53 thf(fact_5736_order__le__less__trans,axiom,
% 5.25/5.53 ! [X3: num,Y: num,Z: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_num @ Y @ Z )
% 5.25/5.53 => ( ord_less_num @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_trans
% 5.25/5.53 thf(fact_5737_order__le__less__trans,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat,Z: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_nat @ Y @ Z )
% 5.25/5.53 => ( ord_less_nat @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_trans
% 5.25/5.53 thf(fact_5738_order__le__less__trans,axiom,
% 5.25/5.53 ! [X3: int,Y: int,Z: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_int @ Y @ Z )
% 5.25/5.53 => ( ord_less_int @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_trans
% 5.25/5.53 thf(fact_5739_order__less__le__trans,axiom,
% 5.25/5.53 ! [X3: real,Y: real,Z: real] :
% 5.25/5.53 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_real @ Y @ Z )
% 5.25/5.53 => ( ord_less_real @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_trans
% 5.25/5.53 thf(fact_5740_order__less__le__trans,axiom,
% 5.25/5.53 ! [X3: set_int,Y: set_int,Z: set_int] :
% 5.25/5.53 ( ( ord_less_set_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_set_int @ Y @ Z )
% 5.25/5.53 => ( ord_less_set_int @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_trans
% 5.25/5.53 thf(fact_5741_order__less__le__trans,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat,Z: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_rat @ Y @ Z )
% 5.25/5.53 => ( ord_less_rat @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_trans
% 5.25/5.53 thf(fact_5742_order__less__le__trans,axiom,
% 5.25/5.53 ! [X3: num,Y: num,Z: num] :
% 5.25/5.53 ( ( ord_less_num @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_num @ Y @ Z )
% 5.25/5.53 => ( ord_less_num @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_trans
% 5.25/5.53 thf(fact_5743_order__less__le__trans,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat,Z: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.25/5.53 => ( ord_less_nat @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_trans
% 5.25/5.53 thf(fact_5744_order__less__le__trans,axiom,
% 5.25/5.53 ! [X3: int,Y: int,Z: int] :
% 5.25/5.53 ( ( ord_less_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_eq_int @ Y @ Z )
% 5.25/5.53 => ( ord_less_int @ X3 @ Z ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_trans
% 5.25/5.53 thf(fact_5745_order__le__less__subst1,axiom,
% 5.25/5.53 ! [A: real,F: real > real,B: real,C: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_real @ B @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst1
% 5.25/5.53 thf(fact_5746_order__le__less__subst1,axiom,
% 5.25/5.53 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst1
% 5.25/5.53 thf(fact_5747_order__le__less__subst1,axiom,
% 5.25/5.53 ! [A: real,F: num > real,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst1
% 5.25/5.53 thf(fact_5748_order__le__less__subst1,axiom,
% 5.25/5.53 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_nat @ B @ C )
% 5.25/5.53 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst1
% 5.25/5.53 thf(fact_5749_order__le__less__subst1,axiom,
% 5.25/5.53 ! [A: real,F: int > real,B: int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_int @ B @ C )
% 5.25/5.53 => ( ! [X5: int,Y3: int] :
% 5.25/5.53 ( ( ord_less_int @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst1
% 5.25/5.53 thf(fact_5750_order__le__less__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_real @ B @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst1
% 5.25/5.53 thf(fact_5751_order__le__less__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst1
% 5.25/5.53 thf(fact_5752_order__le__less__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst1
% 5.25/5.53 thf(fact_5753_order__le__less__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_nat @ B @ C )
% 5.25/5.53 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst1
% 5.25/5.53 thf(fact_5754_order__le__less__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_int @ B @ C )
% 5.25/5.53 => ( ! [X5: int,Y3: int] :
% 5.25/5.53 ( ( ord_less_int @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst1
% 5.25/5.53 thf(fact_5755_order__le__less__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst2
% 5.25/5.53 thf(fact_5756_order__le__less__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst2
% 5.25/5.53 thf(fact_5757_order__le__less__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst2
% 5.25/5.53 thf(fact_5758_order__le__less__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst2
% 5.25/5.53 thf(fact_5759_order__le__less__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst2
% 5.25/5.53 thf(fact_5760_order__le__less__subst2,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > real,C: real] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst2
% 5.25/5.53 thf(fact_5761_order__le__less__subst2,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst2
% 5.25/5.53 thf(fact_5762_order__le__less__subst2,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > num,C: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst2
% 5.25/5.53 thf(fact_5763_order__le__less__subst2,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst2
% 5.25/5.53 thf(fact_5764_order__le__less__subst2,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > int,C: int] :
% 5.25/5.53 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_less_subst2
% 5.25/5.53 thf(fact_5765_order__less__le__subst1,axiom,
% 5.25/5.53 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst1
% 5.25/5.53 thf(fact_5766_order__less__le__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst1
% 5.25/5.53 thf(fact_5767_order__less__le__subst1,axiom,
% 5.25/5.53 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst1
% 5.25/5.53 thf(fact_5768_order__less__le__subst1,axiom,
% 5.25/5.53 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst1
% 5.25/5.53 thf(fact_5769_order__less__le__subst1,axiom,
% 5.25/5.53 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.25/5.53 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst1
% 5.25/5.53 thf(fact_5770_order__less__le__subst1,axiom,
% 5.25/5.53 ! [A: real,F: num > real,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst1
% 5.25/5.53 thf(fact_5771_order__less__le__subst1,axiom,
% 5.25/5.53 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst1
% 5.25/5.53 thf(fact_5772_order__less__le__subst1,axiom,
% 5.25/5.53 ! [A: num,F: num > num,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst1
% 5.25/5.53 thf(fact_5773_order__less__le__subst1,axiom,
% 5.25/5.53 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst1
% 5.25/5.53 thf(fact_5774_order__less__le__subst1,axiom,
% 5.25/5.53 ! [A: int,F: num > int,B: num,C: num] :
% 5.25/5.53 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.25/5.53 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst1
% 5.25/5.53 thf(fact_5775_order__less__le__subst2,axiom,
% 5.25/5.53 ! [A: real,B: real,F: real > real,C: real] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst2
% 5.25/5.53 thf(fact_5776_order__less__le__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst2
% 5.25/5.53 thf(fact_5777_order__less__le__subst2,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > real,C: real] :
% 5.25/5.53 ( ( ord_less_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst2
% 5.25/5.53 thf(fact_5778_order__less__le__subst2,axiom,
% 5.25/5.53 ! [A: nat,B: nat,F: nat > real,C: real] :
% 5.25/5.53 ( ( ord_less_nat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst2
% 5.25/5.53 thf(fact_5779_order__less__le__subst2,axiom,
% 5.25/5.53 ! [A: int,B: int,F: int > real,C: real] :
% 5.25/5.53 ( ( ord_less_int @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: int,Y3: int] :
% 5.25/5.53 ( ( ord_less_int @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst2
% 5.25/5.53 thf(fact_5780_order__less__le__subst2,axiom,
% 5.25/5.53 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_real @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: real,Y3: real] :
% 5.25/5.53 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst2
% 5.25/5.53 thf(fact_5781_order__less__le__subst2,axiom,
% 5.25/5.53 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_rat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.53 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst2
% 5.25/5.53 thf(fact_5782_order__less__le__subst2,axiom,
% 5.25/5.53 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_num @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: num,Y3: num] :
% 5.25/5.53 ( ( ord_less_num @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst2
% 5.25/5.53 thf(fact_5783_order__less__le__subst2,axiom,
% 5.25/5.53 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_nat @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.53 ( ( ord_less_nat @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst2
% 5.25/5.53 thf(fact_5784_order__less__le__subst2,axiom,
% 5.25/5.53 ! [A: int,B: int,F: int > rat,C: rat] :
% 5.25/5.53 ( ( ord_less_int @ A @ B )
% 5.25/5.53 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.53 => ( ! [X5: int,Y3: int] :
% 5.25/5.53 ( ( ord_less_int @ X5 @ Y3 )
% 5.25/5.53 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.53 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_less_le_subst2
% 5.25/5.53 thf(fact_5785_linorder__le__less__linear,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.53 | ( ord_less_real @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_le_less_linear
% 5.25/5.53 thf(fact_5786_linorder__le__less__linear,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.53 | ( ord_less_rat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_le_less_linear
% 5.25/5.53 thf(fact_5787_linorder__le__less__linear,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X3 @ Y )
% 5.25/5.53 | ( ord_less_num @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_le_less_linear
% 5.25/5.53 thf(fact_5788_linorder__le__less__linear,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X3 @ Y )
% 5.25/5.53 | ( ord_less_nat @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_le_less_linear
% 5.25/5.53 thf(fact_5789_linorder__le__less__linear,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ X3 @ Y )
% 5.25/5.53 | ( ord_less_int @ Y @ X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % linorder_le_less_linear
% 5.25/5.53 thf(fact_5790_order__le__imp__less__or__eq,axiom,
% 5.25/5.53 ! [X3: real,Y: real] :
% 5.25/5.53 ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_real @ X3 @ Y )
% 5.25/5.53 | ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_imp_less_or_eq
% 5.25/5.53 thf(fact_5791_order__le__imp__less__or__eq,axiom,
% 5.25/5.53 ! [X3: set_int,Y: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_set_int @ X3 @ Y )
% 5.25/5.53 | ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_imp_less_or_eq
% 5.25/5.53 thf(fact_5792_order__le__imp__less__or__eq,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_rat @ X3 @ Y )
% 5.25/5.53 | ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_imp_less_or_eq
% 5.25/5.53 thf(fact_5793_order__le__imp__less__or__eq,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_num @ X3 @ Y )
% 5.25/5.53 | ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_imp_less_or_eq
% 5.25/5.53 thf(fact_5794_order__le__imp__less__or__eq,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.53 | ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_imp_less_or_eq
% 5.25/5.53 thf(fact_5795_order__le__imp__less__or__eq,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_less_int @ X3 @ Y )
% 5.25/5.53 | ( X3 = Y ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % order_le_imp_less_or_eq
% 5.25/5.53 thf(fact_5796_max__absorb2,axiom,
% 5.25/5.53 ! [X3: extended_enat,Y: extended_enat] :
% 5.25/5.53 ( ( ord_le2932123472753598470d_enat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_ma741700101516333627d_enat @ X3 @ Y )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_absorb2
% 5.25/5.53 thf(fact_5797_max__absorb2,axiom,
% 5.25/5.53 ! [X3: set_int,Y: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_max_set_int @ X3 @ Y )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_absorb2
% 5.25/5.53 thf(fact_5798_max__absorb2,axiom,
% 5.25/5.53 ! [X3: rat,Y: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_max_rat @ X3 @ Y )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_absorb2
% 5.25/5.53 thf(fact_5799_max__absorb2,axiom,
% 5.25/5.53 ! [X3: num,Y: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ X3 @ Y )
% 5.25/5.53 => ( ( ord_max_num @ X3 @ Y )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_absorb2
% 5.25/5.53 thf(fact_5800_max__absorb2,axiom,
% 5.25/5.53 ! [X3: nat,Y: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ X3 @ Y )
% 5.25/5.53 => ( ( ord_max_nat @ X3 @ Y )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_absorb2
% 5.25/5.53 thf(fact_5801_max__absorb2,axiom,
% 5.25/5.53 ! [X3: int,Y: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ X3 @ Y )
% 5.25/5.53 => ( ( ord_max_int @ X3 @ Y )
% 5.25/5.53 = Y ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_absorb2
% 5.25/5.53 thf(fact_5802_max__absorb1,axiom,
% 5.25/5.53 ! [Y: extended_enat,X3: extended_enat] :
% 5.25/5.53 ( ( ord_le2932123472753598470d_enat @ Y @ X3 )
% 5.25/5.53 => ( ( ord_ma741700101516333627d_enat @ X3 @ Y )
% 5.25/5.53 = X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_absorb1
% 5.25/5.53 thf(fact_5803_max__absorb1,axiom,
% 5.25/5.53 ! [Y: set_int,X3: set_int] :
% 5.25/5.53 ( ( ord_less_eq_set_int @ Y @ X3 )
% 5.25/5.53 => ( ( ord_max_set_int @ X3 @ Y )
% 5.25/5.53 = X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_absorb1
% 5.25/5.53 thf(fact_5804_max__absorb1,axiom,
% 5.25/5.53 ! [Y: rat,X3: rat] :
% 5.25/5.53 ( ( ord_less_eq_rat @ Y @ X3 )
% 5.25/5.53 => ( ( ord_max_rat @ X3 @ Y )
% 5.25/5.53 = X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_absorb1
% 5.25/5.53 thf(fact_5805_max__absorb1,axiom,
% 5.25/5.53 ! [Y: num,X3: num] :
% 5.25/5.53 ( ( ord_less_eq_num @ Y @ X3 )
% 5.25/5.53 => ( ( ord_max_num @ X3 @ Y )
% 5.25/5.53 = X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_absorb1
% 5.25/5.53 thf(fact_5806_max__absorb1,axiom,
% 5.25/5.53 ! [Y: nat,X3: nat] :
% 5.25/5.53 ( ( ord_less_eq_nat @ Y @ X3 )
% 5.25/5.53 => ( ( ord_max_nat @ X3 @ Y )
% 5.25/5.53 = X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_absorb1
% 5.25/5.53 thf(fact_5807_max__absorb1,axiom,
% 5.25/5.53 ! [Y: int,X3: int] :
% 5.25/5.53 ( ( ord_less_eq_int @ Y @ X3 )
% 5.25/5.53 => ( ( ord_max_int @ X3 @ Y )
% 5.25/5.53 = X3 ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_absorb1
% 5.25/5.53 thf(fact_5808_max__def,axiom,
% 5.25/5.53 ( ord_ma741700101516333627d_enat
% 5.25/5.53 = ( ^ [A3: extended_enat,B2: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_def
% 5.25/5.53 thf(fact_5809_max__def,axiom,
% 5.25/5.53 ( ord_max_set_int
% 5.25/5.53 = ( ^ [A3: set_int,B2: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_def
% 5.25/5.53 thf(fact_5810_max__def,axiom,
% 5.25/5.53 ( ord_max_rat
% 5.25/5.53 = ( ^ [A3: rat,B2: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_def
% 5.25/5.53 thf(fact_5811_max__def,axiom,
% 5.25/5.53 ( ord_max_num
% 5.25/5.53 = ( ^ [A3: num,B2: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_def
% 5.25/5.53 thf(fact_5812_max__def,axiom,
% 5.25/5.53 ( ord_max_nat
% 5.25/5.53 = ( ^ [A3: nat,B2: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_def
% 5.25/5.53 thf(fact_5813_max__def,axiom,
% 5.25/5.53 ( ord_max_int
% 5.25/5.53 = ( ^ [A3: int,B2: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % max_def
% 5.25/5.53 thf(fact_5814_option_Osize__gen_I1_J,axiom,
% 5.25/5.53 ! [X3: product_prod_nat_nat > nat] :
% 5.25/5.53 ( ( size_o8335143837870341156at_nat @ X3 @ none_P5556105721700978146at_nat )
% 5.25/5.53 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.53
% 5.25/5.53 % option.size_gen(1)
% 5.25/5.53 thf(fact_5815_option_Osize__gen_I1_J,axiom,
% 5.25/5.53 ! [X3: num > nat] :
% 5.25/5.53 ( ( size_option_num @ X3 @ none_num )
% 5.25/5.53 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.53
% 5.25/5.53 % option.size_gen(1)
% 5.25/5.53 thf(fact_5816_floor__exists,axiom,
% 5.25/5.53 ! [X3: real] :
% 5.25/5.53 ? [Z2: int] :
% 5.25/5.53 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X3 )
% 5.25/5.53 & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % floor_exists
% 5.25/5.53 thf(fact_5817_floor__exists,axiom,
% 5.25/5.53 ! [X3: rat] :
% 5.25/5.53 ? [Z2: int] :
% 5.25/5.53 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X3 )
% 5.25/5.53 & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % floor_exists
% 5.25/5.53 thf(fact_5818_floor__exists1,axiom,
% 5.25/5.53 ! [X3: real] :
% 5.25/5.53 ? [X5: int] :
% 5.25/5.53 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X5 ) @ X3 )
% 5.25/5.53 & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ X5 @ one_one_int ) ) )
% 5.25/5.53 & ! [Y4: int] :
% 5.25/5.53 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ X3 )
% 5.25/5.53 & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 5.25/5.53 => ( Y4 = X5 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % floor_exists1
% 5.25/5.53 thf(fact_5819_floor__exists1,axiom,
% 5.25/5.53 ! [X3: rat] :
% 5.25/5.53 ? [X5: int] :
% 5.25/5.53 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X5 ) @ X3 )
% 5.25/5.53 & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X5 @ one_one_int ) ) )
% 5.25/5.53 & ! [Y4: int] :
% 5.25/5.53 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ X3 )
% 5.25/5.53 & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 5.25/5.53 => ( Y4 = X5 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % floor_exists1
% 5.25/5.53 thf(fact_5820_divmod__BitM__2__eq,axiom,
% 5.25/5.53 ! [M: num] :
% 5.25/5.53 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.25/5.53 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.25/5.53
% 5.25/5.53 % divmod_BitM_2_eq
% 5.25/5.53 thf(fact_5821_divmod__algorithm__code_I6_J,axiom,
% 5.25/5.53 ! [M: num,N: num] :
% 5.25/5.53 ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.25/5.53 = ( produc4245557441103728435nt_int
% 5.25/5.53 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 5.25/5.53 @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % divmod_algorithm_code(6)
% 5.25/5.53 thf(fact_5822_divmod__algorithm__code_I6_J,axiom,
% 5.25/5.53 ! [M: num,N: num] :
% 5.25/5.53 ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.25/5.53 = ( produc2626176000494625587at_nat
% 5.25/5.53 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 5.25/5.53 @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % divmod_algorithm_code(6)
% 5.25/5.53 thf(fact_5823_divmod__algorithm__code_I6_J,axiom,
% 5.25/5.53 ! [M: num,N: num] :
% 5.25/5.53 ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.25/5.53 = ( produc6916734918728496179nteger
% 5.25/5.53 @ ^ [Q4: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q4 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 5.25/5.53 @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % divmod_algorithm_code(6)
% 5.25/5.53 thf(fact_5824_flip__bit__0,axiom,
% 5.25/5.53 ! [A: code_integer] :
% 5.25/5.53 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.25/5.53 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % flip_bit_0
% 5.25/5.53 thf(fact_5825_flip__bit__0,axiom,
% 5.25/5.53 ! [A: int] :
% 5.25/5.53 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.25/5.53 = ( 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 ) ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % flip_bit_0
% 5.25/5.53 thf(fact_5826_flip__bit__0,axiom,
% 5.25/5.53 ! [A: nat] :
% 5.25/5.53 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.25/5.53 = ( 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 ) ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % flip_bit_0
% 5.25/5.53 thf(fact_5827_set__decode__0,axiom,
% 5.25/5.53 ! [X3: nat] :
% 5.25/5.53 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X3 ) )
% 5.25/5.53 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X3 ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % set_decode_0
% 5.25/5.53 thf(fact_5828_set__decode__Suc,axiom,
% 5.25/5.53 ! [N: nat,X3: nat] :
% 5.25/5.53 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X3 ) )
% 5.25/5.53 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % set_decode_Suc
% 5.25/5.53 thf(fact_5829_of__bool__less__eq__iff,axiom,
% 5.25/5.53 ! [P: $o,Q: $o] :
% 5.25/5.53 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.25/5.53 = ( P
% 5.25/5.53 => Q ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_less_eq_iff
% 5.25/5.53 thf(fact_5830_of__bool__less__eq__iff,axiom,
% 5.25/5.53 ! [P: $o,Q: $o] :
% 5.25/5.53 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.25/5.53 = ( P
% 5.25/5.53 => Q ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_less_eq_iff
% 5.25/5.53 thf(fact_5831_of__bool__less__eq__iff,axiom,
% 5.25/5.53 ! [P: $o,Q: $o] :
% 5.25/5.53 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.25/5.53 = ( P
% 5.25/5.53 => Q ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_less_eq_iff
% 5.25/5.53 thf(fact_5832_of__bool__less__eq__iff,axiom,
% 5.25/5.53 ! [P: $o,Q: $o] :
% 5.25/5.53 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.25/5.53 = ( P
% 5.25/5.53 => Q ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_less_eq_iff
% 5.25/5.53 thf(fact_5833_of__bool__eq_I1_J,axiom,
% 5.25/5.53 ( ( zero_n1201886186963655149omplex @ $false )
% 5.25/5.53 = zero_zero_complex ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq(1)
% 5.25/5.53 thf(fact_5834_of__bool__eq_I1_J,axiom,
% 5.25/5.53 ( ( zero_n3304061248610475627l_real @ $false )
% 5.25/5.53 = zero_zero_real ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq(1)
% 5.25/5.53 thf(fact_5835_of__bool__eq_I1_J,axiom,
% 5.25/5.53 ( ( zero_n2052037380579107095ol_rat @ $false )
% 5.25/5.53 = zero_zero_rat ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq(1)
% 5.25/5.53 thf(fact_5836_of__bool__eq_I1_J,axiom,
% 5.25/5.53 ( ( zero_n2687167440665602831ol_nat @ $false )
% 5.25/5.53 = zero_zero_nat ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq(1)
% 5.25/5.53 thf(fact_5837_of__bool__eq_I1_J,axiom,
% 5.25/5.53 ( ( zero_n2684676970156552555ol_int @ $false )
% 5.25/5.53 = zero_zero_int ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq(1)
% 5.25/5.53 thf(fact_5838_of__bool__eq_I1_J,axiom,
% 5.25/5.53 ( ( zero_n356916108424825756nteger @ $false )
% 5.25/5.53 = zero_z3403309356797280102nteger ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq(1)
% 5.25/5.53 thf(fact_5839_of__bool__eq__0__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.25/5.53 = zero_zero_complex )
% 5.25/5.53 = ~ P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq_0_iff
% 5.25/5.53 thf(fact_5840_of__bool__eq__0__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.25/5.53 = zero_zero_real )
% 5.25/5.53 = ~ P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq_0_iff
% 5.25/5.53 thf(fact_5841_of__bool__eq__0__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.25/5.53 = zero_zero_rat )
% 5.25/5.53 = ~ P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq_0_iff
% 5.25/5.53 thf(fact_5842_of__bool__eq__0__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.25/5.53 = zero_zero_nat )
% 5.25/5.53 = ~ P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq_0_iff
% 5.25/5.53 thf(fact_5843_of__bool__eq__0__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.25/5.53 = zero_zero_int )
% 5.25/5.53 = ~ P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq_0_iff
% 5.25/5.53 thf(fact_5844_of__bool__eq__0__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ( zero_n356916108424825756nteger @ P )
% 5.25/5.53 = zero_z3403309356797280102nteger )
% 5.25/5.53 = ~ P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq_0_iff
% 5.25/5.53 thf(fact_5845_of__bool__less__iff,axiom,
% 5.25/5.53 ! [P: $o,Q: $o] :
% 5.25/5.53 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.25/5.53 = ( ~ P
% 5.25/5.53 & Q ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_less_iff
% 5.25/5.53 thf(fact_5846_of__bool__less__iff,axiom,
% 5.25/5.53 ! [P: $o,Q: $o] :
% 5.25/5.53 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.25/5.53 = ( ~ P
% 5.25/5.53 & Q ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_less_iff
% 5.25/5.53 thf(fact_5847_of__bool__less__iff,axiom,
% 5.25/5.53 ! [P: $o,Q: $o] :
% 5.25/5.53 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.25/5.53 = ( ~ P
% 5.25/5.53 & Q ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_less_iff
% 5.25/5.53 thf(fact_5848_of__bool__less__iff,axiom,
% 5.25/5.53 ! [P: $o,Q: $o] :
% 5.25/5.53 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.25/5.53 = ( ~ P
% 5.25/5.53 & Q ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_less_iff
% 5.25/5.53 thf(fact_5849_of__bool__less__iff,axiom,
% 5.25/5.53 ! [P: $o,Q: $o] :
% 5.25/5.53 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.25/5.53 = ( ~ P
% 5.25/5.53 & Q ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_less_iff
% 5.25/5.53 thf(fact_5850_of__bool__eq__1__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.25/5.53 = one_one_complex )
% 5.25/5.53 = P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq_1_iff
% 5.25/5.53 thf(fact_5851_of__bool__eq__1__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.25/5.53 = one_one_real )
% 5.25/5.53 = P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq_1_iff
% 5.25/5.53 thf(fact_5852_of__bool__eq__1__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.25/5.53 = one_one_rat )
% 5.25/5.53 = P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq_1_iff
% 5.25/5.53 thf(fact_5853_of__bool__eq__1__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.25/5.53 = one_one_nat )
% 5.25/5.53 = P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq_1_iff
% 5.25/5.53 thf(fact_5854_of__bool__eq__1__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.25/5.53 = one_one_int )
% 5.25/5.53 = P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq_1_iff
% 5.25/5.53 thf(fact_5855_of__bool__eq__1__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ( zero_n356916108424825756nteger @ P )
% 5.25/5.53 = one_one_Code_integer )
% 5.25/5.53 = P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq_1_iff
% 5.25/5.53 thf(fact_5856_of__bool__eq_I2_J,axiom,
% 5.25/5.53 ( ( zero_n1201886186963655149omplex @ $true )
% 5.25/5.53 = one_one_complex ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq(2)
% 5.25/5.53 thf(fact_5857_of__bool__eq_I2_J,axiom,
% 5.25/5.53 ( ( zero_n3304061248610475627l_real @ $true )
% 5.25/5.53 = one_one_real ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq(2)
% 5.25/5.53 thf(fact_5858_of__bool__eq_I2_J,axiom,
% 5.25/5.53 ( ( zero_n2052037380579107095ol_rat @ $true )
% 5.25/5.53 = one_one_rat ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq(2)
% 5.25/5.53 thf(fact_5859_of__bool__eq_I2_J,axiom,
% 5.25/5.53 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.25/5.53 = one_one_nat ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq(2)
% 5.25/5.53 thf(fact_5860_of__bool__eq_I2_J,axiom,
% 5.25/5.53 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.25/5.53 = one_one_int ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq(2)
% 5.25/5.53 thf(fact_5861_of__bool__eq_I2_J,axiom,
% 5.25/5.53 ( ( zero_n356916108424825756nteger @ $true )
% 5.25/5.53 = one_one_Code_integer ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq(2)
% 5.25/5.53 thf(fact_5862_of__bool__or__iff,axiom,
% 5.25/5.53 ! [P: $o,Q: $o] :
% 5.25/5.53 ( ( zero_n2687167440665602831ol_nat
% 5.25/5.53 @ ( P
% 5.25/5.53 | Q ) )
% 5.25/5.53 = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_or_iff
% 5.25/5.53 thf(fact_5863_of__bool__or__iff,axiom,
% 5.25/5.53 ! [P: $o,Q: $o] :
% 5.25/5.53 ( ( zero_n2684676970156552555ol_int
% 5.25/5.53 @ ( P
% 5.25/5.53 | Q ) )
% 5.25/5.53 = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_or_iff
% 5.25/5.53 thf(fact_5864_of__bool__or__iff,axiom,
% 5.25/5.53 ! [P: $o,Q: $o] :
% 5.25/5.53 ( ( zero_n356916108424825756nteger
% 5.25/5.53 @ ( P
% 5.25/5.53 | Q ) )
% 5.25/5.53 = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_or_iff
% 5.25/5.53 thf(fact_5865_zero__less__of__bool__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.25/5.53 = P ) ).
% 5.25/5.53
% 5.25/5.53 % zero_less_of_bool_iff
% 5.25/5.53 thf(fact_5866_zero__less__of__bool__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.25/5.53 = P ) ).
% 5.25/5.53
% 5.25/5.53 % zero_less_of_bool_iff
% 5.25/5.53 thf(fact_5867_zero__less__of__bool__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.25/5.53 = P ) ).
% 5.25/5.53
% 5.25/5.53 % zero_less_of_bool_iff
% 5.25/5.53 thf(fact_5868_zero__less__of__bool__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.25/5.53 = P ) ).
% 5.25/5.53
% 5.25/5.53 % zero_less_of_bool_iff
% 5.25/5.53 thf(fact_5869_zero__less__of__bool__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.25/5.53 = P ) ).
% 5.25/5.53
% 5.25/5.53 % zero_less_of_bool_iff
% 5.25/5.53 thf(fact_5870_of__bool__less__one__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.25/5.53 = ~ P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_less_one_iff
% 5.25/5.53 thf(fact_5871_of__bool__less__one__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.25/5.53 = ~ P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_less_one_iff
% 5.25/5.53 thf(fact_5872_of__bool__less__one__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.25/5.53 = ~ P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_less_one_iff
% 5.25/5.53 thf(fact_5873_of__bool__less__one__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.25/5.53 = ~ P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_less_one_iff
% 5.25/5.53 thf(fact_5874_of__bool__less__one__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.25/5.53 = ~ P ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_less_one_iff
% 5.25/5.53 thf(fact_5875_of__bool__not__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.25/5.53 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_not_iff
% 5.25/5.53 thf(fact_5876_of__bool__not__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.25/5.53 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_not_iff
% 5.25/5.53 thf(fact_5877_of__bool__not__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 5.25/5.53 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_not_iff
% 5.25/5.53 thf(fact_5878_of__bool__not__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.25/5.53 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_not_iff
% 5.25/5.53 thf(fact_5879_of__bool__not__iff,axiom,
% 5.25/5.53 ! [P: $o] :
% 5.25/5.53 ( ( zero_n356916108424825756nteger @ ~ P )
% 5.25/5.53 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_not_iff
% 5.25/5.53 thf(fact_5880_Suc__0__mod__eq,axiom,
% 5.25/5.53 ! [N: nat] :
% 5.25/5.53 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.25/5.53 = ( zero_n2687167440665602831ol_nat
% 5.25/5.53 @ ( N
% 5.25/5.53 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % Suc_0_mod_eq
% 5.25/5.53 thf(fact_5881_dbl__dec__simps_I5_J,axiom,
% 5.25/5.53 ! [K: num] :
% 5.25/5.53 ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.25/5.53 = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dbl_dec_simps(5)
% 5.25/5.53 thf(fact_5882_dbl__dec__simps_I5_J,axiom,
% 5.25/5.53 ! [K: num] :
% 5.25/5.53 ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 5.25/5.53 = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dbl_dec_simps(5)
% 5.25/5.53 thf(fact_5883_dbl__dec__simps_I5_J,axiom,
% 5.25/5.53 ! [K: num] :
% 5.25/5.53 ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 5.25/5.53 = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dbl_dec_simps(5)
% 5.25/5.53 thf(fact_5884_dbl__dec__simps_I5_J,axiom,
% 5.25/5.53 ! [K: num] :
% 5.25/5.53 ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 5.25/5.53 = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % dbl_dec_simps(5)
% 5.25/5.53 thf(fact_5885_pred__numeral__simps_I2_J,axiom,
% 5.25/5.53 ! [K: num] :
% 5.25/5.53 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.25/5.53 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % pred_numeral_simps(2)
% 5.25/5.53 thf(fact_5886_Divides_Oadjust__div__eq,axiom,
% 5.25/5.53 ! [Q2: int,R2: int] :
% 5.25/5.53 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.25/5.53 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % Divides.adjust_div_eq
% 5.25/5.53 thf(fact_5887_odd__of__bool__self,axiom,
% 5.25/5.53 ! [P2: $o] :
% 5.25/5.53 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P2 ) ) )
% 5.25/5.53 = P2 ) ).
% 5.25/5.53
% 5.25/5.53 % odd_of_bool_self
% 5.25/5.53 thf(fact_5888_odd__of__bool__self,axiom,
% 5.25/5.53 ! [P2: $o] :
% 5.25/5.53 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P2 ) ) )
% 5.25/5.53 = P2 ) ).
% 5.25/5.53
% 5.25/5.53 % odd_of_bool_self
% 5.25/5.53 thf(fact_5889_odd__of__bool__self,axiom,
% 5.25/5.53 ! [P2: $o] :
% 5.25/5.53 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P2 ) ) )
% 5.25/5.53 = P2 ) ).
% 5.25/5.53
% 5.25/5.53 % odd_of_bool_self
% 5.25/5.53 thf(fact_5890_of__bool__half__eq__0,axiom,
% 5.25/5.53 ! [B: $o] :
% 5.25/5.53 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.53 = zero_zero_nat ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_half_eq_0
% 5.25/5.53 thf(fact_5891_of__bool__half__eq__0,axiom,
% 5.25/5.53 ! [B: $o] :
% 5.25/5.53 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.53 = zero_zero_int ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_half_eq_0
% 5.25/5.53 thf(fact_5892_of__bool__half__eq__0,axiom,
% 5.25/5.53 ! [B: $o] :
% 5.25/5.53 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.53 = zero_z3403309356797280102nteger ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_half_eq_0
% 5.25/5.53 thf(fact_5893_divmod__algorithm__code_I5_J,axiom,
% 5.25/5.53 ! [M: num,N: num] :
% 5.25/5.53 ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.25/5.53 = ( produc4245557441103728435nt_int
% 5.25/5.53 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 5.25/5.53 @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % divmod_algorithm_code(5)
% 5.25/5.53 thf(fact_5894_divmod__algorithm__code_I5_J,axiom,
% 5.25/5.53 ! [M: num,N: num] :
% 5.25/5.53 ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.25/5.53 = ( produc2626176000494625587at_nat
% 5.25/5.53 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 5.25/5.53 @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % divmod_algorithm_code(5)
% 5.25/5.53 thf(fact_5895_divmod__algorithm__code_I5_J,axiom,
% 5.25/5.53 ! [M: num,N: num] :
% 5.25/5.53 ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.25/5.53 = ( produc6916734918728496179nteger
% 5.25/5.53 @ ^ [Q4: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) )
% 5.25/5.53 @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % divmod_algorithm_code(5)
% 5.25/5.53 thf(fact_5896_one__div__2__pow__eq,axiom,
% 5.25/5.53 ! [N: nat] :
% 5.25/5.53 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.53 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % one_div_2_pow_eq
% 5.25/5.53 thf(fact_5897_one__div__2__pow__eq,axiom,
% 5.25/5.53 ! [N: nat] :
% 5.25/5.53 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.53 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % one_div_2_pow_eq
% 5.25/5.53 thf(fact_5898_one__div__2__pow__eq,axiom,
% 5.25/5.53 ! [N: nat] :
% 5.25/5.53 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.53 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % one_div_2_pow_eq
% 5.25/5.53 thf(fact_5899_bits__1__div__exp,axiom,
% 5.25/5.53 ! [N: nat] :
% 5.25/5.53 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.53 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % bits_1_div_exp
% 5.25/5.53 thf(fact_5900_bits__1__div__exp,axiom,
% 5.25/5.53 ! [N: nat] :
% 5.25/5.53 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.53 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % bits_1_div_exp
% 5.25/5.53 thf(fact_5901_bits__1__div__exp,axiom,
% 5.25/5.53 ! [N: nat] :
% 5.25/5.53 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.53 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % bits_1_div_exp
% 5.25/5.53 thf(fact_5902_one__mod__2__pow__eq,axiom,
% 5.25/5.53 ! [N: nat] :
% 5.25/5.53 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.53 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % one_mod_2_pow_eq
% 5.25/5.53 thf(fact_5903_one__mod__2__pow__eq,axiom,
% 5.25/5.53 ! [N: nat] :
% 5.25/5.53 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.53 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % one_mod_2_pow_eq
% 5.25/5.53 thf(fact_5904_one__mod__2__pow__eq,axiom,
% 5.25/5.53 ! [N: nat] :
% 5.25/5.53 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.53 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.53
% 5.25/5.53 % one_mod_2_pow_eq
% 5.25/5.53 thf(fact_5905_of__bool__eq__iff,axiom,
% 5.25/5.53 ! [P2: $o,Q2: $o] :
% 5.25/5.53 ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 5.25/5.53 = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 5.25/5.53 = ( P2 = Q2 ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq_iff
% 5.25/5.53 thf(fact_5906_of__bool__eq__iff,axiom,
% 5.25/5.53 ! [P2: $o,Q2: $o] :
% 5.25/5.53 ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 5.25/5.53 = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 5.25/5.53 = ( P2 = Q2 ) ) ).
% 5.25/5.53
% 5.25/5.53 % of_bool_eq_iff
% 5.25/5.53 thf(fact_5907_of__bool__eq__iff,axiom,
% 5.25/5.53 ! [P2: $o,Q2: $o] :
% 5.25/5.53 ( ( ( zero_n356916108424825756nteger @ P2 )
% 5.25/5.53 = ( zero_n356916108424825756nteger @ Q2 ) )
% 5.25/5.53 = ( P2 = Q2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_eq_iff
% 5.25/5.54 thf(fact_5908_of__bool__conj,axiom,
% 5.25/5.54 ! [P: $o,Q: $o] :
% 5.25/5.54 ( ( zero_n3304061248610475627l_real
% 5.25/5.54 @ ( P
% 5.25/5.54 & Q ) )
% 5.25/5.54 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_conj
% 5.25/5.54 thf(fact_5909_of__bool__conj,axiom,
% 5.25/5.54 ! [P: $o,Q: $o] :
% 5.25/5.54 ( ( zero_n2052037380579107095ol_rat
% 5.25/5.54 @ ( P
% 5.25/5.54 & Q ) )
% 5.25/5.54 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_conj
% 5.25/5.54 thf(fact_5910_of__bool__conj,axiom,
% 5.25/5.54 ! [P: $o,Q: $o] :
% 5.25/5.54 ( ( zero_n2687167440665602831ol_nat
% 5.25/5.54 @ ( P
% 5.25/5.54 & Q ) )
% 5.25/5.54 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_conj
% 5.25/5.54 thf(fact_5911_of__bool__conj,axiom,
% 5.25/5.54 ! [P: $o,Q: $o] :
% 5.25/5.54 ( ( zero_n2684676970156552555ol_int
% 5.25/5.54 @ ( P
% 5.25/5.54 & Q ) )
% 5.25/5.54 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_conj
% 5.25/5.54 thf(fact_5912_of__bool__conj,axiom,
% 5.25/5.54 ! [P: $o,Q: $o] :
% 5.25/5.54 ( ( zero_n356916108424825756nteger
% 5.25/5.54 @ ( P
% 5.25/5.54 & Q ) )
% 5.25/5.54 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_conj
% 5.25/5.54 thf(fact_5913_semiring__norm_I26_J,axiom,
% 5.25/5.54 ( ( bitM @ one )
% 5.25/5.54 = one ) ).
% 5.25/5.54
% 5.25/5.54 % semiring_norm(26)
% 5.25/5.54 thf(fact_5914_zero__less__eq__of__bool,axiom,
% 5.25/5.54 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.25/5.54
% 5.25/5.54 % zero_less_eq_of_bool
% 5.25/5.54 thf(fact_5915_zero__less__eq__of__bool,axiom,
% 5.25/5.54 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.25/5.54
% 5.25/5.54 % zero_less_eq_of_bool
% 5.25/5.54 thf(fact_5916_zero__less__eq__of__bool,axiom,
% 5.25/5.54 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.25/5.54
% 5.25/5.54 % zero_less_eq_of_bool
% 5.25/5.54 thf(fact_5917_zero__less__eq__of__bool,axiom,
% 5.25/5.54 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.25/5.54
% 5.25/5.54 % zero_less_eq_of_bool
% 5.25/5.54 thf(fact_5918_zero__less__eq__of__bool,axiom,
% 5.25/5.54 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.25/5.54
% 5.25/5.54 % zero_less_eq_of_bool
% 5.25/5.54 thf(fact_5919_of__bool__less__eq__one,axiom,
% 5.25/5.54 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_less_eq_one
% 5.25/5.54 thf(fact_5920_of__bool__less__eq__one,axiom,
% 5.25/5.54 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_less_eq_one
% 5.25/5.54 thf(fact_5921_of__bool__less__eq__one,axiom,
% 5.25/5.54 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_less_eq_one
% 5.25/5.54 thf(fact_5922_of__bool__less__eq__one,axiom,
% 5.25/5.54 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_less_eq_one
% 5.25/5.54 thf(fact_5923_of__bool__less__eq__one,axiom,
% 5.25/5.54 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_less_eq_one
% 5.25/5.54 thf(fact_5924_of__bool__def,axiom,
% 5.25/5.54 ( zero_n1201886186963655149omplex
% 5.25/5.54 = ( ^ [P4: $o] : ( if_complex @ P4 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_def
% 5.25/5.54 thf(fact_5925_of__bool__def,axiom,
% 5.25/5.54 ( zero_n3304061248610475627l_real
% 5.25/5.54 = ( ^ [P4: $o] : ( if_real @ P4 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_def
% 5.25/5.54 thf(fact_5926_of__bool__def,axiom,
% 5.25/5.54 ( zero_n2052037380579107095ol_rat
% 5.25/5.54 = ( ^ [P4: $o] : ( if_rat @ P4 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_def
% 5.25/5.54 thf(fact_5927_of__bool__def,axiom,
% 5.25/5.54 ( zero_n2687167440665602831ol_nat
% 5.25/5.54 = ( ^ [P4: $o] : ( if_nat @ P4 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_def
% 5.25/5.54 thf(fact_5928_of__bool__def,axiom,
% 5.25/5.54 ( zero_n2684676970156552555ol_int
% 5.25/5.54 = ( ^ [P4: $o] : ( if_int @ P4 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_def
% 5.25/5.54 thf(fact_5929_of__bool__def,axiom,
% 5.25/5.54 ( zero_n356916108424825756nteger
% 5.25/5.54 = ( ^ [P4: $o] : ( if_Code_integer @ P4 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_def
% 5.25/5.54 thf(fact_5930_split__of__bool,axiom,
% 5.25/5.54 ! [P: complex > $o,P2: $o] :
% 5.25/5.54 ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 5.25/5.54 = ( ( P2
% 5.25/5.54 => ( P @ one_one_complex ) )
% 5.25/5.54 & ( ~ P2
% 5.25/5.54 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % split_of_bool
% 5.25/5.54 thf(fact_5931_split__of__bool,axiom,
% 5.25/5.54 ! [P: real > $o,P2: $o] :
% 5.25/5.54 ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.25/5.54 = ( ( P2
% 5.25/5.54 => ( P @ one_one_real ) )
% 5.25/5.54 & ( ~ P2
% 5.25/5.54 => ( P @ zero_zero_real ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % split_of_bool
% 5.25/5.54 thf(fact_5932_split__of__bool,axiom,
% 5.25/5.54 ! [P: rat > $o,P2: $o] :
% 5.25/5.54 ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.25/5.54 = ( ( P2
% 5.25/5.54 => ( P @ one_one_rat ) )
% 5.25/5.54 & ( ~ P2
% 5.25/5.54 => ( P @ zero_zero_rat ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % split_of_bool
% 5.25/5.54 thf(fact_5933_split__of__bool,axiom,
% 5.25/5.54 ! [P: nat > $o,P2: $o] :
% 5.25/5.54 ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.25/5.54 = ( ( P2
% 5.25/5.54 => ( P @ one_one_nat ) )
% 5.25/5.54 & ( ~ P2
% 5.25/5.54 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % split_of_bool
% 5.25/5.54 thf(fact_5934_split__of__bool,axiom,
% 5.25/5.54 ! [P: int > $o,P2: $o] :
% 5.25/5.54 ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.25/5.54 = ( ( P2
% 5.25/5.54 => ( P @ one_one_int ) )
% 5.25/5.54 & ( ~ P2
% 5.25/5.54 => ( P @ zero_zero_int ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % split_of_bool
% 5.25/5.54 thf(fact_5935_split__of__bool,axiom,
% 5.25/5.54 ! [P: code_integer > $o,P2: $o] :
% 5.25/5.54 ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.25/5.54 = ( ( P2
% 5.25/5.54 => ( P @ one_one_Code_integer ) )
% 5.25/5.54 & ( ~ P2
% 5.25/5.54 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % split_of_bool
% 5.25/5.54 thf(fact_5936_split__of__bool__asm,axiom,
% 5.25/5.54 ! [P: complex > $o,P2: $o] :
% 5.25/5.54 ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 5.25/5.54 = ( ~ ( ( P2
% 5.25/5.54 & ~ ( P @ one_one_complex ) )
% 5.25/5.54 | ( ~ P2
% 5.25/5.54 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % split_of_bool_asm
% 5.25/5.54 thf(fact_5937_split__of__bool__asm,axiom,
% 5.25/5.54 ! [P: real > $o,P2: $o] :
% 5.25/5.54 ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.25/5.54 = ( ~ ( ( P2
% 5.25/5.54 & ~ ( P @ one_one_real ) )
% 5.25/5.54 | ( ~ P2
% 5.25/5.54 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % split_of_bool_asm
% 5.25/5.54 thf(fact_5938_split__of__bool__asm,axiom,
% 5.25/5.54 ! [P: rat > $o,P2: $o] :
% 5.25/5.54 ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.25/5.54 = ( ~ ( ( P2
% 5.25/5.54 & ~ ( P @ one_one_rat ) )
% 5.25/5.54 | ( ~ P2
% 5.25/5.54 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % split_of_bool_asm
% 5.25/5.54 thf(fact_5939_split__of__bool__asm,axiom,
% 5.25/5.54 ! [P: nat > $o,P2: $o] :
% 5.25/5.54 ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.25/5.54 = ( ~ ( ( P2
% 5.25/5.54 & ~ ( P @ one_one_nat ) )
% 5.25/5.54 | ( ~ P2
% 5.25/5.54 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % split_of_bool_asm
% 5.25/5.54 thf(fact_5940_split__of__bool__asm,axiom,
% 5.25/5.54 ! [P: int > $o,P2: $o] :
% 5.25/5.54 ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.25/5.54 = ( ~ ( ( P2
% 5.25/5.54 & ~ ( P @ one_one_int ) )
% 5.25/5.54 | ( ~ P2
% 5.25/5.54 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % split_of_bool_asm
% 5.25/5.54 thf(fact_5941_split__of__bool__asm,axiom,
% 5.25/5.54 ! [P: code_integer > $o,P2: $o] :
% 5.25/5.54 ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.25/5.54 = ( ~ ( ( P2
% 5.25/5.54 & ~ ( P @ one_one_Code_integer ) )
% 5.25/5.54 | ( ~ P2
% 5.25/5.54 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % split_of_bool_asm
% 5.25/5.54 thf(fact_5942_semiring__norm_I27_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( bitM @ ( bit0 @ N ) )
% 5.25/5.54 = ( bit1 @ ( bitM @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % semiring_norm(27)
% 5.25/5.54 thf(fact_5943_semiring__norm_I28_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( bitM @ ( bit1 @ N ) )
% 5.25/5.54 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % semiring_norm(28)
% 5.25/5.54 thf(fact_5944_eval__nat__numeral_I2_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.25/5.54 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % eval_nat_numeral(2)
% 5.25/5.54 thf(fact_5945_one__plus__BitM,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 5.25/5.54 = ( bit0 @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % one_plus_BitM
% 5.25/5.54 thf(fact_5946_BitM__plus__one,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 5.25/5.54 = ( bit0 @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % BitM_plus_one
% 5.25/5.54 thf(fact_5947_subset__decode__imp__le,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 5.25/5.54 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % subset_decode_imp_le
% 5.25/5.54 thf(fact_5948_numeral__BitM,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( numera6690914467698888265omplex @ ( bitM @ N ) )
% 5.25/5.54 = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N ) ) @ one_one_complex ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_BitM
% 5.25/5.54 thf(fact_5949_numeral__BitM,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( numeral_numeral_real @ ( bitM @ N ) )
% 5.25/5.54 = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N ) ) @ one_one_real ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_BitM
% 5.25/5.54 thf(fact_5950_numeral__BitM,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 5.25/5.54 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_BitM
% 5.25/5.54 thf(fact_5951_numeral__BitM,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( numeral_numeral_int @ ( bitM @ N ) )
% 5.25/5.54 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_BitM
% 5.25/5.54 thf(fact_5952_odd__numeral__BitM,axiom,
% 5.25/5.54 ! [W: num] :
% 5.25/5.54 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % odd_numeral_BitM
% 5.25/5.54 thf(fact_5953_odd__numeral__BitM,axiom,
% 5.25/5.54 ! [W: num] :
% 5.25/5.54 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % odd_numeral_BitM
% 5.25/5.54 thf(fact_5954_odd__numeral__BitM,axiom,
% 5.25/5.54 ! [W: num] :
% 5.25/5.54 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % odd_numeral_BitM
% 5.25/5.54 thf(fact_5955_of__bool__odd__eq__mod__2,axiom,
% 5.25/5.54 ! [A: nat] :
% 5.25/5.54 ( ( zero_n2687167440665602831ol_nat
% 5.25/5.54 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.54 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_odd_eq_mod_2
% 5.25/5.54 thf(fact_5956_of__bool__odd__eq__mod__2,axiom,
% 5.25/5.54 ! [A: int] :
% 5.25/5.54 ( ( zero_n2684676970156552555ol_int
% 5.25/5.54 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.54 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_odd_eq_mod_2
% 5.25/5.54 thf(fact_5957_of__bool__odd__eq__mod__2,axiom,
% 5.25/5.54 ! [A: code_integer] :
% 5.25/5.54 ( ( zero_n356916108424825756nteger
% 5.25/5.54 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.54 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_bool_odd_eq_mod_2
% 5.25/5.54 thf(fact_5958_bits__induct,axiom,
% 5.25/5.54 ! [P: nat > $o,A: nat] :
% 5.25/5.54 ( ! [A5: nat] :
% 5.25/5.54 ( ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.54 = A5 )
% 5.25/5.54 => ( P @ A5 ) )
% 5.25/5.54 => ( ! [A5: nat,B5: $o] :
% 5.25/5.54 ( ( P @ A5 )
% 5.25/5.54 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.54 = A5 )
% 5.25/5.54 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.25/5.54 => ( P @ A ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % bits_induct
% 5.25/5.54 thf(fact_5959_bits__induct,axiom,
% 5.25/5.54 ! [P: int > $o,A: int] :
% 5.25/5.54 ( ! [A5: int] :
% 5.25/5.54 ( ( ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.54 = A5 )
% 5.25/5.54 => ( P @ A5 ) )
% 5.25/5.54 => ( ! [A5: int,B5: $o] :
% 5.25/5.54 ( ( P @ A5 )
% 5.25/5.54 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.54 = A5 )
% 5.25/5.54 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.25/5.54 => ( P @ A ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % bits_induct
% 5.25/5.54 thf(fact_5960_bits__induct,axiom,
% 5.25/5.54 ! [P: code_integer > $o,A: code_integer] :
% 5.25/5.54 ( ! [A5: code_integer] :
% 5.25/5.54 ( ( ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.54 = A5 )
% 5.25/5.54 => ( P @ A5 ) )
% 5.25/5.54 => ( ! [A5: code_integer,B5: $o] :
% 5.25/5.54 ( ( P @ A5 )
% 5.25/5.54 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.54 = A5 )
% 5.25/5.54 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.25/5.54 => ( P @ A ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % bits_induct
% 5.25/5.54 thf(fact_5961_exp__mod__exp,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.54 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % exp_mod_exp
% 5.25/5.54 thf(fact_5962_exp__mod__exp,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.54 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % exp_mod_exp
% 5.25/5.54 thf(fact_5963_exp__mod__exp,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.54 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % exp_mod_exp
% 5.25/5.54 thf(fact_5964_exists__least__lemma,axiom,
% 5.25/5.54 ! [P: nat > $o] :
% 5.25/5.54 ( ~ ( P @ zero_zero_nat )
% 5.25/5.54 => ( ? [X_1: nat] : ( P @ X_1 )
% 5.25/5.54 => ? [N3: nat] :
% 5.25/5.54 ( ~ ( P @ N3 )
% 5.25/5.54 & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % exists_least_lemma
% 5.25/5.54 thf(fact_5965_ex__le__of__int,axiom,
% 5.25/5.54 ! [X3: real] :
% 5.25/5.54 ? [Z2: int] : ( ord_less_eq_real @ X3 @ ( ring_1_of_int_real @ Z2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % ex_le_of_int
% 5.25/5.54 thf(fact_5966_ex__le__of__int,axiom,
% 5.25/5.54 ! [X3: rat] :
% 5.25/5.54 ? [Z2: int] : ( ord_less_eq_rat @ X3 @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % ex_le_of_int
% 5.25/5.54 thf(fact_5967_ex__of__int__less,axiom,
% 5.25/5.54 ! [X3: real] :
% 5.25/5.54 ? [Z2: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ X3 ) ).
% 5.25/5.54
% 5.25/5.54 % ex_of_int_less
% 5.25/5.54 thf(fact_5968_ex__of__int__less,axiom,
% 5.25/5.54 ! [X3: rat] :
% 5.25/5.54 ? [Z2: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ X3 ) ).
% 5.25/5.54
% 5.25/5.54 % ex_of_int_less
% 5.25/5.54 thf(fact_5969_ex__less__of__int,axiom,
% 5.25/5.54 ! [X3: real] :
% 5.25/5.54 ? [Z2: int] : ( ord_less_real @ X3 @ ( ring_1_of_int_real @ Z2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % ex_less_of_int
% 5.25/5.54 thf(fact_5970_ex__less__of__int,axiom,
% 5.25/5.54 ! [X3: rat] :
% 5.25/5.54 ? [Z2: int] : ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % ex_less_of_int
% 5.25/5.54 thf(fact_5971_divmod__step__nat__def,axiom,
% 5.25/5.54 ( unique5026877609467782581ep_nat
% 5.25/5.54 = ( ^ [L: num] :
% 5.25/5.54 ( produc2626176000494625587at_nat
% 5.25/5.54 @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % divmod_step_nat_def
% 5.25/5.54 thf(fact_5972_exp__div__exp__eq,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.54 = ( times_times_nat
% 5.25/5.54 @ ( zero_n2687167440665602831ol_nat
% 5.25/5.54 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.25/5.54 != zero_zero_nat )
% 5.25/5.54 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.25/5.54 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % exp_div_exp_eq
% 5.25/5.54 thf(fact_5973_exp__div__exp__eq,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.54 = ( times_times_int
% 5.25/5.54 @ ( zero_n2684676970156552555ol_int
% 5.25/5.54 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.25/5.54 != zero_zero_int )
% 5.25/5.54 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.25/5.54 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % exp_div_exp_eq
% 5.25/5.54 thf(fact_5974_exp__div__exp__eq,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.54 = ( times_3573771949741848930nteger
% 5.25/5.54 @ ( zero_n356916108424825756nteger
% 5.25/5.54 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.25/5.54 != zero_z3403309356797280102nteger )
% 5.25/5.54 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.25/5.54 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % exp_div_exp_eq
% 5.25/5.54 thf(fact_5975_divmod__step__int__def,axiom,
% 5.25/5.54 ( unique5024387138958732305ep_int
% 5.25/5.54 = ( ^ [L: num] :
% 5.25/5.54 ( produc4245557441103728435nt_int
% 5.25/5.54 @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % divmod_step_int_def
% 5.25/5.54 thf(fact_5976_divmod__step__def,axiom,
% 5.25/5.54 ( unique5026877609467782581ep_nat
% 5.25/5.54 = ( ^ [L: num] :
% 5.25/5.54 ( produc2626176000494625587at_nat
% 5.25/5.54 @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % divmod_step_def
% 5.25/5.54 thf(fact_5977_divmod__step__def,axiom,
% 5.25/5.54 ( unique5024387138958732305ep_int
% 5.25/5.54 = ( ^ [L: num] :
% 5.25/5.54 ( produc4245557441103728435nt_int
% 5.25/5.54 @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % divmod_step_def
% 5.25/5.54 thf(fact_5978_divmod__step__def,axiom,
% 5.25/5.54 ( unique4921790084139445826nteger
% 5.25/5.54 = ( ^ [L: num] :
% 5.25/5.54 ( produc6916734918728496179nteger
% 5.25/5.54 @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % divmod_step_def
% 5.25/5.54 thf(fact_5979_set__decode__def,axiom,
% 5.25/5.54 ( nat_set_decode
% 5.25/5.54 = ( ^ [X2: nat] :
% 5.25/5.54 ( collect_nat
% 5.25/5.54 @ ^ [N2: nat] :
% 5.25/5.54 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % set_decode_def
% 5.25/5.54 thf(fact_5980_round__unique,axiom,
% 5.25/5.54 ! [X3: real,Y: int] :
% 5.25/5.54 ( ( ord_less_real @ ( minus_minus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 5.25/5.54 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.25/5.54 => ( ( archim8280529875227126926d_real @ X3 )
% 5.25/5.54 = Y ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % round_unique
% 5.25/5.54 thf(fact_5981_round__unique,axiom,
% 5.25/5.54 ! [X3: rat,Y: int] :
% 5.25/5.54 ( ( ord_less_rat @ ( minus_minus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 5.25/5.54 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.54 => ( ( archim7778729529865785530nd_rat @ X3 )
% 5.25/5.54 = Y ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % round_unique
% 5.25/5.54 thf(fact_5982_divmod__nat__if,axiom,
% 5.25/5.54 ( divmod_nat
% 5.25/5.54 = ( ^ [M6: nat,N2: nat] :
% 5.25/5.54 ( if_Pro6206227464963214023at_nat
% 5.25/5.54 @ ( ( N2 = zero_zero_nat )
% 5.25/5.54 | ( ord_less_nat @ M6 @ N2 ) )
% 5.25/5.54 @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 5.25/5.54 @ ( produc2626176000494625587at_nat
% 5.25/5.54 @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 5.25/5.54 @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % divmod_nat_if
% 5.25/5.54 thf(fact_5983_of__int__round__gt,axiom,
% 5.25/5.54 ! [X3: real] : ( ord_less_real @ ( minus_minus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_int_round_gt
% 5.25/5.54 thf(fact_5984_of__int__round__gt,axiom,
% 5.25/5.54 ! [X3: rat] : ( ord_less_rat @ ( minus_minus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_int_round_gt
% 5.25/5.54 thf(fact_5985_of__int__round__ge,axiom,
% 5.25/5.54 ! [X3: real] : ( ord_less_eq_real @ ( minus_minus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_int_round_ge
% 5.25/5.54 thf(fact_5986_of__int__round__ge,axiom,
% 5.25/5.54 ! [X3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_int_round_ge
% 5.25/5.54 thf(fact_5987_of__int__round__le,axiom,
% 5.25/5.54 ! [X3: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X3 ) ) @ ( plus_plus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_int_round_le
% 5.25/5.54 thf(fact_5988_of__int__round__le,axiom,
% 5.25/5.54 ! [X3: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X3 ) ) @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_int_round_le
% 5.25/5.54 thf(fact_5989_Sum__Icc__int,axiom,
% 5.25/5.54 ! [M: int,N: int] :
% 5.25/5.54 ( ( ord_less_eq_int @ M @ N )
% 5.25/5.54 => ( ( groups4538972089207619220nt_int
% 5.25/5.54 @ ^ [X2: int] : X2
% 5.25/5.54 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 5.25/5.54 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % Sum_Icc_int
% 5.25/5.54 thf(fact_5990_round__numeral,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 5.25/5.54 = ( numeral_numeral_int @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % round_numeral
% 5.25/5.54 thf(fact_5991_round__numeral,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 5.25/5.54 = ( numeral_numeral_int @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % round_numeral
% 5.25/5.54 thf(fact_5992_round__1,axiom,
% 5.25/5.54 ( ( archim8280529875227126926d_real @ one_one_real )
% 5.25/5.54 = one_one_int ) ).
% 5.25/5.54
% 5.25/5.54 % round_1
% 5.25/5.54 thf(fact_5993_round__1,axiom,
% 5.25/5.54 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 5.25/5.54 = one_one_int ) ).
% 5.25/5.54
% 5.25/5.54 % round_1
% 5.25/5.54 thf(fact_5994_round__neg__numeral,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.25/5.54 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % round_neg_numeral
% 5.25/5.54 thf(fact_5995_round__neg__numeral,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.25/5.54 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % round_neg_numeral
% 5.25/5.54 thf(fact_5996_mod__sum__eq,axiom,
% 5.25/5.54 ! [F: int > int,A: int,A2: set_int] :
% 5.25/5.54 ( ( modulo_modulo_int
% 5.25/5.54 @ ( groups4538972089207619220nt_int
% 5.25/5.54 @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 5.25/5.54 @ A2 )
% 5.25/5.54 @ A )
% 5.25/5.54 = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 5.25/5.54
% 5.25/5.54 % mod_sum_eq
% 5.25/5.54 thf(fact_5997_mod__sum__eq,axiom,
% 5.25/5.54 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.25/5.54 ( ( modulo_modulo_nat
% 5.25/5.54 @ ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 5.25/5.54 @ A2 )
% 5.25/5.54 @ A )
% 5.25/5.54 = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 5.25/5.54
% 5.25/5.54 % mod_sum_eq
% 5.25/5.54 thf(fact_5998_round__mono,axiom,
% 5.25/5.54 ! [X3: rat,Y: rat] :
% 5.25/5.54 ( ( ord_less_eq_rat @ X3 @ Y )
% 5.25/5.54 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X3 ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % round_mono
% 5.25/5.54 thf(fact_5999_divmod__nat__def,axiom,
% 5.25/5.54 ( divmod_nat
% 5.25/5.54 = ( ^ [M6: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N2 ) @ ( modulo_modulo_nat @ M6 @ N2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % divmod_nat_def
% 5.25/5.54 thf(fact_6000_sum__nonneg,axiom,
% 5.25/5.54 ! [A2: set_real,F: real > real] :
% 5.25/5.54 ( ! [X5: real] :
% 5.25/5.54 ( ( member_real @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonneg
% 5.25/5.54 thf(fact_6001_sum__nonneg,axiom,
% 5.25/5.54 ! [A2: set_int,F: int > real] :
% 5.25/5.54 ( ! [X5: int] :
% 5.25/5.54 ( ( member_int @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonneg
% 5.25/5.54 thf(fact_6002_sum__nonneg,axiom,
% 5.25/5.54 ! [A2: set_complex,F: complex > real] :
% 5.25/5.54 ( ! [X5: complex] :
% 5.25/5.54 ( ( member_complex @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonneg
% 5.25/5.54 thf(fact_6003_sum__nonneg,axiom,
% 5.25/5.54 ! [A2: set_nat,F: nat > rat] :
% 5.25/5.54 ( ! [X5: nat] :
% 5.25/5.54 ( ( member_nat @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonneg
% 5.25/5.54 thf(fact_6004_sum__nonneg,axiom,
% 5.25/5.54 ! [A2: set_real,F: real > rat] :
% 5.25/5.54 ( ! [X5: real] :
% 5.25/5.54 ( ( member_real @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonneg
% 5.25/5.54 thf(fact_6005_sum__nonneg,axiom,
% 5.25/5.54 ! [A2: set_int,F: int > rat] :
% 5.25/5.54 ( ! [X5: int] :
% 5.25/5.54 ( ( member_int @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonneg
% 5.25/5.54 thf(fact_6006_sum__nonneg,axiom,
% 5.25/5.54 ! [A2: set_complex,F: complex > rat] :
% 5.25/5.54 ( ! [X5: complex] :
% 5.25/5.54 ( ( member_complex @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonneg
% 5.25/5.54 thf(fact_6007_sum__nonneg,axiom,
% 5.25/5.54 ! [A2: set_real,F: real > nat] :
% 5.25/5.54 ( ! [X5: real] :
% 5.25/5.54 ( ( member_real @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonneg
% 5.25/5.54 thf(fact_6008_sum__nonneg,axiom,
% 5.25/5.54 ! [A2: set_int,F: int > nat] :
% 5.25/5.54 ( ! [X5: int] :
% 5.25/5.54 ( ( member_int @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonneg
% 5.25/5.54 thf(fact_6009_sum__nonneg,axiom,
% 5.25/5.54 ! [A2: set_complex,F: complex > nat] :
% 5.25/5.54 ( ! [X5: complex] :
% 5.25/5.54 ( ( member_complex @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonneg
% 5.25/5.54 thf(fact_6010_sum__nonpos,axiom,
% 5.25/5.54 ! [A2: set_real,F: real > real] :
% 5.25/5.54 ( ! [X5: real] :
% 5.25/5.54 ( ( member_real @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.25/5.54 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonpos
% 5.25/5.54 thf(fact_6011_sum__nonpos,axiom,
% 5.25/5.54 ! [A2: set_int,F: int > real] :
% 5.25/5.54 ( ! [X5: int] :
% 5.25/5.54 ( ( member_int @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.25/5.54 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonpos
% 5.25/5.54 thf(fact_6012_sum__nonpos,axiom,
% 5.25/5.54 ! [A2: set_complex,F: complex > real] :
% 5.25/5.54 ( ! [X5: complex] :
% 5.25/5.54 ( ( member_complex @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.25/5.54 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonpos
% 5.25/5.54 thf(fact_6013_sum__nonpos,axiom,
% 5.25/5.54 ! [A2: set_nat,F: nat > rat] :
% 5.25/5.54 ( ! [X5: nat] :
% 5.25/5.54 ( ( member_nat @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.25/5.54 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonpos
% 5.25/5.54 thf(fact_6014_sum__nonpos,axiom,
% 5.25/5.54 ! [A2: set_real,F: real > rat] :
% 5.25/5.54 ( ! [X5: real] :
% 5.25/5.54 ( ( member_real @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.25/5.54 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonpos
% 5.25/5.54 thf(fact_6015_sum__nonpos,axiom,
% 5.25/5.54 ! [A2: set_int,F: int > rat] :
% 5.25/5.54 ( ! [X5: int] :
% 5.25/5.54 ( ( member_int @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.25/5.54 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonpos
% 5.25/5.54 thf(fact_6016_sum__nonpos,axiom,
% 5.25/5.54 ! [A2: set_complex,F: complex > rat] :
% 5.25/5.54 ( ! [X5: complex] :
% 5.25/5.54 ( ( member_complex @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.25/5.54 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonpos
% 5.25/5.54 thf(fact_6017_sum__nonpos,axiom,
% 5.25/5.54 ! [A2: set_real,F: real > nat] :
% 5.25/5.54 ( ! [X5: real] :
% 5.25/5.54 ( ( member_real @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.25/5.54 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonpos
% 5.25/5.54 thf(fact_6018_sum__nonpos,axiom,
% 5.25/5.54 ! [A2: set_int,F: int > nat] :
% 5.25/5.54 ( ! [X5: int] :
% 5.25/5.54 ( ( member_int @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.25/5.54 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonpos
% 5.25/5.54 thf(fact_6019_sum__nonpos,axiom,
% 5.25/5.54 ! [A2: set_complex,F: complex > nat] :
% 5.25/5.54 ( ! [X5: complex] :
% 5.25/5.54 ( ( member_complex @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.25/5.54 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_nonpos
% 5.25/5.54 thf(fact_6020_mask__numeral,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 5.25/5.54 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_numeral
% 5.25/5.54 thf(fact_6021_mask__numeral,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 5.25/5.54 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_numeral
% 5.25/5.54 thf(fact_6022_num_Osize__gen_I3_J,axiom,
% 5.25/5.54 ! [X32: num] :
% 5.25/5.54 ( ( size_num @ ( bit1 @ X32 ) )
% 5.25/5.54 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % num.size_gen(3)
% 5.25/5.54 thf(fact_6023_take__bit__rec,axiom,
% 5.25/5.54 ( bit_se1745604003318907178nteger
% 5.25/5.54 = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_rec
% 5.25/5.54 thf(fact_6024_take__bit__rec,axiom,
% 5.25/5.54 ( bit_se2923211474154528505it_int
% 5.25/5.54 = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_rec
% 5.25/5.54 thf(fact_6025_take__bit__rec,axiom,
% 5.25/5.54 ( bit_se2925701944663578781it_nat
% 5.25/5.54 = ( ^ [N2: nat,A3: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_rec
% 5.25/5.54 thf(fact_6026_num_Osize__gen_I2_J,axiom,
% 5.25/5.54 ! [X22: num] :
% 5.25/5.54 ( ( size_num @ ( bit0 @ X22 ) )
% 5.25/5.54 = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % num.size_gen(2)
% 5.25/5.54 thf(fact_6027_mask__nat__positive__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.25/5.54 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_nat_positive_iff
% 5.25/5.54 thf(fact_6028_take__bit__of__0,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 5.25/5.54 = zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_0
% 5.25/5.54 thf(fact_6029_take__bit__of__0,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 5.25/5.54 = zero_zero_nat ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_0
% 5.25/5.54 thf(fact_6030_concat__bit__of__zero__2,axiom,
% 5.25/5.54 ! [N: nat,K: int] :
% 5.25/5.54 ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 5.25/5.54 = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.25/5.54
% 5.25/5.54 % concat_bit_of_zero_2
% 5.25/5.54 thf(fact_6031_take__bit__0,axiom,
% 5.25/5.54 ! [A: int] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 5.25/5.54 = zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_0
% 5.25/5.54 thf(fact_6032_take__bit__0,axiom,
% 5.25/5.54 ! [A: nat] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 5.25/5.54 = zero_zero_nat ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_0
% 5.25/5.54 thf(fact_6033_take__bit__Suc__1,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 5.25/5.54 = one_one_int ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc_1
% 5.25/5.54 thf(fact_6034_take__bit__Suc__1,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 5.25/5.54 = one_one_nat ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc_1
% 5.25/5.54 thf(fact_6035_take__bit__numeral__1,axiom,
% 5.25/5.54 ! [L2: num] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ one_one_int )
% 5.25/5.54 = one_one_int ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_numeral_1
% 5.25/5.54 thf(fact_6036_take__bit__numeral__1,axiom,
% 5.25/5.54 ! [L2: num] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ one_one_nat )
% 5.25/5.54 = one_one_nat ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_numeral_1
% 5.25/5.54 thf(fact_6037_mask__0,axiom,
% 5.25/5.54 ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 5.25/5.54 = zero_zero_nat ) ).
% 5.25/5.54
% 5.25/5.54 % mask_0
% 5.25/5.54 thf(fact_6038_mask__0,axiom,
% 5.25/5.54 ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 5.25/5.54 = zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % mask_0
% 5.25/5.54 thf(fact_6039_mask__eq__0__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ( bit_se2002935070580805687sk_nat @ N )
% 5.25/5.54 = zero_zero_nat )
% 5.25/5.54 = ( N = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_eq_0_iff
% 5.25/5.54 thf(fact_6040_mask__eq__0__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ( bit_se2000444600071755411sk_int @ N )
% 5.25/5.54 = zero_zero_int )
% 5.25/5.54 = ( N = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_eq_0_iff
% 5.25/5.54 thf(fact_6041_take__bit__of__1__eq__0__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.25/5.54 = zero_zero_int )
% 5.25/5.54 = ( N = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_1_eq_0_iff
% 5.25/5.54 thf(fact_6042_take__bit__of__1__eq__0__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.25/5.54 = zero_zero_nat )
% 5.25/5.54 = ( N = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_1_eq_0_iff
% 5.25/5.54 thf(fact_6043_mask__Suc__0,axiom,
% 5.25/5.54 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 5.25/5.54 = one_one_nat ) ).
% 5.25/5.54
% 5.25/5.54 % mask_Suc_0
% 5.25/5.54 thf(fact_6044_mask__Suc__0,axiom,
% 5.25/5.54 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 5.25/5.54 = one_one_int ) ).
% 5.25/5.54
% 5.25/5.54 % mask_Suc_0
% 5.25/5.54 thf(fact_6045_take__bit__minus__one__eq__mask,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.54 = ( bit_se2119862282449309892nteger @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_minus_one_eq_mask
% 5.25/5.54 thf(fact_6046_take__bit__minus__one__eq__mask,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.54 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_minus_one_eq_mask
% 5.25/5.54 thf(fact_6047_take__bit__of__Suc__0,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.25/5.54 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_Suc_0
% 5.25/5.54 thf(fact_6048_sum_Ocl__ivl__Suc,axiom,
% 5.25/5.54 ! [N: nat,M: nat,G: nat > complex] :
% 5.25/5.54 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.54 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.54 = zero_zero_complex ) )
% 5.25/5.54 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.54 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.cl_ivl_Suc
% 5.25/5.54 thf(fact_6049_sum_Ocl__ivl__Suc,axiom,
% 5.25/5.54 ! [N: nat,M: nat,G: nat > rat] :
% 5.25/5.54 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.54 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.54 = zero_zero_rat ) )
% 5.25/5.54 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.54 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.cl_ivl_Suc
% 5.25/5.54 thf(fact_6050_sum_Ocl__ivl__Suc,axiom,
% 5.25/5.54 ! [N: nat,M: nat,G: nat > int] :
% 5.25/5.54 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.54 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.54 = zero_zero_int ) )
% 5.25/5.54 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.54 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.cl_ivl_Suc
% 5.25/5.54 thf(fact_6051_sum_Ocl__ivl__Suc,axiom,
% 5.25/5.54 ! [N: nat,M: nat,G: nat > nat] :
% 5.25/5.54 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.54 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.54 = zero_zero_nat ) )
% 5.25/5.54 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.54 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.cl_ivl_Suc
% 5.25/5.54 thf(fact_6052_sum_Ocl__ivl__Suc,axiom,
% 5.25/5.54 ! [N: nat,M: nat,G: nat > real] :
% 5.25/5.54 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.54 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.54 = zero_zero_real ) )
% 5.25/5.54 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.54 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.cl_ivl_Suc
% 5.25/5.54 thf(fact_6053_take__bit__of__1,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 5.25/5.54 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_1
% 5.25/5.54 thf(fact_6054_take__bit__of__1,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.25/5.54 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_1
% 5.25/5.54 thf(fact_6055_take__bit__of__1,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.25/5.54 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_1
% 5.25/5.54 thf(fact_6056_even__take__bit__eq,axiom,
% 5.25/5.54 ! [N: nat,A: code_integer] :
% 5.25/5.54 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 5.25/5.54 = ( ( N = zero_zero_nat )
% 5.25/5.54 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % even_take_bit_eq
% 5.25/5.54 thf(fact_6057_even__take__bit__eq,axiom,
% 5.25/5.54 ! [N: nat,A: int] :
% 5.25/5.54 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.25/5.54 = ( ( N = zero_zero_nat )
% 5.25/5.54 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % even_take_bit_eq
% 5.25/5.54 thf(fact_6058_even__take__bit__eq,axiom,
% 5.25/5.54 ! [N: nat,A: nat] :
% 5.25/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 5.25/5.54 = ( ( N = zero_zero_nat )
% 5.25/5.54 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % even_take_bit_eq
% 5.25/5.54 thf(fact_6059_take__bit__Suc__0,axiom,
% 5.25/5.54 ! [A: code_integer] :
% 5.25/5.54 ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 5.25/5.54 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc_0
% 5.25/5.54 thf(fact_6060_take__bit__Suc__0,axiom,
% 5.25/5.54 ! [A: int] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 5.25/5.54 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc_0
% 5.25/5.54 thf(fact_6061_take__bit__Suc__0,axiom,
% 5.25/5.54 ! [A: nat] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 5.25/5.54 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc_0
% 5.25/5.54 thf(fact_6062_take__bit__of__exp,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.54 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_exp
% 5.25/5.54 thf(fact_6063_take__bit__of__exp,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.54 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_exp
% 5.25/5.54 thf(fact_6064_take__bit__of__exp,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.54 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_exp
% 5.25/5.54 thf(fact_6065_take__bit__of__2,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.54 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_2
% 5.25/5.54 thf(fact_6066_take__bit__of__2,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.54 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_2
% 5.25/5.54 thf(fact_6067_take__bit__of__2,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.54 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_2
% 5.25/5.54 thf(fact_6068_of__int__mask__eq,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.25/5.54 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_int_mask_eq
% 5.25/5.54 thf(fact_6069_take__bit__of__int,axiom,
% 5.25/5.54 ! [N: nat,K: int] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ N @ ( ring_1_of_int_int @ K ) )
% 5.25/5.54 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_int
% 5.25/5.54 thf(fact_6070_take__bit__add,axiom,
% 5.25/5.54 ! [N: nat,A: int,B: int] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) )
% 5.25/5.54 = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_add
% 5.25/5.54 thf(fact_6071_take__bit__add,axiom,
% 5.25/5.54 ! [N: nat,A: nat,B: nat] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) )
% 5.25/5.54 = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_add
% 5.25/5.54 thf(fact_6072_take__bit__tightened,axiom,
% 5.25/5.54 ! [N: nat,A: int,B: int,M: nat] :
% 5.25/5.54 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.25/5.54 = ( bit_se2923211474154528505it_int @ N @ B ) )
% 5.25/5.54 => ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 5.25/5.54 = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_tightened
% 5.25/5.54 thf(fact_6073_take__bit__tightened,axiom,
% 5.25/5.54 ! [N: nat,A: nat,B: nat,M: nat] :
% 5.25/5.54 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.25/5.54 = ( bit_se2925701944663578781it_nat @ N @ B ) )
% 5.25/5.54 => ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 5.25/5.54 = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_tightened
% 5.25/5.54 thf(fact_6074_take__bit__tightened__less__eq__nat,axiom,
% 5.25/5.54 ! [M: nat,N: nat,Q2: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_tightened_less_eq_nat
% 5.25/5.54 thf(fact_6075_take__bit__nat__less__eq__self,axiom,
% 5.25/5.54 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_nat_less_eq_self
% 5.25/5.54 thf(fact_6076_take__bit__minus,axiom,
% 5.25/5.54 ! [N: nat,K: int] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.25/5.54 = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_minus
% 5.25/5.54 thf(fact_6077_take__bit__mult,axiom,
% 5.25/5.54 ! [N: nat,K: int,L2: int] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 5.25/5.54 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_mult
% 5.25/5.54 thf(fact_6078_take__bit__diff,axiom,
% 5.25/5.54 ! [N: nat,K: int,L2: int] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 5.25/5.54 = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_diff
% 5.25/5.54 thf(fact_6079_sum__cong__Suc,axiom,
% 5.25/5.54 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.25/5.54 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.25/5.54 => ( ! [X5: nat] :
% 5.25/5.54 ( ( member_nat @ ( suc @ X5 ) @ A2 )
% 5.25/5.54 => ( ( F @ ( suc @ X5 ) )
% 5.25/5.54 = ( G @ ( suc @ X5 ) ) ) )
% 5.25/5.54 => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.25/5.54 = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_cong_Suc
% 5.25/5.54 thf(fact_6080_sum__cong__Suc,axiom,
% 5.25/5.54 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.25/5.54 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.25/5.54 => ( ! [X5: nat] :
% 5.25/5.54 ( ( member_nat @ ( suc @ X5 ) @ A2 )
% 5.25/5.54 => ( ( F @ ( suc @ X5 ) )
% 5.25/5.54 = ( G @ ( suc @ X5 ) ) ) )
% 5.25/5.54 => ( ( groups6591440286371151544t_real @ F @ A2 )
% 5.25/5.54 = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_cong_Suc
% 5.25/5.54 thf(fact_6081_concat__bit__eq__iff,axiom,
% 5.25/5.54 ! [N: nat,K: int,L2: int,R2: int,S: int] :
% 5.25/5.54 ( ( ( bit_concat_bit @ N @ K @ L2 )
% 5.25/5.54 = ( bit_concat_bit @ N @ R2 @ S ) )
% 5.25/5.54 = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.25/5.54 = ( bit_se2923211474154528505it_int @ N @ R2 ) )
% 5.25/5.54 & ( L2 = S ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % concat_bit_eq_iff
% 5.25/5.54 thf(fact_6082_concat__bit__take__bit__eq,axiom,
% 5.25/5.54 ! [N: nat,B: int] :
% 5.25/5.54 ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 5.25/5.54 = ( bit_concat_bit @ N @ B ) ) ).
% 5.25/5.54
% 5.25/5.54 % concat_bit_take_bit_eq
% 5.25/5.54 thf(fact_6083_less__eq__mask,axiom,
% 5.25/5.54 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % less_eq_mask
% 5.25/5.54 thf(fact_6084_take__bit__eq__mask__iff,axiom,
% 5.25/5.54 ! [N: nat,K: int] :
% 5.25/5.54 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.25/5.54 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.25/5.54 = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.25/5.54 = zero_zero_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_eq_mask_iff
% 5.25/5.54 thf(fact_6085_sum__subtractf__nat,axiom,
% 5.25/5.54 ! [A2: set_real,G: real > nat,F: real > nat] :
% 5.25/5.54 ( ! [X5: real] :
% 5.25/5.54 ( ( member_real @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ( groups1935376822645274424al_nat
% 5.25/5.54 @ ^ [X2: real] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.25/5.54 @ A2 )
% 5.25/5.54 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_subtractf_nat
% 5.25/5.54 thf(fact_6086_sum__subtractf__nat,axiom,
% 5.25/5.54 ! [A2: set_int,G: int > nat,F: int > nat] :
% 5.25/5.54 ( ! [X5: int] :
% 5.25/5.54 ( ( member_int @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ( groups4541462559716669496nt_nat
% 5.25/5.54 @ ^ [X2: int] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.25/5.54 @ A2 )
% 5.25/5.54 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_subtractf_nat
% 5.25/5.54 thf(fact_6087_sum__subtractf__nat,axiom,
% 5.25/5.54 ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 5.25/5.54 ( ! [X5: complex] :
% 5.25/5.54 ( ( member_complex @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ( groups5693394587270226106ex_nat
% 5.25/5.54 @ ^ [X2: complex] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.25/5.54 @ A2 )
% 5.25/5.54 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_subtractf_nat
% 5.25/5.54 thf(fact_6088_sum__subtractf__nat,axiom,
% 5.25/5.54 ! [A2: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,F: product_prod_nat_nat > nat] :
% 5.25/5.54 ( ! [X5: product_prod_nat_nat] :
% 5.25/5.54 ( ( member8440522571783428010at_nat @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ( groups977919841031483927at_nat
% 5.25/5.54 @ ^ [X2: product_prod_nat_nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.25/5.54 @ A2 )
% 5.25/5.54 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( groups977919841031483927at_nat @ G @ A2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_subtractf_nat
% 5.25/5.54 thf(fact_6089_sum__subtractf__nat,axiom,
% 5.25/5.54 ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 5.25/5.54 ( ! [X5: nat] :
% 5.25/5.54 ( ( member_nat @ X5 @ A2 )
% 5.25/5.54 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.25/5.54 => ( ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [X2: nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.25/5.54 @ A2 )
% 5.25/5.54 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_subtractf_nat
% 5.25/5.54 thf(fact_6090_sum__SucD,axiom,
% 5.25/5.54 ! [F: nat > nat,A2: set_nat,N: nat] :
% 5.25/5.54 ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.25/5.54 = ( suc @ N ) )
% 5.25/5.54 => ? [X5: nat] :
% 5.25/5.54 ( ( member_nat @ X5 @ A2 )
% 5.25/5.54 & ( ord_less_nat @ zero_zero_nat @ ( F @ X5 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_SucD
% 5.25/5.54 thf(fact_6091_take__bit__tightened__less__eq__int,axiom,
% 5.25/5.54 ! [M: nat,N: nat,K: int] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_tightened_less_eq_int
% 5.25/5.54 thf(fact_6092_take__bit__nonnegative,axiom,
% 5.25/5.54 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_nonnegative
% 5.25/5.54 thf(fact_6093_take__bit__int__less__eq__self__iff,axiom,
% 5.25/5.54 ! [N: nat,K: int] :
% 5.25/5.54 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.25/5.54 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_int_less_eq_self_iff
% 5.25/5.54 thf(fact_6094_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 5.25/5.54 ! [N: nat,A: int,B: int] :
% 5.25/5.54 ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.25/5.54 = ( bit_ri631733984087533419it_int @ N @ B ) )
% 5.25/5.54 = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.25/5.54 = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % signed_take_bit_eq_iff_take_bit_eq
% 5.25/5.54 thf(fact_6095_take__bit__int__greater__self__iff,axiom,
% 5.25/5.54 ! [K: int,N: nat] :
% 5.25/5.54 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.25/5.54 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_int_greater_self_iff
% 5.25/5.54 thf(fact_6096_not__take__bit__negative,axiom,
% 5.25/5.54 ! [N: nat,K: int] :
% 5.25/5.54 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % not_take_bit_negative
% 5.25/5.54 thf(fact_6097_signed__take__bit__take__bit,axiom,
% 5.25/5.54 ! [M: nat,N: nat,A: int] :
% 5.25/5.54 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.25/5.54 = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 5.25/5.54
% 5.25/5.54 % signed_take_bit_take_bit
% 5.25/5.54 thf(fact_6098_take__bit__unset__bit__eq,axiom,
% 5.25/5.54 ! [N: nat,M: nat,A: int] :
% 5.25/5.54 ( ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.25/5.54 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.25/5.54 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.25/5.54 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_unset_bit_eq
% 5.25/5.54 thf(fact_6099_take__bit__unset__bit__eq,axiom,
% 5.25/5.54 ! [N: nat,M: nat,A: nat] :
% 5.25/5.54 ( ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.25/5.54 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.25/5.54 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.25/5.54 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_unset_bit_eq
% 5.25/5.54 thf(fact_6100_take__bit__set__bit__eq,axiom,
% 5.25/5.54 ! [N: nat,M: nat,A: int] :
% 5.25/5.54 ( ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.25/5.54 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.25/5.54 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.25/5.54 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_set_bit_eq
% 5.25/5.54 thf(fact_6101_take__bit__set__bit__eq,axiom,
% 5.25/5.54 ! [N: nat,M: nat,A: nat] :
% 5.25/5.54 ( ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.25/5.54 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.25/5.54 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.25/5.54 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_set_bit_eq
% 5.25/5.54 thf(fact_6102_take__bit__flip__bit__eq,axiom,
% 5.25/5.54 ! [N: nat,M: nat,A: int] :
% 5.25/5.54 ( ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.25/5.54 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.25/5.54 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.25/5.54 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_flip_bit_eq
% 5.25/5.54 thf(fact_6103_take__bit__flip__bit__eq,axiom,
% 5.25/5.54 ! [N: nat,M: nat,A: nat] :
% 5.25/5.54 ( ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.25/5.54 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.25/5.54 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.25/5.54 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_flip_bit_eq
% 5.25/5.54 thf(fact_6104_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.25/5.54 ! [G: nat > nat,M: nat,N: nat] :
% 5.25/5.54 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.25/5.54 = ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.shift_bounds_cl_Suc_ivl
% 5.25/5.54 thf(fact_6105_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.25/5.54 ! [G: nat > real,M: nat,N: nat] :
% 5.25/5.54 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.25/5.54 = ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.shift_bounds_cl_Suc_ivl
% 5.25/5.54 thf(fact_6106_mask__nonnegative__int,axiom,
% 5.25/5.54 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_nonnegative_int
% 5.25/5.54 thf(fact_6107_not__mask__negative__int,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % not_mask_negative_int
% 5.25/5.54 thf(fact_6108_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.25/5.54 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.25/5.54 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.25/5.54 = ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.shift_bounds_cl_nat_ivl
% 5.25/5.54 thf(fact_6109_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.25/5.54 ! [G: nat > real,M: nat,K: nat,N: nat] :
% 5.25/5.54 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.25/5.54 = ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.shift_bounds_cl_nat_ivl
% 5.25/5.54 thf(fact_6110_take__bit__signed__take__bit,axiom,
% 5.25/5.54 ! [M: nat,N: nat,A: int] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.54 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 5.25/5.54 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_signed_take_bit
% 5.25/5.54 thf(fact_6111_take__bit__decr__eq,axiom,
% 5.25/5.54 ! [N: nat,K: int] :
% 5.25/5.54 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.25/5.54 != zero_zero_int )
% 5.25/5.54 => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 5.25/5.54 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_decr_eq
% 5.25/5.54 thf(fact_6112_sum__power__add,axiom,
% 5.25/5.54 ! [X3: complex,M: nat,I6: set_nat] :
% 5.25/5.54 ( ( groups2073611262835488442omplex
% 5.25/5.54 @ ^ [I3: nat] : ( power_power_complex @ X3 @ ( plus_plus_nat @ M @ I3 ) )
% 5.25/5.54 @ I6 )
% 5.25/5.54 = ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ I6 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_power_add
% 5.25/5.54 thf(fact_6113_sum__power__add,axiom,
% 5.25/5.54 ! [X3: rat,M: nat,I6: set_nat] :
% 5.25/5.54 ( ( groups2906978787729119204at_rat
% 5.25/5.54 @ ^ [I3: nat] : ( power_power_rat @ X3 @ ( plus_plus_nat @ M @ I3 ) )
% 5.25/5.54 @ I6 )
% 5.25/5.54 = ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ I6 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_power_add
% 5.25/5.54 thf(fact_6114_sum__power__add,axiom,
% 5.25/5.54 ! [X3: int,M: nat,I6: set_nat] :
% 5.25/5.54 ( ( groups3539618377306564664at_int
% 5.25/5.54 @ ^ [I3: nat] : ( power_power_int @ X3 @ ( plus_plus_nat @ M @ I3 ) )
% 5.25/5.54 @ I6 )
% 5.25/5.54 = ( times_times_int @ ( power_power_int @ X3 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ I6 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_power_add
% 5.25/5.54 thf(fact_6115_sum__power__add,axiom,
% 5.25/5.54 ! [X3: real,M: nat,I6: set_nat] :
% 5.25/5.54 ( ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [I3: nat] : ( power_power_real @ X3 @ ( plus_plus_nat @ M @ I3 ) )
% 5.25/5.54 @ I6 )
% 5.25/5.54 = ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ I6 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_power_add
% 5.25/5.54 thf(fact_6116_sum_OatLeastAtMost__rev,axiom,
% 5.25/5.54 ! [G: nat > nat,N: nat,M: nat] :
% 5.25/5.54 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.25/5.54 = ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.atLeastAtMost_rev
% 5.25/5.54 thf(fact_6117_sum_OatLeastAtMost__rev,axiom,
% 5.25/5.54 ! [G: nat > real,N: nat,M: nat] :
% 5.25/5.54 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.25/5.54 = ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.atLeastAtMost_rev
% 5.25/5.54 thf(fact_6118_less__mask,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.25/5.54 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % less_mask
% 5.25/5.54 thf(fact_6119_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.25/5.54 ! [N: nat,K: int] :
% 5.25/5.54 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.25/5.54 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.25/5.54 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_eq_mask_iff_exp_dvd
% 5.25/5.54 thf(fact_6120_sum__shift__lb__Suc0__0,axiom,
% 5.25/5.54 ! [F: nat > complex,K: nat] :
% 5.25/5.54 ( ( ( F @ zero_zero_nat )
% 5.25/5.54 = zero_zero_complex )
% 5.25/5.54 => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.25/5.54 = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_shift_lb_Suc0_0
% 5.25/5.54 thf(fact_6121_sum__shift__lb__Suc0__0,axiom,
% 5.25/5.54 ! [F: nat > rat,K: nat] :
% 5.25/5.54 ( ( ( F @ zero_zero_nat )
% 5.25/5.54 = zero_zero_rat )
% 5.25/5.54 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.25/5.54 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_shift_lb_Suc0_0
% 5.25/5.54 thf(fact_6122_sum__shift__lb__Suc0__0,axiom,
% 5.25/5.54 ! [F: nat > int,K: nat] :
% 5.25/5.54 ( ( ( F @ zero_zero_nat )
% 5.25/5.54 = zero_zero_int )
% 5.25/5.54 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.25/5.54 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_shift_lb_Suc0_0
% 5.25/5.54 thf(fact_6123_sum__shift__lb__Suc0__0,axiom,
% 5.25/5.54 ! [F: nat > nat,K: nat] :
% 5.25/5.54 ( ( ( F @ zero_zero_nat )
% 5.25/5.54 = zero_zero_nat )
% 5.25/5.54 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.25/5.54 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_shift_lb_Suc0_0
% 5.25/5.54 thf(fact_6124_sum__shift__lb__Suc0__0,axiom,
% 5.25/5.54 ! [F: nat > real,K: nat] :
% 5.25/5.54 ( ( ( F @ zero_zero_nat )
% 5.25/5.54 = zero_zero_real )
% 5.25/5.54 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.25/5.54 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_shift_lb_Suc0_0
% 5.25/5.54 thf(fact_6125_sum_OatLeast0__atMost__Suc,axiom,
% 5.25/5.54 ! [G: nat > rat,N: nat] :
% 5.25/5.54 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.atLeast0_atMost_Suc
% 5.25/5.54 thf(fact_6126_sum_OatLeast0__atMost__Suc,axiom,
% 5.25/5.54 ! [G: nat > int,N: nat] :
% 5.25/5.54 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.atLeast0_atMost_Suc
% 5.25/5.54 thf(fact_6127_sum_OatLeast0__atMost__Suc,axiom,
% 5.25/5.54 ! [G: nat > nat,N: nat] :
% 5.25/5.54 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.atLeast0_atMost_Suc
% 5.25/5.54 thf(fact_6128_sum_OatLeast0__atMost__Suc,axiom,
% 5.25/5.54 ! [G: nat > real,N: nat] :
% 5.25/5.54 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.atLeast0_atMost_Suc
% 5.25/5.54 thf(fact_6129_sum_Onat__ivl__Suc_H,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > rat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.54 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.nat_ivl_Suc'
% 5.25/5.54 thf(fact_6130_sum_Onat__ivl__Suc_H,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > int] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.54 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.nat_ivl_Suc'
% 5.25/5.54 thf(fact_6131_sum_Onat__ivl__Suc_H,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.54 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.nat_ivl_Suc'
% 5.25/5.54 thf(fact_6132_sum_Onat__ivl__Suc_H,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > real] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.54 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.nat_ivl_Suc'
% 5.25/5.54 thf(fact_6133_sum_OatLeast__Suc__atMost,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > rat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.atLeast_Suc_atMost
% 5.25/5.54 thf(fact_6134_sum_OatLeast__Suc__atMost,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > int] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.atLeast_Suc_atMost
% 5.25/5.54 thf(fact_6135_sum_OatLeast__Suc__atMost,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.atLeast_Suc_atMost
% 5.25/5.54 thf(fact_6136_sum_OatLeast__Suc__atMost,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > real] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.atLeast_Suc_atMost
% 5.25/5.54 thf(fact_6137_sum_OSuc__reindex__ivl,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > rat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_rat @ ( G @ M )
% 5.25/5.54 @ ( groups2906978787729119204at_rat
% 5.25/5.54 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.Suc_reindex_ivl
% 5.25/5.54 thf(fact_6138_sum_OSuc__reindex__ivl,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > int] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_int @ ( G @ M )
% 5.25/5.54 @ ( groups3539618377306564664at_int
% 5.25/5.54 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.Suc_reindex_ivl
% 5.25/5.54 thf(fact_6139_sum_OSuc__reindex__ivl,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_nat @ ( G @ M )
% 5.25/5.54 @ ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.Suc_reindex_ivl
% 5.25/5.54 thf(fact_6140_sum_OSuc__reindex__ivl,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > real] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.25/5.54 = ( plus_plus_real @ ( G @ M )
% 5.25/5.54 @ ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.Suc_reindex_ivl
% 5.25/5.54 thf(fact_6141_sum__Suc__diff,axiom,
% 5.25/5.54 ! [M: nat,N: nat,F: nat > rat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.54 => ( ( groups2906978787729119204at_rat
% 5.25/5.54 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_Suc_diff
% 5.25/5.54 thf(fact_6142_sum__Suc__diff,axiom,
% 5.25/5.54 ! [M: nat,N: nat,F: nat > int] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.54 => ( ( groups3539618377306564664at_int
% 5.25/5.54 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_Suc_diff
% 5.25/5.54 thf(fact_6143_sum__Suc__diff,axiom,
% 5.25/5.54 ! [M: nat,N: nat,F: nat > real] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.54 => ( ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [I3: nat] : ( minus_minus_real @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_Suc_diff
% 5.25/5.54 thf(fact_6144_take__bit__Suc__bit0,axiom,
% 5.25/5.54 ! [N: nat,K: num] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.25/5.54 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc_bit0
% 5.25/5.54 thf(fact_6145_take__bit__Suc__bit0,axiom,
% 5.25/5.54 ! [N: nat,K: num] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.25/5.54 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc_bit0
% 5.25/5.54 thf(fact_6146_take__bit__eq__mod,axiom,
% 5.25/5.54 ( bit_se1745604003318907178nteger
% 5.25/5.54 = ( ^ [N2: nat,A3: code_integer] : ( modulo364778990260209775nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_eq_mod
% 5.25/5.54 thf(fact_6147_take__bit__eq__mod,axiom,
% 5.25/5.54 ( bit_se2923211474154528505it_int
% 5.25/5.54 = ( ^ [N2: nat,A3: int] : ( modulo_modulo_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_eq_mod
% 5.25/5.54 thf(fact_6148_take__bit__eq__mod,axiom,
% 5.25/5.54 ( bit_se2925701944663578781it_nat
% 5.25/5.54 = ( ^ [N2: nat,A3: nat] : ( modulo_modulo_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_eq_mod
% 5.25/5.54 thf(fact_6149_take__bit__nat__eq__self__iff,axiom,
% 5.25/5.54 ! [N: nat,M: nat] :
% 5.25/5.54 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.25/5.54 = M )
% 5.25/5.54 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_nat_eq_self_iff
% 5.25/5.54 thf(fact_6150_take__bit__nat__less__exp,axiom,
% 5.25/5.54 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_nat_less_exp
% 5.25/5.54 thf(fact_6151_take__bit__nat__eq__self,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.54 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.25/5.54 = M ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_nat_eq_self
% 5.25/5.54 thf(fact_6152_take__bit__nat__def,axiom,
% 5.25/5.54 ( bit_se2925701944663578781it_nat
% 5.25/5.54 = ( ^ [N2: nat,M6: nat] : ( modulo_modulo_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_nat_def
% 5.25/5.54 thf(fact_6153_take__bit__int__less__exp,axiom,
% 5.25/5.54 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_int_less_exp
% 5.25/5.54 thf(fact_6154_sum_Oub__add__nat,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > rat,P2: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.25/5.54 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.25/5.54 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.ub_add_nat
% 5.25/5.54 thf(fact_6155_sum_Oub__add__nat,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > int,P2: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.25/5.54 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.25/5.54 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.ub_add_nat
% 5.25/5.54 thf(fact_6156_sum_Oub__add__nat,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > nat,P2: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.25/5.54 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.25/5.54 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.ub_add_nat
% 5.25/5.54 thf(fact_6157_sum_Oub__add__nat,axiom,
% 5.25/5.54 ! [M: nat,N: nat,G: nat > real,P2: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.25/5.54 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.25/5.54 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.ub_add_nat
% 5.25/5.54 thf(fact_6158_take__bit__int__def,axiom,
% 5.25/5.54 ( bit_se2923211474154528505it_int
% 5.25/5.54 = ( ^ [N2: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_int_def
% 5.25/5.54 thf(fact_6159_num_Osize__gen_I1_J,axiom,
% 5.25/5.54 ( ( size_num @ one )
% 5.25/5.54 = zero_zero_nat ) ).
% 5.25/5.54
% 5.25/5.54 % num.size_gen(1)
% 5.25/5.54 thf(fact_6160_take__bit__eq__0__iff,axiom,
% 5.25/5.54 ! [N: nat,A: code_integer] :
% 5.25/5.54 ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.25/5.54 = zero_z3403309356797280102nteger )
% 5.25/5.54 = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_eq_0_iff
% 5.25/5.54 thf(fact_6161_take__bit__eq__0__iff,axiom,
% 5.25/5.54 ! [N: nat,A: int] :
% 5.25/5.54 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.25/5.54 = zero_zero_int )
% 5.25/5.54 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_eq_0_iff
% 5.25/5.54 thf(fact_6162_take__bit__eq__0__iff,axiom,
% 5.25/5.54 ! [N: nat,A: nat] :
% 5.25/5.54 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.25/5.54 = zero_zero_nat )
% 5.25/5.54 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_eq_0_iff
% 5.25/5.54 thf(fact_6163_take__bit__numeral__bit0,axiom,
% 5.25/5.54 ! [L2: num,K: num] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.25/5.54 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_numeral_bit0
% 5.25/5.54 thf(fact_6164_take__bit__numeral__bit0,axiom,
% 5.25/5.54 ! [L2: num,K: num] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.25/5.54 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_numeral_bit0
% 5.25/5.54 thf(fact_6165_take__bit__nat__less__self__iff,axiom,
% 5.25/5.54 ! [N: nat,M: nat] :
% 5.25/5.54 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 5.25/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_nat_less_self_iff
% 5.25/5.54 thf(fact_6166_Suc__mask__eq__exp,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.25/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % Suc_mask_eq_exp
% 5.25/5.54 thf(fact_6167_mask__nat__less__exp,axiom,
% 5.25/5.54 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_nat_less_exp
% 5.25/5.54 thf(fact_6168_take__bit__Suc__minus__bit0,axiom,
% 5.25/5.54 ! [N: nat,K: num] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.25/5.54 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc_minus_bit0
% 5.25/5.54 thf(fact_6169_take__bit__int__less__self__iff,axiom,
% 5.25/5.54 ! [N: nat,K: int] :
% 5.25/5.54 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.25/5.54 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_int_less_self_iff
% 5.25/5.54 thf(fact_6170_take__bit__int__greater__eq__self__iff,axiom,
% 5.25/5.54 ! [K: int,N: nat] :
% 5.25/5.54 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.25/5.54 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_int_greater_eq_self_iff
% 5.25/5.54 thf(fact_6171_sum__natinterval__diff,axiom,
% 5.25/5.54 ! [M: nat,N: nat,F: nat > complex] :
% 5.25/5.54 ( ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups2073611262835488442omplex
% 5.25/5.54 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.25/5.54 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups2073611262835488442omplex
% 5.25/5.54 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = zero_zero_complex ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_natinterval_diff
% 5.25/5.54 thf(fact_6172_sum__natinterval__diff,axiom,
% 5.25/5.54 ! [M: nat,N: nat,F: nat > rat] :
% 5.25/5.54 ( ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups2906978787729119204at_rat
% 5.25/5.54 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.25/5.54 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups2906978787729119204at_rat
% 5.25/5.54 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = zero_zero_rat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_natinterval_diff
% 5.25/5.54 thf(fact_6173_sum__natinterval__diff,axiom,
% 5.25/5.54 ! [M: nat,N: nat,F: nat > int] :
% 5.25/5.54 ( ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups3539618377306564664at_int
% 5.25/5.54 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.25/5.54 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups3539618377306564664at_int
% 5.25/5.54 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = zero_zero_int ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_natinterval_diff
% 5.25/5.54 thf(fact_6174_sum__natinterval__diff,axiom,
% 5.25/5.54 ! [M: nat,N: nat,F: nat > real] :
% 5.25/5.54 ( ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.25/5.54 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = zero_zero_real ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_natinterval_diff
% 5.25/5.54 thf(fact_6175_sum__telescope_H_H,axiom,
% 5.25/5.54 ! [M: nat,N: nat,F: nat > rat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups2906978787729119204at_rat
% 5.25/5.54 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.25/5.54 = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_telescope''
% 5.25/5.54 thf(fact_6176_sum__telescope_H_H,axiom,
% 5.25/5.54 ! [M: nat,N: nat,F: nat > int] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups3539618377306564664at_int
% 5.25/5.54 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.25/5.54 = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_telescope''
% 5.25/5.54 thf(fact_6177_sum__telescope_H_H,axiom,
% 5.25/5.54 ! [M: nat,N: nat,F: nat > real] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.25/5.54 = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_telescope''
% 5.25/5.54 thf(fact_6178_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N ) )
% 5.25/5.54 = ( N = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % semiring_bit_operations_class.even_mask_iff
% 5.25/5.54 thf(fact_6179_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.25/5.54 = ( N = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % semiring_bit_operations_class.even_mask_iff
% 5.25/5.54 thf(fact_6180_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.25/5.54 = ( N = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % semiring_bit_operations_class.even_mask_iff
% 5.25/5.54 thf(fact_6181_take__bit__int__eq__self,axiom,
% 5.25/5.54 ! [K: int,N: nat] :
% 5.25/5.54 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.54 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.54 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.25/5.54 = K ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_int_eq_self
% 5.25/5.54 thf(fact_6182_take__bit__int__eq__self__iff,axiom,
% 5.25/5.54 ! [N: nat,K: int] :
% 5.25/5.54 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.25/5.54 = K )
% 5.25/5.54 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.54 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_int_eq_self_iff
% 5.25/5.54 thf(fact_6183_take__bit__numeral__minus__bit0,axiom,
% 5.25/5.54 ! [L2: num,K: num] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.25/5.54 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_numeral_minus_bit0
% 5.25/5.54 thf(fact_6184_mask__nat__def,axiom,
% 5.25/5.54 ( bit_se2002935070580805687sk_nat
% 5.25/5.54 = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_nat_def
% 5.25/5.54 thf(fact_6185_mask__half__int,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.54 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_half_int
% 5.25/5.54 thf(fact_6186_take__bit__incr__eq,axiom,
% 5.25/5.54 ! [N: nat,K: int] :
% 5.25/5.54 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.25/5.54 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.25/5.54 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.25/5.54 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_incr_eq
% 5.25/5.54 thf(fact_6187_mask__eq__sum__exp,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 5.25/5.54 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.54 @ ( collect_nat
% 5.25/5.54 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_eq_sum_exp
% 5.25/5.54 thf(fact_6188_mask__eq__sum__exp,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 5.25/5.54 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.54 @ ( collect_nat
% 5.25/5.54 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_eq_sum_exp
% 5.25/5.54 thf(fact_6189_mask__int__def,axiom,
% 5.25/5.54 ( bit_se2000444600071755411sk_int
% 5.25/5.54 = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_int_def
% 5.25/5.54 thf(fact_6190_sum__gp__multiplied,axiom,
% 5.25/5.54 ! [M: nat,N: nat,X3: complex] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.25/5.54 = ( minus_minus_complex @ ( power_power_complex @ X3 @ M ) @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_gp_multiplied
% 5.25/5.54 thf(fact_6191_sum__gp__multiplied,axiom,
% 5.25/5.54 ! [M: nat,N: nat,X3: rat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.25/5.54 = ( minus_minus_rat @ ( power_power_rat @ X3 @ M ) @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_gp_multiplied
% 5.25/5.54 thf(fact_6192_sum__gp__multiplied,axiom,
% 5.25/5.54 ! [M: nat,N: nat,X3: int] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.25/5.54 = ( minus_minus_int @ ( power_power_int @ X3 @ M ) @ ( power_power_int @ X3 @ ( suc @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_gp_multiplied
% 5.25/5.54 thf(fact_6193_sum__gp__multiplied,axiom,
% 5.25/5.54 ! [M: nat,N: nat,X3: real] :
% 5.25/5.54 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.54 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.25/5.54 = ( minus_minus_real @ ( power_power_real @ X3 @ M ) @ ( power_power_real @ X3 @ ( suc @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_gp_multiplied
% 5.25/5.54 thf(fact_6194_sum_Oin__pairs,axiom,
% 5.25/5.54 ! [G: nat > rat,M: nat,N: nat] :
% 5.25/5.54 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.54 = ( groups2906978787729119204at_rat
% 5.25/5.54 @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.in_pairs
% 5.25/5.54 thf(fact_6195_sum_Oin__pairs,axiom,
% 5.25/5.54 ! [G: nat > int,M: nat,N: nat] :
% 5.25/5.54 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.54 = ( groups3539618377306564664at_int
% 5.25/5.54 @ ^ [I3: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.in_pairs
% 5.25/5.54 thf(fact_6196_sum_Oin__pairs,axiom,
% 5.25/5.54 ! [G: nat > nat,M: nat,N: nat] :
% 5.25/5.54 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.54 = ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.in_pairs
% 5.25/5.54 thf(fact_6197_sum_Oin__pairs,axiom,
% 5.25/5.54 ! [G: nat > real,M: nat,N: nat] :
% 5.25/5.54 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.54 = ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [I3: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.in_pairs
% 5.25/5.54 thf(fact_6198_take__bit__Suc__minus__1__eq,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.54 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc_minus_1_eq
% 5.25/5.54 thf(fact_6199_take__bit__Suc__minus__1__eq,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.54 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc_minus_1_eq
% 5.25/5.54 thf(fact_6200_take__bit__Suc__bit1,axiom,
% 5.25/5.54 ! [N: nat,K: num] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.25/5.54 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc_bit1
% 5.25/5.54 thf(fact_6201_take__bit__Suc__bit1,axiom,
% 5.25/5.54 ! [N: nat,K: num] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.25/5.54 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc_bit1
% 5.25/5.54 thf(fact_6202_take__bit__numeral__minus__1__eq,axiom,
% 5.25/5.54 ! [K: num] :
% 5.25/5.54 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.54 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_numeral_minus_1_eq
% 5.25/5.54 thf(fact_6203_take__bit__numeral__minus__1__eq,axiom,
% 5.25/5.54 ! [K: num] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.54 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_numeral_minus_1_eq
% 5.25/5.54 thf(fact_6204_take__bit__Suc,axiom,
% 5.25/5.54 ! [N: nat,A: code_integer] :
% 5.25/5.54 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 5.25/5.54 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc
% 5.25/5.54 thf(fact_6205_take__bit__Suc,axiom,
% 5.25/5.54 ! [N: nat,A: int] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.25/5.54 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc
% 5.25/5.54 thf(fact_6206_take__bit__Suc,axiom,
% 5.25/5.54 ! [N: nat,A: nat] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 5.25/5.54 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc
% 5.25/5.54 thf(fact_6207_mask__eq__exp__minus__1,axiom,
% 5.25/5.54 ( bit_se2002935070580805687sk_nat
% 5.25/5.54 = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_eq_exp_minus_1
% 5.25/5.54 thf(fact_6208_mask__eq__exp__minus__1,axiom,
% 5.25/5.54 ( bit_se2000444600071755411sk_int
% 5.25/5.54 = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_eq_exp_minus_1
% 5.25/5.54 thf(fact_6209_take__bit__int__less__eq,axiom,
% 5.25/5.54 ! [N: nat,K: int] :
% 5.25/5.54 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.25/5.54 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.54 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_int_less_eq
% 5.25/5.54 thf(fact_6210_take__bit__int__greater__eq,axiom,
% 5.25/5.54 ! [K: int,N: nat] :
% 5.25/5.54 ( ( ord_less_int @ K @ zero_zero_int )
% 5.25/5.54 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_int_greater_eq
% 5.25/5.54 thf(fact_6211_signed__take__bit__eq__take__bit__shift,axiom,
% 5.25/5.54 ( bit_ri631733984087533419it_int
% 5.25/5.54 = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % signed_take_bit_eq_take_bit_shift
% 5.25/5.54 thf(fact_6212_mask__eq__sum__exp__nat,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 5.25/5.54 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.54 @ ( collect_nat
% 5.25/5.54 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mask_eq_sum_exp_nat
% 5.25/5.54 thf(fact_6213_stable__imp__take__bit__eq,axiom,
% 5.25/5.54 ! [A: code_integer,N: nat] :
% 5.25/5.54 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.54 = A )
% 5.25/5.54 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.54 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.25/5.54 = zero_z3403309356797280102nteger ) )
% 5.25/5.54 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.54 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.25/5.54 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % stable_imp_take_bit_eq
% 5.25/5.54 thf(fact_6214_stable__imp__take__bit__eq,axiom,
% 5.25/5.54 ! [A: int,N: nat] :
% 5.25/5.54 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.54 = A )
% 5.25/5.54 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.54 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.25/5.54 = zero_zero_int ) )
% 5.25/5.54 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.54 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.25/5.54 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % stable_imp_take_bit_eq
% 5.25/5.54 thf(fact_6215_stable__imp__take__bit__eq,axiom,
% 5.25/5.54 ! [A: nat,N: nat] :
% 5.25/5.54 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.54 = A )
% 5.25/5.54 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.54 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.25/5.54 = zero_zero_nat ) )
% 5.25/5.54 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.54 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.25/5.54 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % stable_imp_take_bit_eq
% 5.25/5.54 thf(fact_6216_gauss__sum__nat,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [X2: nat] : X2
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.25/5.54 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % gauss_sum_nat
% 5.25/5.54 thf(fact_6217_sum__mono,axiom,
% 5.25/5.54 ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 5.25/5.54 ( ! [I4: nat] :
% 5.25/5.54 ( ( member_nat @ I4 @ K5 )
% 5.25/5.54 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.25/5.54 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_mono
% 5.25/5.54 thf(fact_6218_sum__mono,axiom,
% 5.25/5.54 ! [K5: set_real,F: real > rat,G: real > rat] :
% 5.25/5.54 ( ! [I4: real] :
% 5.25/5.54 ( ( member_real @ I4 @ K5 )
% 5.25/5.54 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.25/5.54 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_mono
% 5.25/5.54 thf(fact_6219_sum__mono,axiom,
% 5.25/5.54 ! [K5: set_int,F: int > rat,G: int > rat] :
% 5.25/5.54 ( ! [I4: int] :
% 5.25/5.54 ( ( member_int @ I4 @ K5 )
% 5.25/5.54 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.25/5.54 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_mono
% 5.25/5.54 thf(fact_6220_sum__mono,axiom,
% 5.25/5.54 ! [K5: set_complex,F: complex > rat,G: complex > rat] :
% 5.25/5.54 ( ! [I4: complex] :
% 5.25/5.54 ( ( member_complex @ I4 @ K5 )
% 5.25/5.54 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.25/5.54 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ K5 ) @ ( groups5058264527183730370ex_rat @ G @ K5 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_mono
% 5.25/5.54 thf(fact_6221_sum__mono,axiom,
% 5.25/5.54 ! [K5: set_real,F: real > nat,G: real > nat] :
% 5.25/5.54 ( ! [I4: real] :
% 5.25/5.54 ( ( member_real @ I4 @ K5 )
% 5.25/5.54 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.25/5.54 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_mono
% 5.25/5.54 thf(fact_6222_sum__mono,axiom,
% 5.25/5.54 ! [K5: set_int,F: int > nat,G: int > nat] :
% 5.25/5.54 ( ! [I4: int] :
% 5.25/5.54 ( ( member_int @ I4 @ K5 )
% 5.25/5.54 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.25/5.54 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_mono
% 5.25/5.54 thf(fact_6223_sum__mono,axiom,
% 5.25/5.54 ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 5.25/5.54 ( ! [I4: complex] :
% 5.25/5.54 ( ( member_complex @ I4 @ K5 )
% 5.25/5.54 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.25/5.54 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_mono
% 5.25/5.54 thf(fact_6224_sum__mono,axiom,
% 5.25/5.54 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 5.25/5.54 ( ! [I4: nat] :
% 5.25/5.54 ( ( member_nat @ I4 @ K5 )
% 5.25/5.54 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.25/5.54 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_mono
% 5.25/5.54 thf(fact_6225_sum__mono,axiom,
% 5.25/5.54 ! [K5: set_real,F: real > int,G: real > int] :
% 5.25/5.54 ( ! [I4: real] :
% 5.25/5.54 ( ( member_real @ I4 @ K5 )
% 5.25/5.54 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.25/5.54 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_mono
% 5.25/5.54 thf(fact_6226_sum__mono,axiom,
% 5.25/5.54 ! [K5: set_complex,F: complex > int,G: complex > int] :
% 5.25/5.54 ( ! [I4: complex] :
% 5.25/5.54 ( ( member_complex @ I4 @ K5 )
% 5.25/5.54 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.25/5.54 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_mono
% 5.25/5.54 thf(fact_6227_take__bit__numeral__bit1,axiom,
% 5.25/5.54 ! [L2: num,K: num] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.25/5.54 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_numeral_bit1
% 5.25/5.54 thf(fact_6228_take__bit__numeral__bit1,axiom,
% 5.25/5.54 ! [L2: num,K: num] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.25/5.54 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_numeral_bit1
% 5.25/5.54 thf(fact_6229_sum__distrib__left,axiom,
% 5.25/5.54 ! [R2: int,F: int > int,A2: set_int] :
% 5.25/5.54 ( ( times_times_int @ R2 @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.25/5.54 = ( groups4538972089207619220nt_int
% 5.25/5.54 @ ^ [N2: int] : ( times_times_int @ R2 @ ( F @ N2 ) )
% 5.25/5.54 @ A2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_distrib_left
% 5.25/5.54 thf(fact_6230_sum__distrib__left,axiom,
% 5.25/5.54 ! [R2: nat,F: nat > nat,A2: set_nat] :
% 5.25/5.54 ( ( times_times_nat @ R2 @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.25/5.54 = ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [N2: nat] : ( times_times_nat @ R2 @ ( F @ N2 ) )
% 5.25/5.54 @ A2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_distrib_left
% 5.25/5.54 thf(fact_6231_sum__distrib__left,axiom,
% 5.25/5.54 ! [R2: real,F: nat > real,A2: set_nat] :
% 5.25/5.54 ( ( times_times_real @ R2 @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.25/5.54 = ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [N2: nat] : ( times_times_real @ R2 @ ( F @ N2 ) )
% 5.25/5.54 @ A2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_distrib_left
% 5.25/5.54 thf(fact_6232_sum__distrib__left,axiom,
% 5.25/5.54 ! [R2: complex,F: complex > complex,A2: set_complex] :
% 5.25/5.54 ( ( times_times_complex @ R2 @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.25/5.54 = ( groups7754918857620584856omplex
% 5.25/5.54 @ ^ [N2: complex] : ( times_times_complex @ R2 @ ( F @ N2 ) )
% 5.25/5.54 @ A2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_distrib_left
% 5.25/5.54 thf(fact_6233_sum__distrib__right,axiom,
% 5.25/5.54 ! [F: int > int,A2: set_int,R2: int] :
% 5.25/5.54 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ R2 )
% 5.25/5.54 = ( groups4538972089207619220nt_int
% 5.25/5.54 @ ^ [N2: int] : ( times_times_int @ ( F @ N2 ) @ R2 )
% 5.25/5.54 @ A2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_distrib_right
% 5.25/5.54 thf(fact_6234_sum__distrib__right,axiom,
% 5.25/5.54 ! [F: nat > nat,A2: set_nat,R2: nat] :
% 5.25/5.54 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R2 )
% 5.25/5.54 = ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [N2: nat] : ( times_times_nat @ ( F @ N2 ) @ R2 )
% 5.25/5.54 @ A2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_distrib_right
% 5.25/5.54 thf(fact_6235_sum__distrib__right,axiom,
% 5.25/5.54 ! [F: nat > real,A2: set_nat,R2: real] :
% 5.25/5.54 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R2 )
% 5.25/5.54 = ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ R2 )
% 5.25/5.54 @ A2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_distrib_right
% 5.25/5.54 thf(fact_6236_sum__distrib__right,axiom,
% 5.25/5.54 ! [F: complex > complex,A2: set_complex,R2: complex] :
% 5.25/5.54 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R2 )
% 5.25/5.54 = ( groups7754918857620584856omplex
% 5.25/5.54 @ ^ [N2: complex] : ( times_times_complex @ ( F @ N2 ) @ R2 )
% 5.25/5.54 @ A2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_distrib_right
% 5.25/5.54 thf(fact_6237_sum__product,axiom,
% 5.25/5.54 ! [F: int > int,A2: set_int,G: int > int,B3: set_int] :
% 5.25/5.54 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ B3 ) )
% 5.25/5.54 = ( groups4538972089207619220nt_int
% 5.25/5.54 @ ^ [I3: int] :
% 5.25/5.54 ( groups4538972089207619220nt_int
% 5.25/5.54 @ ^ [J3: int] : ( times_times_int @ ( F @ I3 ) @ ( G @ J3 ) )
% 5.25/5.54 @ B3 )
% 5.25/5.54 @ A2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_product
% 5.25/5.54 thf(fact_6238_sum__product,axiom,
% 5.25/5.54 ! [F: nat > nat,A2: set_nat,G: nat > nat,B3: set_nat] :
% 5.25/5.54 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B3 ) )
% 5.25/5.54 = ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [I3: nat] :
% 5.25/5.54 ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [J3: nat] : ( times_times_nat @ ( F @ I3 ) @ ( G @ J3 ) )
% 5.25/5.54 @ B3 )
% 5.25/5.54 @ A2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_product
% 5.25/5.54 thf(fact_6239_sum__product,axiom,
% 5.25/5.54 ! [F: nat > real,A2: set_nat,G: nat > real,B3: set_nat] :
% 5.25/5.54 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ B3 ) )
% 5.25/5.54 = ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [I3: nat] :
% 5.25/5.54 ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [J3: nat] : ( times_times_real @ ( F @ I3 ) @ ( G @ J3 ) )
% 5.25/5.54 @ B3 )
% 5.25/5.54 @ A2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_product
% 5.25/5.54 thf(fact_6240_sum__product,axiom,
% 5.25/5.54 ! [F: complex > complex,A2: set_complex,G: complex > complex,B3: set_complex] :
% 5.25/5.54 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ B3 ) )
% 5.25/5.54 = ( groups7754918857620584856omplex
% 5.25/5.54 @ ^ [I3: complex] :
% 5.25/5.54 ( groups7754918857620584856omplex
% 5.25/5.54 @ ^ [J3: complex] : ( times_times_complex @ ( F @ I3 ) @ ( G @ J3 ) )
% 5.25/5.54 @ B3 )
% 5.25/5.54 @ A2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_product
% 5.25/5.54 thf(fact_6241_sum_Odistrib,axiom,
% 5.25/5.54 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.25/5.54 ( ( groups4538972089207619220nt_int
% 5.25/5.54 @ ^ [X2: int] : ( plus_plus_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.25/5.54 @ A2 )
% 5.25/5.54 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.distrib
% 5.25/5.54 thf(fact_6242_sum_Odistrib,axiom,
% 5.25/5.54 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.25/5.54 ( ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [X2: nat] : ( plus_plus_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.25/5.54 @ A2 )
% 5.25/5.54 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.distrib
% 5.25/5.54 thf(fact_6243_sum_Odistrib,axiom,
% 5.25/5.54 ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 5.25/5.54 ( ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [X2: nat] : ( plus_plus_real @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.25/5.54 @ A2 )
% 5.25/5.54 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.distrib
% 5.25/5.54 thf(fact_6244_sum_Odistrib,axiom,
% 5.25/5.54 ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 5.25/5.54 ( ( groups7754918857620584856omplex
% 5.25/5.54 @ ^ [X2: complex] : ( plus_plus_complex @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.25/5.54 @ A2 )
% 5.25/5.54 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum.distrib
% 5.25/5.54 thf(fact_6245_sum__divide__distrib,axiom,
% 5.25/5.54 ! [F: nat > real,A2: set_nat,R2: real] :
% 5.25/5.54 ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R2 )
% 5.25/5.54 = ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ R2 )
% 5.25/5.54 @ A2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_divide_distrib
% 5.25/5.54 thf(fact_6246_sum__divide__distrib,axiom,
% 5.25/5.54 ! [F: complex > complex,A2: set_complex,R2: complex] :
% 5.25/5.54 ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R2 )
% 5.25/5.54 = ( groups7754918857620584856omplex
% 5.25/5.54 @ ^ [N2: complex] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ R2 )
% 5.25/5.54 @ A2 ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_divide_distrib
% 5.25/5.54 thf(fact_6247_take__bit__minus__small__eq,axiom,
% 5.25/5.54 ! [K: int,N: nat] :
% 5.25/5.54 ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.54 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.54 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 5.25/5.54 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_minus_small_eq
% 5.25/5.54 thf(fact_6248_arith__series__nat,axiom,
% 5.25/5.54 ! [A: nat,D: nat,N: nat] :
% 5.25/5.54 ( ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.25/5.54 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % arith_series_nat
% 5.25/5.54 thf(fact_6249_Sum__Icc__nat,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [X2: nat] : X2
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % Sum_Icc_nat
% 5.25/5.54 thf(fact_6250_take__bit__numeral__minus__bit1,axiom,
% 5.25/5.54 ! [L2: num,K: num] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.25/5.54 = ( 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 ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_numeral_minus_bit1
% 5.25/5.54 thf(fact_6251_take__bit__Suc__minus__bit1,axiom,
% 5.25/5.54 ! [N: nat,K: num] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.25/5.54 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_Suc_minus_bit1
% 5.25/5.54 thf(fact_6252_sum__gp,axiom,
% 5.25/5.54 ! [N: nat,M: nat,X3: complex] :
% 5.25/5.54 ( ( ( ord_less_nat @ N @ M )
% 5.25/5.54 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = zero_zero_complex ) )
% 5.25/5.54 & ( ~ ( ord_less_nat @ N @ M )
% 5.25/5.54 => ( ( ( X3 = one_one_complex )
% 5.25/5.54 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.25/5.54 & ( ( X3 != one_one_complex )
% 5.25/5.54 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X3 @ M ) @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_gp
% 5.25/5.54 thf(fact_6253_sum__gp,axiom,
% 5.25/5.54 ! [N: nat,M: nat,X3: rat] :
% 5.25/5.54 ( ( ( ord_less_nat @ N @ M )
% 5.25/5.54 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = zero_zero_rat ) )
% 5.25/5.54 & ( ~ ( ord_less_nat @ N @ M )
% 5.25/5.54 => ( ( ( X3 = one_one_rat )
% 5.25/5.54 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.25/5.54 & ( ( X3 != one_one_rat )
% 5.25/5.54 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X3 @ M ) @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_gp
% 5.25/5.54 thf(fact_6254_sum__gp,axiom,
% 5.25/5.54 ! [N: nat,M: nat,X3: real] :
% 5.25/5.54 ( ( ( ord_less_nat @ N @ M )
% 5.25/5.54 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = zero_zero_real ) )
% 5.25/5.54 & ( ~ ( ord_less_nat @ N @ M )
% 5.25/5.54 => ( ( ( X3 = one_one_real )
% 5.25/5.54 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.25/5.54 & ( ( X3 != one_one_real )
% 5.25/5.54 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.54 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X3 @ M ) @ ( power_power_real @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % sum_gp
% 5.25/5.54 thf(fact_6255_gauss__sum__from__Suc__0,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.25/5.54 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % gauss_sum_from_Suc_0
% 5.25/5.54 thf(fact_6256_gauss__sum__from__Suc__0,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.25/5.54 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % gauss_sum_from_Suc_0
% 5.25/5.54 thf(fact_6257_and__int__unfold,axiom,
% 5.25/5.54 ( bit_se725231765392027082nd_int
% 5.25/5.54 = ( ^ [K3: int,L: int] :
% 5.25/5.54 ( if_int
% 5.25/5.54 @ ( ( K3 = zero_zero_int )
% 5.25/5.54 | ( L = zero_zero_int ) )
% 5.25/5.54 @ zero_zero_int
% 5.25/5.54 @ ( if_int
% 5.25/5.54 @ ( K3
% 5.25/5.54 = ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.54 @ L
% 5.25/5.54 @ ( if_int
% 5.25/5.54 @ ( L
% 5.25/5.54 = ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.54 @ K3
% 5.25/5.54 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_int_unfold
% 5.25/5.54 thf(fact_6258_buildup__gives__empty,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 5.25/5.54 = bot_bot_set_nat ) ).
% 5.25/5.54
% 5.25/5.54 % buildup_gives_empty
% 5.25/5.54 thf(fact_6259_of__nat__eq__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ( semiri1314217659103216013at_int @ M )
% 5.25/5.54 = ( semiri1314217659103216013at_int @ N ) )
% 5.25/5.54 = ( M = N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_iff
% 5.25/5.54 thf(fact_6260_of__nat__eq__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ( semiri5074537144036343181t_real @ M )
% 5.25/5.54 = ( semiri5074537144036343181t_real @ N ) )
% 5.25/5.54 = ( M = N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_iff
% 5.25/5.54 thf(fact_6261_of__nat__eq__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.25/5.54 = ( semiri1316708129612266289at_nat @ N ) )
% 5.25/5.54 = ( M = N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_iff
% 5.25/5.54 thf(fact_6262_of__nat__eq__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ( semiri681578069525770553at_rat @ M )
% 5.25/5.54 = ( semiri681578069525770553at_rat @ N ) )
% 5.25/5.54 = ( M = N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_iff
% 5.25/5.54 thf(fact_6263_and_Oright__idem,axiom,
% 5.25/5.54 ! [A: int,B: int] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 5.25/5.54 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.25/5.54
% 5.25/5.54 % and.right_idem
% 5.25/5.54 thf(fact_6264_and_Oright__idem,axiom,
% 5.25/5.54 ! [A: nat,B: nat] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 5.25/5.54 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.25/5.54
% 5.25/5.54 % and.right_idem
% 5.25/5.54 thf(fact_6265_and_Oleft__idem,axiom,
% 5.25/5.54 ! [A: int,B: int] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.25/5.54 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.25/5.54
% 5.25/5.54 % and.left_idem
% 5.25/5.54 thf(fact_6266_and_Oleft__idem,axiom,
% 5.25/5.54 ! [A: nat,B: nat] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.25/5.54 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.25/5.54
% 5.25/5.54 % and.left_idem
% 5.25/5.54 thf(fact_6267_and_Oidem,axiom,
% 5.25/5.54 ! [A: int] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ A @ A )
% 5.25/5.54 = A ) ).
% 5.25/5.54
% 5.25/5.54 % and.idem
% 5.25/5.54 thf(fact_6268_and_Oidem,axiom,
% 5.25/5.54 ! [A: nat] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ A @ A )
% 5.25/5.54 = A ) ).
% 5.25/5.54
% 5.25/5.54 % and.idem
% 5.25/5.54 thf(fact_6269_empty__subsetI,axiom,
% 5.25/5.54 ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 5.25/5.54
% 5.25/5.54 % empty_subsetI
% 5.25/5.54 thf(fact_6270_empty__subsetI,axiom,
% 5.25/5.54 ! [A2: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A2 ) ).
% 5.25/5.54
% 5.25/5.54 % empty_subsetI
% 5.25/5.54 thf(fact_6271_empty__subsetI,axiom,
% 5.25/5.54 ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 5.25/5.54
% 5.25/5.54 % empty_subsetI
% 5.25/5.54 thf(fact_6272_subset__empty,axiom,
% 5.25/5.54 ! [A2: set_nat] :
% 5.25/5.54 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 5.25/5.54 = ( A2 = bot_bot_set_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % subset_empty
% 5.25/5.54 thf(fact_6273_subset__empty,axiom,
% 5.25/5.54 ! [A2: set_real] :
% 5.25/5.54 ( ( ord_less_eq_set_real @ A2 @ bot_bot_set_real )
% 5.25/5.54 = ( A2 = bot_bot_set_real ) ) ).
% 5.25/5.54
% 5.25/5.54 % subset_empty
% 5.25/5.54 thf(fact_6274_subset__empty,axiom,
% 5.25/5.54 ! [A2: set_int] :
% 5.25/5.54 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 5.25/5.54 = ( A2 = bot_bot_set_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % subset_empty
% 5.25/5.54 thf(fact_6275_int__eq__iff__numeral,axiom,
% 5.25/5.54 ! [M: nat,V: num] :
% 5.25/5.54 ( ( ( semiri1314217659103216013at_int @ M )
% 5.25/5.54 = ( numeral_numeral_int @ V ) )
% 5.25/5.54 = ( M
% 5.25/5.54 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % int_eq_iff_numeral
% 5.25/5.54 thf(fact_6276_bit_Oconj__zero__right,axiom,
% 5.25/5.54 ! [X3: int] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ X3 @ zero_zero_int )
% 5.25/5.54 = zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % bit.conj_zero_right
% 5.25/5.54 thf(fact_6277_bit_Oconj__zero__left,axiom,
% 5.25/5.54 ! [X3: int] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X3 )
% 5.25/5.54 = zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % bit.conj_zero_left
% 5.25/5.54 thf(fact_6278_zero__and__eq,axiom,
% 5.25/5.54 ! [A: int] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 5.25/5.54 = zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % zero_and_eq
% 5.25/5.54 thf(fact_6279_zero__and__eq,axiom,
% 5.25/5.54 ! [A: nat] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 5.25/5.54 = zero_zero_nat ) ).
% 5.25/5.54
% 5.25/5.54 % zero_and_eq
% 5.25/5.54 thf(fact_6280_and__zero__eq,axiom,
% 5.25/5.54 ! [A: int] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 5.25/5.54 = zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % and_zero_eq
% 5.25/5.54 thf(fact_6281_and__zero__eq,axiom,
% 5.25/5.54 ! [A: nat] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 5.25/5.54 = zero_zero_nat ) ).
% 5.25/5.54
% 5.25/5.54 % and_zero_eq
% 5.25/5.54 thf(fact_6282_negative__zle,axiom,
% 5.25/5.54 ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.25/5.54
% 5.25/5.54 % negative_zle
% 5.25/5.54 thf(fact_6283_take__bit__and,axiom,
% 5.25/5.54 ! [N: nat,A: int,B: int] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.25/5.54 = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_and
% 5.25/5.54 thf(fact_6284_take__bit__and,axiom,
% 5.25/5.54 ! [N: nat,A: nat,B: nat] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.25/5.54 = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_and
% 5.25/5.54 thf(fact_6285_of__nat__eq__0__iff,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ( ( ( semiri8010041392384452111omplex @ M )
% 5.25/5.54 = zero_zero_complex )
% 5.25/5.54 = ( M = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_0_iff
% 5.25/5.54 thf(fact_6286_of__nat__eq__0__iff,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ( ( ( semiri1314217659103216013at_int @ M )
% 5.25/5.54 = zero_zero_int )
% 5.25/5.54 = ( M = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_0_iff
% 5.25/5.54 thf(fact_6287_of__nat__eq__0__iff,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ( ( ( semiri5074537144036343181t_real @ M )
% 5.25/5.54 = zero_zero_real )
% 5.25/5.54 = ( M = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_0_iff
% 5.25/5.54 thf(fact_6288_of__nat__eq__0__iff,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.25/5.54 = zero_zero_nat )
% 5.25/5.54 = ( M = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_0_iff
% 5.25/5.54 thf(fact_6289_of__nat__eq__0__iff,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ( ( ( semiri681578069525770553at_rat @ M )
% 5.25/5.54 = zero_zero_rat )
% 5.25/5.54 = ( M = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_0_iff
% 5.25/5.54 thf(fact_6290_of__nat__0__eq__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( zero_zero_complex
% 5.25/5.54 = ( semiri8010041392384452111omplex @ N ) )
% 5.25/5.54 = ( zero_zero_nat = N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0_eq_iff
% 5.25/5.54 thf(fact_6291_of__nat__0__eq__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( zero_zero_int
% 5.25/5.54 = ( semiri1314217659103216013at_int @ N ) )
% 5.25/5.54 = ( zero_zero_nat = N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0_eq_iff
% 5.25/5.54 thf(fact_6292_of__nat__0__eq__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( zero_zero_real
% 5.25/5.54 = ( semiri5074537144036343181t_real @ N ) )
% 5.25/5.54 = ( zero_zero_nat = N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0_eq_iff
% 5.25/5.54 thf(fact_6293_of__nat__0__eq__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( zero_zero_nat
% 5.25/5.54 = ( semiri1316708129612266289at_nat @ N ) )
% 5.25/5.54 = ( zero_zero_nat = N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0_eq_iff
% 5.25/5.54 thf(fact_6294_of__nat__0__eq__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( zero_zero_rat
% 5.25/5.54 = ( semiri681578069525770553at_rat @ N ) )
% 5.25/5.54 = ( zero_zero_nat = N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0_eq_iff
% 5.25/5.54 thf(fact_6295_of__nat__0,axiom,
% 5.25/5.54 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.25/5.54 = zero_zero_complex ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0
% 5.25/5.54 thf(fact_6296_of__nat__0,axiom,
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.25/5.54 = zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0
% 5.25/5.54 thf(fact_6297_of__nat__0,axiom,
% 5.25/5.54 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.25/5.54 = zero_zero_real ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0
% 5.25/5.54 thf(fact_6298_of__nat__0,axiom,
% 5.25/5.54 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.25/5.54 = zero_zero_nat ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0
% 5.25/5.54 thf(fact_6299_of__nat__0,axiom,
% 5.25/5.54 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.25/5.54 = zero_zero_rat ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0
% 5.25/5.54 thf(fact_6300_of__nat__less__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.25/5.54 = ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_iff
% 5.25/5.54 thf(fact_6301_of__nat__less__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.25/5.54 = ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_iff
% 5.25/5.54 thf(fact_6302_of__nat__less__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.25/5.54 = ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_iff
% 5.25/5.54 thf(fact_6303_of__nat__less__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.25/5.54 = ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_iff
% 5.25/5.54 thf(fact_6304_of__nat__le__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.25/5.54 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_iff
% 5.25/5.54 thf(fact_6305_of__nat__le__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.25/5.54 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_iff
% 5.25/5.54 thf(fact_6306_of__nat__le__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.25/5.54 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_iff
% 5.25/5.54 thf(fact_6307_of__nat__le__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.25/5.54 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_iff
% 5.25/5.54 thf(fact_6308_of__nat__numeral,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 5.25/5.54 = ( numera6690914467698888265omplex @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_numeral
% 5.25/5.54 thf(fact_6309_of__nat__numeral,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.25/5.54 = ( numeral_numeral_int @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_numeral
% 5.25/5.54 thf(fact_6310_of__nat__numeral,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 5.25/5.54 = ( numeral_numeral_real @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_numeral
% 5.25/5.54 thf(fact_6311_of__nat__numeral,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 5.25/5.54 = ( numeral_numeral_nat @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_numeral
% 5.25/5.54 thf(fact_6312_of__nat__numeral,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 5.25/5.54 = ( numeral_numeral_rat @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_numeral
% 5.25/5.54 thf(fact_6313_atLeastatMost__empty__iff,axiom,
% 5.25/5.54 ! [A: set_int,B: set_int] :
% 5.25/5.54 ( ( ( set_or370866239135849197et_int @ A @ B )
% 5.25/5.54 = bot_bot_set_set_int )
% 5.25/5.54 = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty_iff
% 5.25/5.54 thf(fact_6314_atLeastatMost__empty__iff,axiom,
% 5.25/5.54 ! [A: rat,B: rat] :
% 5.25/5.54 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.25/5.54 = bot_bot_set_rat )
% 5.25/5.54 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty_iff
% 5.25/5.54 thf(fact_6315_atLeastatMost__empty__iff,axiom,
% 5.25/5.54 ! [A: num,B: num] :
% 5.25/5.54 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 5.25/5.54 = bot_bot_set_num )
% 5.25/5.54 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty_iff
% 5.25/5.54 thf(fact_6316_atLeastatMost__empty__iff,axiom,
% 5.25/5.54 ! [A: nat,B: nat] :
% 5.25/5.54 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.25/5.54 = bot_bot_set_nat )
% 5.25/5.54 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty_iff
% 5.25/5.54 thf(fact_6317_atLeastatMost__empty__iff,axiom,
% 5.25/5.54 ! [A: int,B: int] :
% 5.25/5.54 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.25/5.54 = bot_bot_set_int )
% 5.25/5.54 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty_iff
% 5.25/5.54 thf(fact_6318_atLeastatMost__empty__iff,axiom,
% 5.25/5.54 ! [A: real,B: real] :
% 5.25/5.54 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.25/5.54 = bot_bot_set_real )
% 5.25/5.54 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty_iff
% 5.25/5.54 thf(fact_6319_atLeastatMost__empty__iff2,axiom,
% 5.25/5.54 ! [A: set_int,B: set_int] :
% 5.25/5.54 ( ( bot_bot_set_set_int
% 5.25/5.54 = ( set_or370866239135849197et_int @ A @ B ) )
% 5.25/5.54 = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty_iff2
% 5.25/5.54 thf(fact_6320_atLeastatMost__empty__iff2,axiom,
% 5.25/5.54 ! [A: rat,B: rat] :
% 5.25/5.54 ( ( bot_bot_set_rat
% 5.25/5.54 = ( set_or633870826150836451st_rat @ A @ B ) )
% 5.25/5.54 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty_iff2
% 5.25/5.54 thf(fact_6321_atLeastatMost__empty__iff2,axiom,
% 5.25/5.54 ! [A: num,B: num] :
% 5.25/5.54 ( ( bot_bot_set_num
% 5.25/5.54 = ( set_or7049704709247886629st_num @ A @ B ) )
% 5.25/5.54 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty_iff2
% 5.25/5.54 thf(fact_6322_atLeastatMost__empty__iff2,axiom,
% 5.25/5.54 ! [A: nat,B: nat] :
% 5.25/5.54 ( ( bot_bot_set_nat
% 5.25/5.54 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.25/5.54 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty_iff2
% 5.25/5.54 thf(fact_6323_atLeastatMost__empty__iff2,axiom,
% 5.25/5.54 ! [A: int,B: int] :
% 5.25/5.54 ( ( bot_bot_set_int
% 5.25/5.54 = ( set_or1266510415728281911st_int @ A @ B ) )
% 5.25/5.54 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty_iff2
% 5.25/5.54 thf(fact_6324_atLeastatMost__empty__iff2,axiom,
% 5.25/5.54 ! [A: real,B: real] :
% 5.25/5.54 ( ( bot_bot_set_real
% 5.25/5.54 = ( set_or1222579329274155063t_real @ A @ B ) )
% 5.25/5.54 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty_iff2
% 5.25/5.54 thf(fact_6325_atLeastatMost__empty,axiom,
% 5.25/5.54 ! [B: rat,A: rat] :
% 5.25/5.54 ( ( ord_less_rat @ B @ A )
% 5.25/5.54 => ( ( set_or633870826150836451st_rat @ A @ B )
% 5.25/5.54 = bot_bot_set_rat ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty
% 5.25/5.54 thf(fact_6326_atLeastatMost__empty,axiom,
% 5.25/5.54 ! [B: num,A: num] :
% 5.25/5.54 ( ( ord_less_num @ B @ A )
% 5.25/5.54 => ( ( set_or7049704709247886629st_num @ A @ B )
% 5.25/5.54 = bot_bot_set_num ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty
% 5.25/5.54 thf(fact_6327_atLeastatMost__empty,axiom,
% 5.25/5.54 ! [B: nat,A: nat] :
% 5.25/5.54 ( ( ord_less_nat @ B @ A )
% 5.25/5.54 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.25/5.54 = bot_bot_set_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty
% 5.25/5.54 thf(fact_6328_atLeastatMost__empty,axiom,
% 5.25/5.54 ! [B: int,A: int] :
% 5.25/5.54 ( ( ord_less_int @ B @ A )
% 5.25/5.54 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.25/5.54 = bot_bot_set_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty
% 5.25/5.54 thf(fact_6329_atLeastatMost__empty,axiom,
% 5.25/5.54 ! [B: real,A: real] :
% 5.25/5.54 ( ( ord_less_real @ B @ A )
% 5.25/5.54 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.25/5.54 = bot_bot_set_real ) ) ).
% 5.25/5.54
% 5.25/5.54 % atLeastatMost_empty
% 5.25/5.54 thf(fact_6330_of__nat__add,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.54 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_add
% 5.25/5.54 thf(fact_6331_of__nat__add,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.54 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_add
% 5.25/5.54 thf(fact_6332_of__nat__add,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.54 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_add
% 5.25/5.54 thf(fact_6333_of__nat__add,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.54 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_add
% 5.25/5.54 thf(fact_6334_of__nat__mult,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 5.25/5.54 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_mult
% 5.25/5.54 thf(fact_6335_of__nat__mult,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 5.25/5.54 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_mult
% 5.25/5.54 thf(fact_6336_of__nat__mult,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 5.25/5.54 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_mult
% 5.25/5.54 thf(fact_6337_of__nat__mult,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 5.25/5.54 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_mult
% 5.25/5.54 thf(fact_6338_Diff__eq__empty__iff,axiom,
% 5.25/5.54 ! [A2: set_real,B3: set_real] :
% 5.25/5.54 ( ( ( minus_minus_set_real @ A2 @ B3 )
% 5.25/5.54 = bot_bot_set_real )
% 5.25/5.54 = ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % Diff_eq_empty_iff
% 5.25/5.54 thf(fact_6339_Diff__eq__empty__iff,axiom,
% 5.25/5.54 ! [A2: set_nat,B3: set_nat] :
% 5.25/5.54 ( ( ( minus_minus_set_nat @ A2 @ B3 )
% 5.25/5.54 = bot_bot_set_nat )
% 5.25/5.54 = ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % Diff_eq_empty_iff
% 5.25/5.54 thf(fact_6340_Diff__eq__empty__iff,axiom,
% 5.25/5.54 ! [A2: set_int,B3: set_int] :
% 5.25/5.54 ( ( ( minus_minus_set_int @ A2 @ B3 )
% 5.25/5.54 = bot_bot_set_int )
% 5.25/5.54 = ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % Diff_eq_empty_iff
% 5.25/5.54 thf(fact_6341_of__nat__1,axiom,
% 5.25/5.54 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.25/5.54 = one_one_complex ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_1
% 5.25/5.54 thf(fact_6342_of__nat__1,axiom,
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.25/5.54 = one_one_int ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_1
% 5.25/5.54 thf(fact_6343_of__nat__1,axiom,
% 5.25/5.54 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.25/5.54 = one_one_real ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_1
% 5.25/5.54 thf(fact_6344_of__nat__1,axiom,
% 5.25/5.54 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.25/5.54 = one_one_nat ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_1
% 5.25/5.54 thf(fact_6345_of__nat__1,axiom,
% 5.25/5.54 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.25/5.54 = one_one_rat ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_1
% 5.25/5.54 thf(fact_6346_of__nat__1__eq__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( one_one_complex
% 5.25/5.54 = ( semiri8010041392384452111omplex @ N ) )
% 5.25/5.54 = ( N = one_one_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_1_eq_iff
% 5.25/5.54 thf(fact_6347_of__nat__1__eq__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( one_one_int
% 5.25/5.54 = ( semiri1314217659103216013at_int @ N ) )
% 5.25/5.54 = ( N = one_one_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_1_eq_iff
% 5.25/5.54 thf(fact_6348_of__nat__1__eq__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( one_one_real
% 5.25/5.54 = ( semiri5074537144036343181t_real @ N ) )
% 5.25/5.54 = ( N = one_one_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_1_eq_iff
% 5.25/5.54 thf(fact_6349_of__nat__1__eq__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( one_one_nat
% 5.25/5.54 = ( semiri1316708129612266289at_nat @ N ) )
% 5.25/5.54 = ( N = one_one_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_1_eq_iff
% 5.25/5.54 thf(fact_6350_of__nat__1__eq__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( one_one_rat
% 5.25/5.54 = ( semiri681578069525770553at_rat @ N ) )
% 5.25/5.54 = ( N = one_one_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_1_eq_iff
% 5.25/5.54 thf(fact_6351_of__nat__eq__1__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ( semiri8010041392384452111omplex @ N )
% 5.25/5.54 = one_one_complex )
% 5.25/5.54 = ( N = one_one_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_1_iff
% 5.25/5.54 thf(fact_6352_of__nat__eq__1__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ( semiri1314217659103216013at_int @ N )
% 5.25/5.54 = one_one_int )
% 5.25/5.54 = ( N = one_one_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_1_iff
% 5.25/5.54 thf(fact_6353_of__nat__eq__1__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ( semiri5074537144036343181t_real @ N )
% 5.25/5.54 = one_one_real )
% 5.25/5.54 = ( N = one_one_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_1_iff
% 5.25/5.54 thf(fact_6354_of__nat__eq__1__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ( semiri1316708129612266289at_nat @ N )
% 5.25/5.54 = one_one_nat )
% 5.25/5.54 = ( N = one_one_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_1_iff
% 5.25/5.54 thf(fact_6355_of__nat__eq__1__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ( semiri681578069525770553at_rat @ N )
% 5.25/5.54 = one_one_rat )
% 5.25/5.54 = ( N = one_one_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_1_iff
% 5.25/5.54 thf(fact_6356_and_Oleft__neutral,axiom,
% 5.25/5.54 ! [A: code_integer] :
% 5.25/5.54 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 5.25/5.54 = A ) ).
% 5.25/5.54
% 5.25/5.54 % and.left_neutral
% 5.25/5.54 thf(fact_6357_and_Oleft__neutral,axiom,
% 5.25/5.54 ! [A: int] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 5.25/5.54 = A ) ).
% 5.25/5.54
% 5.25/5.54 % and.left_neutral
% 5.25/5.54 thf(fact_6358_and_Oright__neutral,axiom,
% 5.25/5.54 ! [A: code_integer] :
% 5.25/5.54 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.54 = A ) ).
% 5.25/5.54
% 5.25/5.54 % and.right_neutral
% 5.25/5.54 thf(fact_6359_and_Oright__neutral,axiom,
% 5.25/5.54 ! [A: int] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.54 = A ) ).
% 5.25/5.54
% 5.25/5.54 % and.right_neutral
% 5.25/5.54 thf(fact_6360_bit_Oconj__one__right,axiom,
% 5.25/5.54 ! [X3: code_integer] :
% 5.25/5.54 ( ( bit_se3949692690581998587nteger @ X3 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.54 = X3 ) ).
% 5.25/5.54
% 5.25/5.54 % bit.conj_one_right
% 5.25/5.54 thf(fact_6361_bit_Oconj__one__right,axiom,
% 5.25/5.54 ! [X3: int] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ X3 @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.54 = X3 ) ).
% 5.25/5.54
% 5.25/5.54 % bit.conj_one_right
% 5.25/5.54 thf(fact_6362_of__nat__power,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 5.25/5.54 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power
% 5.25/5.54 thf(fact_6363_of__nat__power,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 5.25/5.54 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power
% 5.25/5.54 thf(fact_6364_of__nat__power,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 5.25/5.54 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power
% 5.25/5.54 thf(fact_6365_of__nat__power,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 5.25/5.54 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power
% 5.25/5.54 thf(fact_6366_of__nat__power,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N ) )
% 5.25/5.54 = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power
% 5.25/5.54 thf(fact_6367_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.25/5.54 ! [B: nat,W: nat,X3: nat] :
% 5.25/5.54 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 5.25/5.54 = ( semiri8010041392384452111omplex @ X3 ) )
% 5.25/5.54 = ( ( power_power_nat @ B @ W )
% 5.25/5.54 = X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_of_nat_power_cancel_iff
% 5.25/5.54 thf(fact_6368_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.25/5.54 ! [B: nat,W: nat,X3: nat] :
% 5.25/5.54 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 5.25/5.54 = ( semiri1314217659103216013at_int @ X3 ) )
% 5.25/5.54 = ( ( power_power_nat @ B @ W )
% 5.25/5.54 = X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_of_nat_power_cancel_iff
% 5.25/5.54 thf(fact_6369_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.25/5.54 ! [B: nat,W: nat,X3: nat] :
% 5.25/5.54 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 5.25/5.54 = ( semiri5074537144036343181t_real @ X3 ) )
% 5.25/5.54 = ( ( power_power_nat @ B @ W )
% 5.25/5.54 = X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_of_nat_power_cancel_iff
% 5.25/5.54 thf(fact_6370_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.25/5.54 ! [B: nat,W: nat,X3: nat] :
% 5.25/5.54 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 5.25/5.54 = ( semiri1316708129612266289at_nat @ X3 ) )
% 5.25/5.54 = ( ( power_power_nat @ B @ W )
% 5.25/5.54 = X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_of_nat_power_cancel_iff
% 5.25/5.54 thf(fact_6371_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.25/5.54 ! [B: nat,W: nat,X3: nat] :
% 5.25/5.54 ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W )
% 5.25/5.54 = ( semiri681578069525770553at_rat @ X3 ) )
% 5.25/5.54 = ( ( power_power_nat @ B @ W )
% 5.25/5.54 = X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_eq_of_nat_power_cancel_iff
% 5.25/5.54 thf(fact_6372_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,B: nat,W: nat] :
% 5.25/5.54 ( ( ( semiri8010041392384452111omplex @ X3 )
% 5.25/5.54 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 5.25/5.54 = ( X3
% 5.25/5.54 = ( power_power_nat @ B @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power_eq_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6373_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,B: nat,W: nat] :
% 5.25/5.54 ( ( ( semiri1314217659103216013at_int @ X3 )
% 5.25/5.54 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.25/5.54 = ( X3
% 5.25/5.54 = ( power_power_nat @ B @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power_eq_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6374_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,B: nat,W: nat] :
% 5.25/5.54 ( ( ( semiri5074537144036343181t_real @ X3 )
% 5.25/5.54 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.25/5.54 = ( X3
% 5.25/5.54 = ( power_power_nat @ B @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power_eq_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6375_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,B: nat,W: nat] :
% 5.25/5.54 ( ( ( semiri1316708129612266289at_nat @ X3 )
% 5.25/5.54 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.25/5.54 = ( X3
% 5.25/5.54 = ( power_power_nat @ B @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power_eq_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6376_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,B: nat,W: nat] :
% 5.25/5.54 ( ( ( semiri681578069525770553at_rat @ X3 )
% 5.25/5.54 = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.25/5.54 = ( X3
% 5.25/5.54 = ( power_power_nat @ B @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power_eq_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6377_negative__zless,axiom,
% 5.25/5.54 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.25/5.54
% 5.25/5.54 % negative_zless
% 5.25/5.54 thf(fact_6378_and__nonnegative__int__iff,axiom,
% 5.25/5.54 ! [K: int,L2: int] :
% 5.25/5.54 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.25/5.54 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.54 | ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_nonnegative_int_iff
% 5.25/5.54 thf(fact_6379_and__negative__int__iff,axiom,
% 5.25/5.54 ! [K: int,L2: int] :
% 5.25/5.54 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ zero_zero_int )
% 5.25/5.54 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.25/5.54 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_negative_int_iff
% 5.25/5.54 thf(fact_6380_pred__numeral__inc,axiom,
% 5.25/5.54 ! [K: num] :
% 5.25/5.54 ( ( pred_numeral @ ( inc @ K ) )
% 5.25/5.54 = ( numeral_numeral_nat @ K ) ) ).
% 5.25/5.54
% 5.25/5.54 % pred_numeral_inc
% 5.25/5.54 thf(fact_6381_of__nat__of__bool,axiom,
% 5.25/5.54 ! [P: $o] :
% 5.25/5.54 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.25/5.54 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_of_bool
% 5.25/5.54 thf(fact_6382_of__nat__of__bool,axiom,
% 5.25/5.54 ! [P: $o] :
% 5.25/5.54 ( ( semiri681578069525770553at_rat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.25/5.54 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_of_bool
% 5.25/5.54 thf(fact_6383_of__nat__of__bool,axiom,
% 5.25/5.54 ! [P: $o] :
% 5.25/5.54 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.25/5.54 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_of_bool
% 5.25/5.54 thf(fact_6384_of__nat__of__bool,axiom,
% 5.25/5.54 ! [P: $o] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.25/5.54 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_of_bool
% 5.25/5.54 thf(fact_6385_of__nat__of__bool,axiom,
% 5.25/5.54 ! [P: $o] :
% 5.25/5.54 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.25/5.54 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_of_bool
% 5.25/5.54 thf(fact_6386_of__nat__le__0__iff,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.25/5.54 = ( M = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_0_iff
% 5.25/5.54 thf(fact_6387_of__nat__le__0__iff,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.25/5.54 = ( M = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_0_iff
% 5.25/5.54 thf(fact_6388_of__nat__le__0__iff,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.25/5.54 = ( M = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_0_iff
% 5.25/5.54 thf(fact_6389_of__nat__le__0__iff,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.25/5.54 = ( M = zero_zero_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_0_iff
% 5.25/5.54 thf(fact_6390_of__nat__Suc,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.25/5.54 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_Suc
% 5.25/5.54 thf(fact_6391_of__nat__Suc,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.25/5.54 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_Suc
% 5.25/5.54 thf(fact_6392_of__nat__Suc,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.25/5.54 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_Suc
% 5.25/5.54 thf(fact_6393_of__nat__Suc,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.25/5.54 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_Suc
% 5.25/5.54 thf(fact_6394_of__nat__Suc,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.25/5.54 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_Suc
% 5.25/5.54 thf(fact_6395_and__numerals_I8_J,axiom,
% 5.25/5.54 ! [X3: num] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ one_one_int )
% 5.25/5.54 = one_one_int ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(8)
% 5.25/5.54 thf(fact_6396_and__numerals_I8_J,axiom,
% 5.25/5.54 ! [X3: num] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ one_one_nat )
% 5.25/5.54 = one_one_nat ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(8)
% 5.25/5.54 thf(fact_6397_and__numerals_I2_J,axiom,
% 5.25/5.54 ! [Y: num] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.25/5.54 = one_one_int ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(2)
% 5.25/5.54 thf(fact_6398_and__numerals_I2_J,axiom,
% 5.25/5.54 ! [Y: num] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.25/5.54 = one_one_nat ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(2)
% 5.25/5.54 thf(fact_6399_numeral__less__real__of__nat__iff,axiom,
% 5.25/5.54 ! [W: num,N: nat] :
% 5.25/5.54 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.25/5.54 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_less_real_of_nat_iff
% 5.25/5.54 thf(fact_6400_real__of__nat__less__numeral__iff,axiom,
% 5.25/5.54 ! [N: nat,W: num] :
% 5.25/5.54 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 5.25/5.54 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % real_of_nat_less_numeral_iff
% 5.25/5.54 thf(fact_6401_numeral__le__real__of__nat__iff,axiom,
% 5.25/5.54 ! [N: num,M: nat] :
% 5.25/5.54 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.25/5.54 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_le_real_of_nat_iff
% 5.25/5.54 thf(fact_6402_of__nat__0__less__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.25/5.54 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0_less_iff
% 5.25/5.54 thf(fact_6403_of__nat__0__less__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.25/5.54 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0_less_iff
% 5.25/5.54 thf(fact_6404_of__nat__0__less__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 5.25/5.54 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0_less_iff
% 5.25/5.54 thf(fact_6405_of__nat__0__less__iff,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.25/5.54 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0_less_iff
% 5.25/5.54 thf(fact_6406_and__numerals_I5_J,axiom,
% 5.25/5.54 ! [X3: num] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ one_one_int )
% 5.25/5.54 = zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(5)
% 5.25/5.54 thf(fact_6407_and__numerals_I5_J,axiom,
% 5.25/5.54 ! [X3: num] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ one_one_nat )
% 5.25/5.54 = zero_zero_nat ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(5)
% 5.25/5.54 thf(fact_6408_and__numerals_I1_J,axiom,
% 5.25/5.54 ! [Y: num] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.25/5.54 = zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(1)
% 5.25/5.54 thf(fact_6409_and__numerals_I1_J,axiom,
% 5.25/5.54 ! [Y: num] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.25/5.54 = zero_zero_nat ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(1)
% 5.25/5.54 thf(fact_6410_and__numerals_I3_J,axiom,
% 5.25/5.54 ! [X3: num,Y: num] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.25/5.54 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(3)
% 5.25/5.54 thf(fact_6411_and__numerals_I3_J,axiom,
% 5.25/5.54 ! [X3: num,Y: num] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.25/5.54 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(3)
% 5.25/5.54 thf(fact_6412_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.25/5.54 ! [B: nat,W: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 5.25/5.54 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_of_nat_power_cancel_iff
% 5.25/5.54 thf(fact_6413_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.25/5.54 ! [B: nat,W: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 5.25/5.54 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_of_nat_power_cancel_iff
% 5.25/5.54 thf(fact_6414_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.25/5.54 ! [B: nat,W: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 5.25/5.54 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_of_nat_power_cancel_iff
% 5.25/5.54 thf(fact_6415_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.25/5.54 ! [B: nat,W: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 5.25/5.54 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_of_nat_power_cancel_iff
% 5.25/5.54 thf(fact_6416_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,B: nat,W: nat] :
% 5.25/5.54 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.25/5.54 = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power_less_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6417_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,B: nat,W: nat] :
% 5.25/5.54 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.25/5.54 = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power_less_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6418_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,B: nat,W: nat] :
% 5.25/5.54 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.25/5.54 = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power_less_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6419_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,B: nat,W: nat] :
% 5.25/5.54 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.25/5.54 = ( ord_less_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power_less_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6420_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.25/5.54 ! [B: nat,W: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 5.25/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_of_nat_power_cancel_iff
% 5.25/5.54 thf(fact_6421_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.25/5.54 ! [B: nat,W: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 5.25/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_of_nat_power_cancel_iff
% 5.25/5.54 thf(fact_6422_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.25/5.54 ! [B: nat,W: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 5.25/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_of_nat_power_cancel_iff
% 5.25/5.54 thf(fact_6423_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.25/5.54 ! [B: nat,W: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 5.25/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_of_nat_power_cancel_iff
% 5.25/5.54 thf(fact_6424_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,B: nat,W: nat] :
% 5.25/5.54 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.25/5.54 = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power_le_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6425_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,B: nat,W: nat] :
% 5.25/5.54 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.25/5.54 = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power_le_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6426_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,B: nat,W: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.25/5.54 = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power_le_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6427_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,B: nat,W: nat] :
% 5.25/5.54 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.25/5.54 = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_power_le_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6428_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: num,N: nat,Y: nat] :
% 5.25/5.54 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N )
% 5.25/5.54 = ( semiri8010041392384452111omplex @ Y ) )
% 5.25/5.54 = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 5.25/5.54 = Y ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_power_eq_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6429_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: num,N: nat,Y: nat] :
% 5.25/5.54 ( ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 5.25/5.54 = ( semiri1314217659103216013at_int @ Y ) )
% 5.25/5.54 = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 5.25/5.54 = Y ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_power_eq_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6430_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: num,N: nat,Y: nat] :
% 5.25/5.54 ( ( ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N )
% 5.25/5.54 = ( semiri5074537144036343181t_real @ Y ) )
% 5.25/5.54 = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 5.25/5.54 = Y ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_power_eq_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6431_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: num,N: nat,Y: nat] :
% 5.25/5.54 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 5.25/5.54 = ( semiri1316708129612266289at_nat @ Y ) )
% 5.25/5.54 = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 5.25/5.54 = Y ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_power_eq_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6432_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [X3: num,N: nat,Y: nat] :
% 5.25/5.54 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N )
% 5.25/5.54 = ( semiri681578069525770553at_rat @ Y ) )
% 5.25/5.54 = ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 5.25/5.54 = Y ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_power_eq_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6433_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.25/5.54 ! [Y: nat,X3: num,N: nat] :
% 5.25/5.54 ( ( ( semiri8010041392384452111omplex @ Y )
% 5.25/5.54 = ( power_power_complex @ ( numera6690914467698888265omplex @ X3 ) @ N ) )
% 5.25/5.54 = ( Y
% 5.25/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % real_of_nat_eq_numeral_power_cancel_iff
% 5.25/5.54 thf(fact_6434_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.25/5.54 ! [Y: nat,X3: num,N: nat] :
% 5.25/5.54 ( ( ( semiri1314217659103216013at_int @ Y )
% 5.25/5.54 = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) )
% 5.25/5.54 = ( Y
% 5.25/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % real_of_nat_eq_numeral_power_cancel_iff
% 5.25/5.54 thf(fact_6435_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.25/5.54 ! [Y: nat,X3: num,N: nat] :
% 5.25/5.54 ( ( ( semiri5074537144036343181t_real @ Y )
% 5.25/5.54 = ( power_power_real @ ( numeral_numeral_real @ X3 ) @ N ) )
% 5.25/5.54 = ( Y
% 5.25/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % real_of_nat_eq_numeral_power_cancel_iff
% 5.25/5.54 thf(fact_6436_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.25/5.54 ! [Y: nat,X3: num,N: nat] :
% 5.25/5.54 ( ( ( semiri1316708129612266289at_nat @ Y )
% 5.25/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) )
% 5.25/5.54 = ( Y
% 5.25/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % real_of_nat_eq_numeral_power_cancel_iff
% 5.25/5.54 thf(fact_6437_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.25/5.54 ! [Y: nat,X3: num,N: nat] :
% 5.25/5.54 ( ( ( semiri681578069525770553at_rat @ Y )
% 5.25/5.54 = ( power_power_rat @ ( numeral_numeral_rat @ X3 ) @ N ) )
% 5.25/5.54 = ( Y
% 5.25/5.54 = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % real_of_nat_eq_numeral_power_cancel_iff
% 5.25/5.54 thf(fact_6438_add__neg__numeral__special_I5_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.54 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % add_neg_numeral_special(5)
% 5.25/5.54 thf(fact_6439_add__neg__numeral__special_I5_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.25/5.54 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % add_neg_numeral_special(5)
% 5.25/5.54 thf(fact_6440_add__neg__numeral__special_I5_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.25/5.54 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % add_neg_numeral_special(5)
% 5.25/5.54 thf(fact_6441_add__neg__numeral__special_I5_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.25/5.54 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % add_neg_numeral_special(5)
% 5.25/5.54 thf(fact_6442_add__neg__numeral__special_I5_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.25/5.54 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % add_neg_numeral_special(5)
% 5.25/5.54 thf(fact_6443_add__neg__numeral__special_I6_J,axiom,
% 5.25/5.54 ! [M: num] :
% 5.25/5.54 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.54 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % add_neg_numeral_special(6)
% 5.25/5.54 thf(fact_6444_add__neg__numeral__special_I6_J,axiom,
% 5.25/5.54 ! [M: num] :
% 5.25/5.54 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.54 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % add_neg_numeral_special(6)
% 5.25/5.54 thf(fact_6445_add__neg__numeral__special_I6_J,axiom,
% 5.25/5.54 ! [M: num] :
% 5.25/5.54 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.25/5.54 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % add_neg_numeral_special(6)
% 5.25/5.54 thf(fact_6446_add__neg__numeral__special_I6_J,axiom,
% 5.25/5.54 ! [M: num] :
% 5.25/5.54 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.54 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % add_neg_numeral_special(6)
% 5.25/5.54 thf(fact_6447_add__neg__numeral__special_I6_J,axiom,
% 5.25/5.54 ! [M: num] :
% 5.25/5.54 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.54 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % add_neg_numeral_special(6)
% 5.25/5.54 thf(fact_6448_diff__numeral__special_I6_J,axiom,
% 5.25/5.54 ! [M: num] :
% 5.25/5.54 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.54 = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % diff_numeral_special(6)
% 5.25/5.54 thf(fact_6449_diff__numeral__special_I6_J,axiom,
% 5.25/5.54 ! [M: num] :
% 5.25/5.54 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.54 = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % diff_numeral_special(6)
% 5.25/5.54 thf(fact_6450_diff__numeral__special_I6_J,axiom,
% 5.25/5.54 ! [M: num] :
% 5.25/5.54 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.25/5.54 = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % diff_numeral_special(6)
% 5.25/5.54 thf(fact_6451_diff__numeral__special_I6_J,axiom,
% 5.25/5.54 ! [M: num] :
% 5.25/5.54 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.54 = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % diff_numeral_special(6)
% 5.25/5.54 thf(fact_6452_diff__numeral__special_I6_J,axiom,
% 5.25/5.54 ! [M: num] :
% 5.25/5.54 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.54 = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % diff_numeral_special(6)
% 5.25/5.54 thf(fact_6453_diff__numeral__special_I5_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.54 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % diff_numeral_special(5)
% 5.25/5.54 thf(fact_6454_diff__numeral__special_I5_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 5.25/5.54 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % diff_numeral_special(5)
% 5.25/5.54 thf(fact_6455_diff__numeral__special_I5_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 5.25/5.54 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % diff_numeral_special(5)
% 5.25/5.54 thf(fact_6456_diff__numeral__special_I5_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 5.25/5.54 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % diff_numeral_special(5)
% 5.25/5.54 thf(fact_6457_diff__numeral__special_I5_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 5.25/5.54 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % diff_numeral_special(5)
% 5.25/5.54 thf(fact_6458_and__minus__numerals_I6_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.25/5.54 = one_one_int ) ).
% 5.25/5.54
% 5.25/5.54 % and_minus_numerals(6)
% 5.25/5.54 thf(fact_6459_and__minus__numerals_I2_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.25/5.54 = one_one_int ) ).
% 5.25/5.54
% 5.25/5.54 % and_minus_numerals(2)
% 5.25/5.54 thf(fact_6460_of__nat__zero__less__power__iff,axiom,
% 5.25/5.54 ! [X3: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X3 ) @ N ) )
% 5.25/5.54 = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 5.25/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_zero_less_power_iff
% 5.25/5.54 thf(fact_6461_of__nat__zero__less__power__iff,axiom,
% 5.25/5.54 ! [X3: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X3 ) @ N ) )
% 5.25/5.54 = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 5.25/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_zero_less_power_iff
% 5.25/5.54 thf(fact_6462_of__nat__zero__less__power__iff,axiom,
% 5.25/5.54 ! [X3: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ N ) )
% 5.25/5.54 = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 5.25/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_zero_less_power_iff
% 5.25/5.54 thf(fact_6463_of__nat__zero__less__power__iff,axiom,
% 5.25/5.54 ! [X3: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X3 ) @ N ) )
% 5.25/5.54 = ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 5.25/5.54 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_zero_less_power_iff
% 5.25/5.54 thf(fact_6464_and__numerals_I6_J,axiom,
% 5.25/5.54 ! [X3: num,Y: num] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.25/5.54 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(6)
% 5.25/5.54 thf(fact_6465_and__numerals_I6_J,axiom,
% 5.25/5.54 ! [X3: num,Y: num] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.25/5.54 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(6)
% 5.25/5.54 thf(fact_6466_and__numerals_I4_J,axiom,
% 5.25/5.54 ! [X3: num,Y: num] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X3 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.25/5.54 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(4)
% 5.25/5.54 thf(fact_6467_and__numerals_I4_J,axiom,
% 5.25/5.54 ! [X3: num,Y: num] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.25/5.54 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(4)
% 5.25/5.54 thf(fact_6468_and__minus__numerals_I1_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.25/5.54 = zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % and_minus_numerals(1)
% 5.25/5.54 thf(fact_6469_and__minus__numerals_I5_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.25/5.54 = zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % and_minus_numerals(5)
% 5.25/5.54 thf(fact_6470_even__of__nat,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.25/5.54 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % even_of_nat
% 5.25/5.54 thf(fact_6471_even__of__nat,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.25/5.54 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % even_of_nat
% 5.25/5.54 thf(fact_6472_even__of__nat,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.25/5.54 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % even_of_nat
% 5.25/5.54 thf(fact_6473_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [I2: num,N: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 5.25/5.54 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_power_less_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6474_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [I2: num,N: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 5.25/5.54 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_power_less_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6475_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [I2: num,N: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 5.25/5.54 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_power_less_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6476_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [I2: num,N: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 5.25/5.54 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_power_less_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6477_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,I2: num,N: nat] :
% 5.25/5.54 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) )
% 5.25/5.54 = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_numeral_power_cancel_iff
% 5.25/5.54 thf(fact_6478_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,I2: num,N: nat] :
% 5.25/5.54 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) )
% 5.25/5.54 = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_numeral_power_cancel_iff
% 5.25/5.54 thf(fact_6479_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,I2: num,N: nat] :
% 5.25/5.54 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) )
% 5.25/5.54 = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_numeral_power_cancel_iff
% 5.25/5.54 thf(fact_6480_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,I2: num,N: nat] :
% 5.25/5.54 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) )
% 5.25/5.54 = ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_numeral_power_cancel_iff
% 5.25/5.54 thf(fact_6481_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [I2: num,N: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) @ ( semiri5074537144036343181t_real @ X3 ) )
% 5.25/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_power_le_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6482_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [I2: num,N: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) @ ( semiri681578069525770553at_rat @ X3 ) )
% 5.25/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_power_le_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6483_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [I2: num,N: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ ( semiri1316708129612266289at_nat @ X3 ) )
% 5.25/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_power_le_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6484_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.25/5.54 ! [I2: num,N: nat,X3: nat] :
% 5.25/5.54 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) @ ( semiri1314217659103216013at_int @ X3 ) )
% 5.25/5.54 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_power_le_of_nat_cancel_iff
% 5.25/5.54 thf(fact_6485_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,I2: num,N: nat] :
% 5.25/5.54 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) )
% 5.25/5.54 = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_numeral_power_cancel_iff
% 5.25/5.54 thf(fact_6486_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,I2: num,N: nat] :
% 5.25/5.54 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) )
% 5.25/5.54 = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_numeral_power_cancel_iff
% 5.25/5.54 thf(fact_6487_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,I2: num,N: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) )
% 5.25/5.54 = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_numeral_power_cancel_iff
% 5.25/5.54 thf(fact_6488_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.25/5.54 ! [X3: nat,I2: num,N: nat] :
% 5.25/5.54 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) )
% 5.25/5.54 = ( ord_less_eq_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_le_numeral_power_cancel_iff
% 5.25/5.54 thf(fact_6489_and__numerals_I7_J,axiom,
% 5.25/5.54 ! [X3: num,Y: num] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X3 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.25/5.54 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X3 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(7)
% 5.25/5.54 thf(fact_6490_and__numerals_I7_J,axiom,
% 5.25/5.54 ! [X3: num,Y: num] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.25/5.54 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X3 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_numerals(7)
% 5.25/5.54 thf(fact_6491_of__int__and__eq,axiom,
% 5.25/5.54 ! [K: int,L2: int] :
% 5.25/5.54 ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.25/5.54 = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_int_and_eq
% 5.25/5.54 thf(fact_6492_and_Oleft__commute,axiom,
% 5.25/5.54 ! [B: int,A: int,C: int] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 5.25/5.54 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and.left_commute
% 5.25/5.54 thf(fact_6493_and_Oleft__commute,axiom,
% 5.25/5.54 ! [B: nat,A: nat,C: nat] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 5.25/5.54 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and.left_commute
% 5.25/5.54 thf(fact_6494_of__nat__and__eq,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.25/5.54 = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_and_eq
% 5.25/5.54 thf(fact_6495_of__nat__and__eq,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.25/5.54 = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_and_eq
% 5.25/5.54 thf(fact_6496_and_Ocommute,axiom,
% 5.25/5.54 ( bit_se725231765392027082nd_int
% 5.25/5.54 = ( ^ [A3: int,B2: int] : ( bit_se725231765392027082nd_int @ B2 @ A3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and.commute
% 5.25/5.54 thf(fact_6497_and_Ocommute,axiom,
% 5.25/5.54 ( bit_se727722235901077358nd_nat
% 5.25/5.54 = ( ^ [A3: nat,B2: nat] : ( bit_se727722235901077358nd_nat @ B2 @ A3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and.commute
% 5.25/5.54 thf(fact_6498_and_Oassoc,axiom,
% 5.25/5.54 ! [A: int,B: int,C: int] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 5.25/5.54 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and.assoc
% 5.25/5.54 thf(fact_6499_and_Oassoc,axiom,
% 5.25/5.54 ! [A: nat,B: nat,C: nat] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 5.25/5.54 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and.assoc
% 5.25/5.54 thf(fact_6500_bot_Oextremum__uniqueI,axiom,
% 5.25/5.54 ! [A: set_nat] :
% 5.25/5.54 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.25/5.54 => ( A = bot_bot_set_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_uniqueI
% 5.25/5.54 thf(fact_6501_bot_Oextremum__uniqueI,axiom,
% 5.25/5.54 ! [A: extended_enat] :
% 5.25/5.54 ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 5.25/5.54 => ( A = bot_bo4199563552545308370d_enat ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_uniqueI
% 5.25/5.54 thf(fact_6502_bot_Oextremum__uniqueI,axiom,
% 5.25/5.54 ! [A: set_real] :
% 5.25/5.54 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.25/5.54 => ( A = bot_bot_set_real ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_uniqueI
% 5.25/5.54 thf(fact_6503_bot_Oextremum__uniqueI,axiom,
% 5.25/5.54 ! [A: set_int] :
% 5.25/5.54 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.25/5.54 => ( A = bot_bot_set_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_uniqueI
% 5.25/5.54 thf(fact_6504_bot_Oextremum__uniqueI,axiom,
% 5.25/5.54 ! [A: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.25/5.54 => ( A = bot_bot_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_uniqueI
% 5.25/5.54 thf(fact_6505_bot_Oextremum__unique,axiom,
% 5.25/5.54 ! [A: set_nat] :
% 5.25/5.54 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.25/5.54 = ( A = bot_bot_set_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_unique
% 5.25/5.54 thf(fact_6506_bot_Oextremum__unique,axiom,
% 5.25/5.54 ! [A: extended_enat] :
% 5.25/5.54 ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 5.25/5.54 = ( A = bot_bo4199563552545308370d_enat ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_unique
% 5.25/5.54 thf(fact_6507_bot_Oextremum__unique,axiom,
% 5.25/5.54 ! [A: set_real] :
% 5.25/5.54 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.25/5.54 = ( A = bot_bot_set_real ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_unique
% 5.25/5.54 thf(fact_6508_bot_Oextremum__unique,axiom,
% 5.25/5.54 ! [A: set_int] :
% 5.25/5.54 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.25/5.54 = ( A = bot_bot_set_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_unique
% 5.25/5.54 thf(fact_6509_bot_Oextremum__unique,axiom,
% 5.25/5.54 ! [A: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.25/5.54 = ( A = bot_bot_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_unique
% 5.25/5.54 thf(fact_6510_bot_Oextremum,axiom,
% 5.25/5.54 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum
% 5.25/5.54 thf(fact_6511_bot_Oextremum,axiom,
% 5.25/5.54 ! [A: extended_enat] : ( ord_le2932123472753598470d_enat @ bot_bo4199563552545308370d_enat @ A ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum
% 5.25/5.54 thf(fact_6512_bot_Oextremum,axiom,
% 5.25/5.54 ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum
% 5.25/5.54 thf(fact_6513_bot_Oextremum,axiom,
% 5.25/5.54 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum
% 5.25/5.54 thf(fact_6514_bot_Oextremum,axiom,
% 5.25/5.54 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum
% 5.25/5.54 thf(fact_6515_bot_Oextremum__strict,axiom,
% 5.25/5.54 ! [A: set_nat] :
% 5.25/5.54 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_strict
% 5.25/5.54 thf(fact_6516_bot_Oextremum__strict,axiom,
% 5.25/5.54 ! [A: extended_enat] :
% 5.25/5.54 ~ ( ord_le72135733267957522d_enat @ A @ bot_bo4199563552545308370d_enat ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_strict
% 5.25/5.54 thf(fact_6517_bot_Oextremum__strict,axiom,
% 5.25/5.54 ! [A: set_int] :
% 5.25/5.54 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_strict
% 5.25/5.54 thf(fact_6518_bot_Oextremum__strict,axiom,
% 5.25/5.54 ! [A: set_real] :
% 5.25/5.54 ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_strict
% 5.25/5.54 thf(fact_6519_bot_Oextremum__strict,axiom,
% 5.25/5.54 ! [A: nat] :
% 5.25/5.54 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 5.25/5.54
% 5.25/5.54 % bot.extremum_strict
% 5.25/5.54 thf(fact_6520_bot_Onot__eq__extremum,axiom,
% 5.25/5.54 ! [A: set_nat] :
% 5.25/5.54 ( ( A != bot_bot_set_nat )
% 5.25/5.54 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.not_eq_extremum
% 5.25/5.54 thf(fact_6521_bot_Onot__eq__extremum,axiom,
% 5.25/5.54 ! [A: extended_enat] :
% 5.25/5.54 ( ( A != bot_bo4199563552545308370d_enat )
% 5.25/5.54 = ( ord_le72135733267957522d_enat @ bot_bo4199563552545308370d_enat @ A ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.not_eq_extremum
% 5.25/5.54 thf(fact_6522_bot_Onot__eq__extremum,axiom,
% 5.25/5.54 ! [A: set_int] :
% 5.25/5.54 ( ( A != bot_bot_set_int )
% 5.25/5.54 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.not_eq_extremum
% 5.25/5.54 thf(fact_6523_bot_Onot__eq__extremum,axiom,
% 5.25/5.54 ! [A: set_real] :
% 5.25/5.54 ( ( A != bot_bot_set_real )
% 5.25/5.54 = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.not_eq_extremum
% 5.25/5.54 thf(fact_6524_bot_Onot__eq__extremum,axiom,
% 5.25/5.54 ! [A: nat] :
% 5.25/5.54 ( ( A != bot_bot_nat )
% 5.25/5.54 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 5.25/5.54
% 5.25/5.54 % bot.not_eq_extremum
% 5.25/5.54 thf(fact_6525_real__arch__simple,axiom,
% 5.25/5.54 ! [X3: real] :
% 5.25/5.54 ? [N3: nat] : ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % real_arch_simple
% 5.25/5.54 thf(fact_6526_real__arch__simple,axiom,
% 5.25/5.54 ! [X3: rat] :
% 5.25/5.54 ? [N3: nat] : ( ord_less_eq_rat @ X3 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % real_arch_simple
% 5.25/5.54 thf(fact_6527_reals__Archimedean2,axiom,
% 5.25/5.54 ! [X3: real] :
% 5.25/5.54 ? [N3: nat] : ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % reals_Archimedean2
% 5.25/5.54 thf(fact_6528_reals__Archimedean2,axiom,
% 5.25/5.54 ! [X3: rat] :
% 5.25/5.54 ? [N3: nat] : ( ord_less_rat @ X3 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % reals_Archimedean2
% 5.25/5.54 thf(fact_6529_mult__of__nat__commute,axiom,
% 5.25/5.54 ! [X3: nat,Y: int] :
% 5.25/5.54 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X3 ) @ Y )
% 5.25/5.54 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mult_of_nat_commute
% 5.25/5.54 thf(fact_6530_mult__of__nat__commute,axiom,
% 5.25/5.54 ! [X3: nat,Y: real] :
% 5.25/5.54 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ Y )
% 5.25/5.54 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mult_of_nat_commute
% 5.25/5.54 thf(fact_6531_mult__of__nat__commute,axiom,
% 5.25/5.54 ! [X3: nat,Y: nat] :
% 5.25/5.54 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ Y )
% 5.25/5.54 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mult_of_nat_commute
% 5.25/5.54 thf(fact_6532_mult__of__nat__commute,axiom,
% 5.25/5.54 ! [X3: nat,Y: rat] :
% 5.25/5.54 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X3 ) @ Y )
% 5.25/5.54 = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mult_of_nat_commute
% 5.25/5.54 thf(fact_6533_take__bit__of__nat,axiom,
% 5.25/5.54 ! [N: nat,M: nat] :
% 5.25/5.54 ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 5.25/5.54 = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_nat
% 5.25/5.54 thf(fact_6534_take__bit__of__nat,axiom,
% 5.25/5.54 ! [N: nat,M: nat] :
% 5.25/5.54 ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 5.25/5.54 = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_of_nat
% 5.25/5.54 thf(fact_6535_of__nat__mask__eq,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.25/5.54 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_mask_eq
% 5.25/5.54 thf(fact_6536_of__nat__mask__eq,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.25/5.54 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_mask_eq
% 5.25/5.54 thf(fact_6537_of__nat__less__of__int__iff,axiom,
% 5.25/5.54 ! [N: nat,X3: int] :
% 5.25/5.54 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X3 ) )
% 5.25/5.54 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_of_int_iff
% 5.25/5.54 thf(fact_6538_of__nat__less__of__int__iff,axiom,
% 5.25/5.54 ! [N: nat,X3: int] :
% 5.25/5.54 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X3 ) )
% 5.25/5.54 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_of_int_iff
% 5.25/5.54 thf(fact_6539_of__nat__less__of__int__iff,axiom,
% 5.25/5.54 ! [N: nat,X3: int] :
% 5.25/5.54 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X3 ) )
% 5.25/5.54 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_of_int_iff
% 5.25/5.54 thf(fact_6540_num__induct,axiom,
% 5.25/5.54 ! [P: num > $o,X3: num] :
% 5.25/5.54 ( ( P @ one )
% 5.25/5.54 => ( ! [X5: num] :
% 5.25/5.54 ( ( P @ X5 )
% 5.25/5.54 => ( P @ ( inc @ X5 ) ) )
% 5.25/5.54 => ( P @ X3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % num_induct
% 5.25/5.54 thf(fact_6541_add__inc,axiom,
% 5.25/5.54 ! [X3: num,Y: num] :
% 5.25/5.54 ( ( plus_plus_num @ X3 @ ( inc @ Y ) )
% 5.25/5.54 = ( inc @ ( plus_plus_num @ X3 @ Y ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % add_inc
% 5.25/5.54 thf(fact_6542_and__eq__minus__1__iff,axiom,
% 5.25/5.54 ! [A: code_integer,B: code_integer] :
% 5.25/5.54 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 5.25/5.54 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.54 = ( ( A
% 5.25/5.54 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.54 & ( B
% 5.25/5.54 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_eq_minus_1_iff
% 5.25/5.54 thf(fact_6543_and__eq__minus__1__iff,axiom,
% 5.25/5.54 ! [A: int,B: int] :
% 5.25/5.54 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 5.25/5.54 = ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.54 = ( ( A
% 5.25/5.54 = ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.54 & ( B
% 5.25/5.54 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_eq_minus_1_iff
% 5.25/5.54 thf(fact_6544_of__nat__0__le__iff,axiom,
% 5.25/5.54 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0_le_iff
% 5.25/5.54 thf(fact_6545_of__nat__0__le__iff,axiom,
% 5.25/5.54 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0_le_iff
% 5.25/5.54 thf(fact_6546_of__nat__0__le__iff,axiom,
% 5.25/5.54 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0_le_iff
% 5.25/5.54 thf(fact_6547_of__nat__0__le__iff,axiom,
% 5.25/5.54 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_0_le_iff
% 5.25/5.54 thf(fact_6548_diff__shunt__var,axiom,
% 5.25/5.54 ! [X3: set_real,Y: set_real] :
% 5.25/5.54 ( ( ( minus_minus_set_real @ X3 @ Y )
% 5.25/5.54 = bot_bot_set_real )
% 5.25/5.54 = ( ord_less_eq_set_real @ X3 @ Y ) ) ).
% 5.25/5.54
% 5.25/5.54 % diff_shunt_var
% 5.25/5.54 thf(fact_6549_diff__shunt__var,axiom,
% 5.25/5.54 ! [X3: set_nat,Y: set_nat] :
% 5.25/5.54 ( ( ( minus_minus_set_nat @ X3 @ Y )
% 5.25/5.54 = bot_bot_set_nat )
% 5.25/5.54 = ( ord_less_eq_set_nat @ X3 @ Y ) ) ).
% 5.25/5.54
% 5.25/5.54 % diff_shunt_var
% 5.25/5.54 thf(fact_6550_diff__shunt__var,axiom,
% 5.25/5.54 ! [X3: set_int,Y: set_int] :
% 5.25/5.54 ( ( ( minus_minus_set_int @ X3 @ Y )
% 5.25/5.54 = bot_bot_set_int )
% 5.25/5.54 = ( ord_less_eq_set_int @ X3 @ Y ) ) ).
% 5.25/5.54
% 5.25/5.54 % diff_shunt_var
% 5.25/5.54 thf(fact_6551_of__nat__less__0__iff,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_0_iff
% 5.25/5.54 thf(fact_6552_of__nat__less__0__iff,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_0_iff
% 5.25/5.54 thf(fact_6553_of__nat__less__0__iff,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_0_iff
% 5.25/5.54 thf(fact_6554_of__nat__less__0__iff,axiom,
% 5.25/5.54 ! [M: nat] :
% 5.25/5.54 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_0_iff
% 5.25/5.54 thf(fact_6555_of__nat__neq__0,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 5.25/5.54 != zero_zero_complex ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_neq_0
% 5.25/5.54 thf(fact_6556_of__nat__neq__0,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.25/5.54 != zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_neq_0
% 5.25/5.54 thf(fact_6557_of__nat__neq__0,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 5.25/5.54 != zero_zero_real ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_neq_0
% 5.25/5.54 thf(fact_6558_of__nat__neq__0,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 5.25/5.54 != zero_zero_nat ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_neq_0
% 5.25/5.54 thf(fact_6559_of__nat__neq__0,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 5.25/5.54 != zero_zero_rat ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_neq_0
% 5.25/5.54 thf(fact_6560_div__mult2__eq_H,axiom,
% 5.25/5.54 ! [A: int,M: nat,N: nat] :
% 5.25/5.54 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.25/5.54 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % div_mult2_eq'
% 5.25/5.54 thf(fact_6561_div__mult2__eq_H,axiom,
% 5.25/5.54 ! [A: nat,M: nat,N: nat] :
% 5.25/5.54 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.25/5.54 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % div_mult2_eq'
% 5.25/5.54 thf(fact_6562_less__imp__of__nat__less,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_nat @ M @ N )
% 5.25/5.54 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % less_imp_of_nat_less
% 5.25/5.54 thf(fact_6563_less__imp__of__nat__less,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_nat @ M @ N )
% 5.25/5.54 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % less_imp_of_nat_less
% 5.25/5.54 thf(fact_6564_less__imp__of__nat__less,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_nat @ M @ N )
% 5.25/5.54 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % less_imp_of_nat_less
% 5.25/5.54 thf(fact_6565_less__imp__of__nat__less,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_nat @ M @ N )
% 5.25/5.54 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % less_imp_of_nat_less
% 5.25/5.54 thf(fact_6566_of__nat__less__imp__less,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.25/5.54 => ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_imp_less
% 5.25/5.54 thf(fact_6567_of__nat__less__imp__less,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.25/5.54 => ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_imp_less
% 5.25/5.54 thf(fact_6568_of__nat__less__imp__less,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.25/5.54 => ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_imp_less
% 5.25/5.54 thf(fact_6569_of__nat__less__imp__less,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.25/5.54 => ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_imp_less
% 5.25/5.54 thf(fact_6570_AND__upper2_H,axiom,
% 5.25/5.54 ! [Y: int,Z: int,X3: int] :
% 5.25/5.54 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.54 => ( ( ord_less_eq_int @ Y @ Z )
% 5.25/5.54 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X3 @ Y ) @ Z ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % AND_upper2'
% 5.25/5.54 thf(fact_6571_AND__upper1_H,axiom,
% 5.25/5.54 ! [Y: int,Z: int,Ya: int] :
% 5.25/5.54 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.54 => ( ( ord_less_eq_int @ Y @ Z )
% 5.25/5.54 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % AND_upper1'
% 5.25/5.54 thf(fact_6572_AND__upper2,axiom,
% 5.25/5.54 ! [Y: int,X3: int] :
% 5.25/5.54 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.54 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X3 @ Y ) @ Y ) ) ).
% 5.25/5.54
% 5.25/5.54 % AND_upper2
% 5.25/5.54 thf(fact_6573_AND__upper1,axiom,
% 5.25/5.54 ! [X3: int,Y: int] :
% 5.25/5.54 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.54 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X3 @ Y ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % AND_upper1
% 5.25/5.54 thf(fact_6574_AND__lower,axiom,
% 5.25/5.54 ! [X3: int,Y: int] :
% 5.25/5.54 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.54 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X3 @ Y ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % AND_lower
% 5.25/5.54 thf(fact_6575_of__nat__mono,axiom,
% 5.25/5.54 ! [I2: nat,J2: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.54 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I2 ) @ ( semiri5074537144036343181t_real @ J2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_mono
% 5.25/5.54 thf(fact_6576_of__nat__mono,axiom,
% 5.25/5.54 ! [I2: nat,J2: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.54 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I2 ) @ ( semiri681578069525770553at_rat @ J2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_mono
% 5.25/5.54 thf(fact_6577_of__nat__mono,axiom,
% 5.25/5.54 ! [I2: nat,J2: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.54 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_mono
% 5.25/5.54 thf(fact_6578_of__nat__mono,axiom,
% 5.25/5.54 ! [I2: nat,J2: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.54 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_mono
% 5.25/5.54 thf(fact_6579_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 5.25/5.54 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.25/5.54 thf(fact_6580_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 5.25/5.54 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.25/5.54 thf(fact_6581_of__nat__dvd__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.25/5.54 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_dvd_iff
% 5.25/5.54 thf(fact_6582_of__nat__dvd__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.25/5.54 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_dvd_iff
% 5.25/5.54 thf(fact_6583_of__nat__dvd__iff,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.25/5.54 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_dvd_iff
% 5.25/5.54 thf(fact_6584_take__bit__eq__mask,axiom,
% 5.25/5.54 ( bit_se2923211474154528505it_int
% 5.25/5.54 = ( ^ [N2: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_eq_mask
% 5.25/5.54 thf(fact_6585_take__bit__eq__mask,axiom,
% 5.25/5.54 ( bit_se2925701944663578781it_nat
% 5.25/5.54 = ( ^ [N2: nat,A3: nat] : ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % take_bit_eq_mask
% 5.25/5.54 thf(fact_6586_int__ops_I3_J,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.25/5.54 = ( numeral_numeral_int @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % int_ops(3)
% 5.25/5.54 thf(fact_6587_int__cases,axiom,
% 5.25/5.54 ! [Z: int] :
% 5.25/5.54 ( ! [N3: nat] :
% 5.25/5.54 ( Z
% 5.25/5.54 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.25/5.54 => ~ ! [N3: nat] :
% 5.25/5.54 ( Z
% 5.25/5.54 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % int_cases
% 5.25/5.54 thf(fact_6588_int__of__nat__induct,axiom,
% 5.25/5.54 ! [P: int > $o,Z: int] :
% 5.25/5.54 ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 5.25/5.54 => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 5.25/5.54 => ( P @ Z ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % int_of_nat_induct
% 5.25/5.54 thf(fact_6589_nat__int__comparison_I2_J,axiom,
% 5.25/5.54 ( ord_less_nat
% 5.25/5.54 = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % nat_int_comparison(2)
% 5.25/5.54 thf(fact_6590_zle__int,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.25/5.54 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % zle_int
% 5.25/5.54 thf(fact_6591_nat__int__comparison_I3_J,axiom,
% 5.25/5.54 ( ord_less_eq_nat
% 5.25/5.54 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % nat_int_comparison(3)
% 5.25/5.54 thf(fact_6592_zero__le__imp__eq__int,axiom,
% 5.25/5.54 ! [K: int] :
% 5.25/5.54 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.54 => ? [N3: nat] :
% 5.25/5.54 ( K
% 5.25/5.54 = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % zero_le_imp_eq_int
% 5.25/5.54 thf(fact_6593_nonneg__int__cases,axiom,
% 5.25/5.54 ! [K: int] :
% 5.25/5.54 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.54 => ~ ! [N3: nat] :
% 5.25/5.54 ( K
% 5.25/5.54 != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % nonneg_int_cases
% 5.25/5.54 thf(fact_6594_of__nat__mod,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 5.25/5.54 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_mod
% 5.25/5.54 thf(fact_6595_of__nat__mod,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 5.25/5.54 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_mod
% 5.25/5.54 thf(fact_6596_of__nat__mod,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.25/5.54 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_mod
% 5.25/5.54 thf(fact_6597_zadd__int__left,axiom,
% 5.25/5.54 ! [M: nat,N: nat,Z: int] :
% 5.25/5.54 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 5.25/5.54 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 5.25/5.54
% 5.25/5.54 % zadd_int_left
% 5.25/5.54 thf(fact_6598_int__plus,axiom,
% 5.25/5.54 ! [N: nat,M: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 5.25/5.54 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % int_plus
% 5.25/5.54 thf(fact_6599_int__ops_I5_J,axiom,
% 5.25/5.54 ! [A: nat,B: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.25/5.54 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % int_ops(5)
% 5.25/5.54 thf(fact_6600_int__ops_I7_J,axiom,
% 5.25/5.54 ! [A: nat,B: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.25/5.54 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % int_ops(7)
% 5.25/5.54 thf(fact_6601_int__ops_I2_J,axiom,
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.25/5.54 = one_one_int ) ).
% 5.25/5.54
% 5.25/5.54 % int_ops(2)
% 5.25/5.54 thf(fact_6602_zle__iff__zadd,axiom,
% 5.25/5.54 ( ord_less_eq_int
% 5.25/5.54 = ( ^ [W3: int,Z5: int] :
% 5.25/5.54 ? [N2: nat] :
% 5.25/5.54 ( Z5
% 5.25/5.54 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % zle_iff_zadd
% 5.25/5.54 thf(fact_6603_zdiv__int,axiom,
% 5.25/5.54 ! [A: nat,B: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.25/5.54 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % zdiv_int
% 5.25/5.54 thf(fact_6604_of__nat__max,axiom,
% 5.25/5.54 ! [X3: nat,Y: nat] :
% 5.25/5.54 ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X3 @ Y ) )
% 5.25/5.54 = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X3 ) @ ( semiri4216267220026989637d_enat @ Y ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_max
% 5.25/5.54 thf(fact_6605_of__nat__max,axiom,
% 5.25/5.54 ! [X3: nat,Y: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X3 @ Y ) )
% 5.25/5.54 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_max
% 5.25/5.54 thf(fact_6606_of__nat__max,axiom,
% 5.25/5.54 ! [X3: nat,Y: nat] :
% 5.25/5.54 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X3 @ Y ) )
% 5.25/5.54 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_max
% 5.25/5.54 thf(fact_6607_of__nat__max,axiom,
% 5.25/5.54 ! [X3: nat,Y: nat] :
% 5.25/5.54 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X3 @ Y ) )
% 5.25/5.54 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X3 ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_max
% 5.25/5.54 thf(fact_6608_of__nat__max,axiom,
% 5.25/5.54 ! [X3: nat,Y: nat] :
% 5.25/5.54 ( ( semiri681578069525770553at_rat @ ( ord_max_nat @ X3 @ Y ) )
% 5.25/5.54 = ( ord_max_rat @ ( semiri681578069525770553at_rat @ X3 ) @ ( semiri681578069525770553at_rat @ Y ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_max
% 5.25/5.54 thf(fact_6609_zmod__int,axiom,
% 5.25/5.54 ! [A: nat,B: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 5.25/5.54 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % zmod_int
% 5.25/5.54 thf(fact_6610_subset__Compl__self__eq,axiom,
% 5.25/5.54 ! [A2: set_nat] :
% 5.25/5.54 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 5.25/5.54 = ( A2 = bot_bot_set_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % subset_Compl_self_eq
% 5.25/5.54 thf(fact_6611_subset__Compl__self__eq,axiom,
% 5.25/5.54 ! [A2: set_real] :
% 5.25/5.54 ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ A2 ) )
% 5.25/5.54 = ( A2 = bot_bot_set_real ) ) ).
% 5.25/5.54
% 5.25/5.54 % subset_Compl_self_eq
% 5.25/5.54 thf(fact_6612_subset__Compl__self__eq,axiom,
% 5.25/5.54 ! [A2: set_int] :
% 5.25/5.54 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 5.25/5.54 = ( A2 = bot_bot_set_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % subset_Compl_self_eq
% 5.25/5.54 thf(fact_6613_nat__less__as__int,axiom,
% 5.25/5.54 ( ord_less_nat
% 5.25/5.54 = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % nat_less_as_int
% 5.25/5.54 thf(fact_6614_nat__leq__as__int,axiom,
% 5.25/5.54 ( ord_less_eq_nat
% 5.25/5.54 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % nat_leq_as_int
% 5.25/5.54 thf(fact_6615_inc_Osimps_I1_J,axiom,
% 5.25/5.54 ( ( inc @ one )
% 5.25/5.54 = ( bit0 @ one ) ) ).
% 5.25/5.54
% 5.25/5.54 % inc.simps(1)
% 5.25/5.54 thf(fact_6616_inc_Osimps_I3_J,axiom,
% 5.25/5.54 ! [X3: num] :
% 5.25/5.54 ( ( inc @ ( bit1 @ X3 ) )
% 5.25/5.54 = ( bit0 @ ( inc @ X3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % inc.simps(3)
% 5.25/5.54 thf(fact_6617_inc_Osimps_I2_J,axiom,
% 5.25/5.54 ! [X3: num] :
% 5.25/5.54 ( ( inc @ ( bit0 @ X3 ) )
% 5.25/5.54 = ( bit1 @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % inc.simps(2)
% 5.25/5.54 thf(fact_6618_ex__less__of__nat__mult,axiom,
% 5.25/5.54 ! [X3: real,Y: real] :
% 5.25/5.54 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.54 => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % ex_less_of_nat_mult
% 5.25/5.54 thf(fact_6619_ex__less__of__nat__mult,axiom,
% 5.25/5.54 ! [X3: rat,Y: rat] :
% 5.25/5.54 ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 5.25/5.54 => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % ex_less_of_nat_mult
% 5.25/5.54 thf(fact_6620_add__One,axiom,
% 5.25/5.54 ! [X3: num] :
% 5.25/5.54 ( ( plus_plus_num @ X3 @ one )
% 5.25/5.54 = ( inc @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % add_One
% 5.25/5.54 thf(fact_6621_AND__upper2_H_H,axiom,
% 5.25/5.54 ! [Y: int,Z: int,X3: int] :
% 5.25/5.54 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.54 => ( ( ord_less_int @ Y @ Z )
% 5.25/5.54 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X3 @ Y ) @ Z ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % AND_upper2''
% 5.25/5.54 thf(fact_6622_AND__upper1_H_H,axiom,
% 5.25/5.54 ! [Y: int,Z: int,Ya: int] :
% 5.25/5.54 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.54 => ( ( ord_less_int @ Y @ Z )
% 5.25/5.54 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % AND_upper1''
% 5.25/5.54 thf(fact_6623_and__less__eq,axiom,
% 5.25/5.54 ! [L2: int,K: int] :
% 5.25/5.54 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.25/5.54 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ K ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_less_eq
% 5.25/5.54 thf(fact_6624_inc__BitM__eq,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( inc @ ( bitM @ N ) )
% 5.25/5.54 = ( bit0 @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % inc_BitM_eq
% 5.25/5.54 thf(fact_6625_of__nat__diff,axiom,
% 5.25/5.54 ! [N: nat,M: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 5.25/5.54 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_diff
% 5.25/5.54 thf(fact_6626_of__nat__diff,axiom,
% 5.25/5.54 ! [N: nat,M: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 5.25/5.54 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_diff
% 5.25/5.54 thf(fact_6627_of__nat__diff,axiom,
% 5.25/5.54 ! [N: nat,M: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 5.25/5.54 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_diff
% 5.25/5.54 thf(fact_6628_of__nat__diff,axiom,
% 5.25/5.54 ! [N: nat,M: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 5.25/5.54 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_diff
% 5.25/5.54 thf(fact_6629_BitM__inc__eq,axiom,
% 5.25/5.54 ! [N: num] :
% 5.25/5.54 ( ( bitM @ ( inc @ N ) )
% 5.25/5.54 = ( bit1 @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % BitM_inc_eq
% 5.25/5.54 thf(fact_6630_reals__Archimedean3,axiom,
% 5.25/5.54 ! [X3: real] :
% 5.25/5.54 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.54 => ! [Y4: real] :
% 5.25/5.54 ? [N3: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % reals_Archimedean3
% 5.25/5.54 thf(fact_6631_int__cases4,axiom,
% 5.25/5.54 ! [M: int] :
% 5.25/5.54 ( ! [N3: nat] :
% 5.25/5.54 ( M
% 5.25/5.54 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.25/5.54 => ~ ! [N3: nat] :
% 5.25/5.54 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.25/5.54 => ( M
% 5.25/5.54 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % int_cases4
% 5.25/5.54 thf(fact_6632_real__of__nat__div4,axiom,
% 5.25/5.54 ! [N: nat,X3: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X3 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % real_of_nat_div4
% 5.25/5.54 thf(fact_6633_int__zle__neg,axiom,
% 5.25/5.54 ! [N: nat,M: nat] :
% 5.25/5.54 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.25/5.54 = ( ( N = zero_zero_nat )
% 5.25/5.54 & ( M = zero_zero_nat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % int_zle_neg
% 5.25/5.54 thf(fact_6634_int__ops_I4_J,axiom,
% 5.25/5.54 ! [A: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.25/5.54 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % int_ops(4)
% 5.25/5.54 thf(fact_6635_int__Suc,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.25/5.54 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % int_Suc
% 5.25/5.54 thf(fact_6636_zless__iff__Suc__zadd,axiom,
% 5.25/5.54 ( ord_less_int
% 5.25/5.54 = ( ^ [W3: int,Z5: int] :
% 5.25/5.54 ? [N2: nat] :
% 5.25/5.54 ( Z5
% 5.25/5.54 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % zless_iff_Suc_zadd
% 5.25/5.54 thf(fact_6637_nonpos__int__cases,axiom,
% 5.25/5.54 ! [K: int] :
% 5.25/5.54 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.25/5.54 => ~ ! [N3: nat] :
% 5.25/5.54 ( K
% 5.25/5.54 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % nonpos_int_cases
% 5.25/5.54 thf(fact_6638_negative__zle__0,axiom,
% 5.25/5.54 ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % negative_zle_0
% 5.25/5.54 thf(fact_6639_real__of__nat__div,axiom,
% 5.25/5.54 ! [D: nat,N: nat] :
% 5.25/5.54 ( ( dvd_dvd_nat @ D @ N )
% 5.25/5.54 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D ) )
% 5.25/5.54 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % real_of_nat_div
% 5.25/5.54 thf(fact_6640_mult__inc,axiom,
% 5.25/5.54 ! [X3: num,Y: num] :
% 5.25/5.54 ( ( times_times_num @ X3 @ ( inc @ Y ) )
% 5.25/5.54 = ( plus_plus_num @ ( times_times_num @ X3 @ Y ) @ X3 ) ) ).
% 5.25/5.54
% 5.25/5.54 % mult_inc
% 5.25/5.54 thf(fact_6641_even__and__iff,axiom,
% 5.25/5.54 ! [A: code_integer,B: code_integer] :
% 5.25/5.54 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 5.25/5.54 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.54 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % even_and_iff
% 5.25/5.54 thf(fact_6642_even__and__iff,axiom,
% 5.25/5.54 ! [A: int,B: int] :
% 5.25/5.54 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.25/5.54 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.54 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % even_and_iff
% 5.25/5.54 thf(fact_6643_even__and__iff,axiom,
% 5.25/5.54 ! [A: nat,B: nat] :
% 5.25/5.54 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.25/5.54 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.54 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % even_and_iff
% 5.25/5.54 thf(fact_6644_even__and__iff__int,axiom,
% 5.25/5.54 ! [K: int,L2: int] :
% 5.25/5.54 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.25/5.54 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.25/5.54 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % even_and_iff_int
% 5.25/5.54 thf(fact_6645_numeral__inc,axiom,
% 5.25/5.54 ! [X3: num] :
% 5.25/5.54 ( ( numera6690914467698888265omplex @ ( inc @ X3 ) )
% 5.25/5.54 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X3 ) @ one_one_complex ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_inc
% 5.25/5.54 thf(fact_6646_numeral__inc,axiom,
% 5.25/5.54 ! [X3: num] :
% 5.25/5.54 ( ( numeral_numeral_real @ ( inc @ X3 ) )
% 5.25/5.54 = ( plus_plus_real @ ( numeral_numeral_real @ X3 ) @ one_one_real ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_inc
% 5.25/5.54 thf(fact_6647_numeral__inc,axiom,
% 5.25/5.54 ! [X3: num] :
% 5.25/5.54 ( ( numeral_numeral_rat @ ( inc @ X3 ) )
% 5.25/5.54 = ( plus_plus_rat @ ( numeral_numeral_rat @ X3 ) @ one_one_rat ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_inc
% 5.25/5.54 thf(fact_6648_numeral__inc,axiom,
% 5.25/5.54 ! [X3: num] :
% 5.25/5.54 ( ( numeral_numeral_nat @ ( inc @ X3 ) )
% 5.25/5.54 = ( plus_plus_nat @ ( numeral_numeral_nat @ X3 ) @ one_one_nat ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_inc
% 5.25/5.54 thf(fact_6649_numeral__inc,axiom,
% 5.25/5.54 ! [X3: num] :
% 5.25/5.54 ( ( numeral_numeral_int @ ( inc @ X3 ) )
% 5.25/5.54 = ( plus_plus_int @ ( numeral_numeral_int @ X3 ) @ one_one_int ) ) ).
% 5.25/5.54
% 5.25/5.54 % numeral_inc
% 5.25/5.54 thf(fact_6650_mod__mult2__eq_H,axiom,
% 5.25/5.54 ! [A: code_integer,M: nat,N: nat] :
% 5.25/5.54 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 5.25/5.54 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mod_mult2_eq'
% 5.25/5.54 thf(fact_6651_mod__mult2__eq_H,axiom,
% 5.25/5.54 ! [A: int,M: nat,N: nat] :
% 5.25/5.54 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.25/5.54 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mod_mult2_eq'
% 5.25/5.54 thf(fact_6652_mod__mult2__eq_H,axiom,
% 5.25/5.54 ! [A: nat,M: nat,N: nat] :
% 5.25/5.54 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.25/5.54 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % mod_mult2_eq'
% 5.25/5.54 thf(fact_6653_field__char__0__class_Oof__nat__div,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 5.25/5.54 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % field_char_0_class.of_nat_div
% 5.25/5.54 thf(fact_6654_field__char__0__class_Oof__nat__div,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 5.25/5.54 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % field_char_0_class.of_nat_div
% 5.25/5.54 thf(fact_6655_field__char__0__class_Oof__nat__div,axiom,
% 5.25/5.54 ! [M: nat,N: nat] :
% 5.25/5.54 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 5.25/5.54 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % field_char_0_class.of_nat_div
% 5.25/5.54 thf(fact_6656_zero__less__imp__eq__int,axiom,
% 5.25/5.54 ! [K: int] :
% 5.25/5.54 ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.54 => ? [N3: nat] :
% 5.25/5.54 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.25/5.54 & ( K
% 5.25/5.54 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % zero_less_imp_eq_int
% 5.25/5.54 thf(fact_6657_pos__int__cases,axiom,
% 5.25/5.54 ! [K: int] :
% 5.25/5.54 ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.54 => ~ ! [N3: nat] :
% 5.25/5.54 ( ( K
% 5.25/5.54 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.25/5.54 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % pos_int_cases
% 5.25/5.54 thf(fact_6658_int__cases3,axiom,
% 5.25/5.54 ! [K: int] :
% 5.25/5.54 ( ( K != zero_zero_int )
% 5.25/5.54 => ( ! [N3: nat] :
% 5.25/5.54 ( ( K
% 5.25/5.54 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.25/5.54 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 5.25/5.54 => ~ ! [N3: nat] :
% 5.25/5.54 ( ( K
% 5.25/5.54 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.25/5.54 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % int_cases3
% 5.25/5.54 thf(fact_6659_nat__less__real__le,axiom,
% 5.25/5.54 ( ord_less_nat
% 5.25/5.54 = ( ^ [N2: nat,M6: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M6 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % nat_less_real_le
% 5.25/5.54 thf(fact_6660_nat__le__real__less,axiom,
% 5.25/5.54 ( ord_less_eq_nat
% 5.25/5.54 = ( ^ [N2: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % nat_le_real_less
% 5.25/5.54 thf(fact_6661_zmult__zless__mono2__lemma,axiom,
% 5.25/5.54 ! [I2: int,J2: int,K: nat] :
% 5.25/5.54 ( ( ord_less_int @ I2 @ J2 )
% 5.25/5.54 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.54 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J2 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % zmult_zless_mono2_lemma
% 5.25/5.54 thf(fact_6662_not__zle__0__negative,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % not_zle_0_negative
% 5.25/5.54 thf(fact_6663_negD,axiom,
% 5.25/5.54 ! [X3: int] :
% 5.25/5.54 ( ( ord_less_int @ X3 @ zero_zero_int )
% 5.25/5.54 => ? [N3: nat] :
% 5.25/5.54 ( X3
% 5.25/5.54 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % negD
% 5.25/5.54 thf(fact_6664_negative__zless__0,axiom,
% 5.25/5.54 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 5.25/5.54
% 5.25/5.54 % negative_zless_0
% 5.25/5.54 thf(fact_6665_real__of__nat__div__aux,axiom,
% 5.25/5.54 ! [X3: nat,D: nat] :
% 5.25/5.54 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( semiri5074537144036343181t_real @ D ) )
% 5.25/5.54 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X3 @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X3 @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % real_of_nat_div_aux
% 5.25/5.54 thf(fact_6666_and__one__eq,axiom,
% 5.25/5.54 ! [A: code_integer] :
% 5.25/5.54 ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 5.25/5.54 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_one_eq
% 5.25/5.54 thf(fact_6667_and__one__eq,axiom,
% 5.25/5.54 ! [A: int] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 5.25/5.54 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_one_eq
% 5.25/5.54 thf(fact_6668_and__one__eq,axiom,
% 5.25/5.54 ! [A: nat] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 5.25/5.54 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_one_eq
% 5.25/5.54 thf(fact_6669_one__and__eq,axiom,
% 5.25/5.54 ! [A: code_integer] :
% 5.25/5.54 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 5.25/5.54 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % one_and_eq
% 5.25/5.54 thf(fact_6670_one__and__eq,axiom,
% 5.25/5.54 ! [A: int] :
% 5.25/5.54 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 5.25/5.54 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % one_and_eq
% 5.25/5.54 thf(fact_6671_one__and__eq,axiom,
% 5.25/5.54 ! [A: nat] :
% 5.25/5.54 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 5.25/5.54 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % one_and_eq
% 5.25/5.54 thf(fact_6672_nat__approx__posE,axiom,
% 5.25/5.54 ! [E: real] :
% 5.25/5.54 ( ( ord_less_real @ zero_zero_real @ E )
% 5.25/5.54 => ~ ! [N3: nat] :
% 5.25/5.54 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.25/5.54
% 5.25/5.54 % nat_approx_posE
% 5.25/5.54 thf(fact_6673_nat__approx__posE,axiom,
% 5.25/5.54 ! [E: rat] :
% 5.25/5.54 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.25/5.54 => ~ ! [N3: nat] :
% 5.25/5.54 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.25/5.54
% 5.25/5.54 % nat_approx_posE
% 5.25/5.54 thf(fact_6674_of__nat__less__two__power,axiom,
% 5.25/5.54 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_two_power
% 5.25/5.54 thf(fact_6675_of__nat__less__two__power,axiom,
% 5.25/5.54 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_two_power
% 5.25/5.54 thf(fact_6676_of__nat__less__two__power,axiom,
% 5.25/5.54 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.54
% 5.25/5.54 % of_nat_less_two_power
% 5.25/5.54 thf(fact_6677_inverse__of__nat__le,axiom,
% 5.25/5.54 ! [N: nat,M: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( N != zero_zero_nat )
% 5.25/5.54 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % inverse_of_nat_le
% 5.25/5.54 thf(fact_6678_inverse__of__nat__le,axiom,
% 5.25/5.54 ! [N: nat,M: nat] :
% 5.25/5.54 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.54 => ( ( N != zero_zero_nat )
% 5.25/5.54 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % inverse_of_nat_le
% 5.25/5.54 thf(fact_6679_real__archimedian__rdiv__eq__0,axiom,
% 5.25/5.54 ! [X3: real,C: real] :
% 5.25/5.54 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.54 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.54 => ( ! [M5: nat] :
% 5.25/5.54 ( ( ord_less_nat @ zero_zero_nat @ M5 )
% 5.25/5.54 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M5 ) @ X3 ) @ C ) )
% 5.25/5.54 => ( X3 = zero_zero_real ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % real_archimedian_rdiv_eq_0
% 5.25/5.54 thf(fact_6680_neg__int__cases,axiom,
% 5.25/5.54 ! [K: int] :
% 5.25/5.54 ( ( ord_less_int @ K @ zero_zero_int )
% 5.25/5.54 => ~ ! [N3: nat] :
% 5.25/5.54 ( ( K
% 5.25/5.54 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.25/5.54 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % neg_int_cases
% 5.25/5.54 thf(fact_6681_zdiff__int__split,axiom,
% 5.25/5.54 ! [P: int > $o,X3: nat,Y: nat] :
% 5.25/5.54 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X3 @ Y ) ) )
% 5.25/5.54 = ( ( ( ord_less_eq_nat @ Y @ X3 )
% 5.25/5.54 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X3 ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 5.25/5.54 & ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.54 => ( P @ zero_zero_int ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % zdiff_int_split
% 5.25/5.54 thf(fact_6682_real__of__nat__div2,axiom,
% 5.25/5.54 ! [N: nat,X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X3 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X3 ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % real_of_nat_div2
% 5.25/5.54 thf(fact_6683_real__of__nat__div3,axiom,
% 5.25/5.54 ! [N: nat,X3: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X3 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X3 ) ) ) @ one_one_real ) ).
% 5.25/5.54
% 5.25/5.54 % real_of_nat_div3
% 5.25/5.54 thf(fact_6684_linear__plus__1__le__power,axiom,
% 5.25/5.54 ! [X3: real,N: nat] :
% 5.25/5.54 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.54 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X3 ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X3 @ one_one_real ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % linear_plus_1_le_power
% 5.25/5.54 thf(fact_6685_Bernoulli__inequality,axiom,
% 5.25/5.54 ! [X3: real,N: nat] :
% 5.25/5.54 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.54 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X3 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X3 ) @ N ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % Bernoulli_inequality
% 5.25/5.54 thf(fact_6686_and__int__rec,axiom,
% 5.25/5.54 ( bit_se725231765392027082nd_int
% 5.25/5.54 = ( ^ [K3: int,L: int] :
% 5.25/5.54 ( plus_plus_int
% 5.25/5.54 @ ( zero_n2684676970156552555ol_int
% 5.25/5.54 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.25/5.54 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.25/5.54 @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % and_int_rec
% 5.25/5.54 thf(fact_6687_double__gauss__sum,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.25/5.54 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % double_gauss_sum
% 5.25/5.54 thf(fact_6688_double__gauss__sum,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.25/5.54 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % double_gauss_sum
% 5.25/5.54 thf(fact_6689_double__gauss__sum,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.25/5.54 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % double_gauss_sum
% 5.25/5.54 thf(fact_6690_double__gauss__sum,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.25/5.54 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % double_gauss_sum
% 5.25/5.54 thf(fact_6691_double__gauss__sum,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.25/5.54 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % double_gauss_sum
% 5.25/5.54 thf(fact_6692_double__arith__series,axiom,
% 5.25/5.54 ! [A: complex,D: complex,N: nat] :
% 5.25/5.54 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.25/5.54 @ ( groups2073611262835488442omplex
% 5.25/5.54 @ ^ [I3: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I3 ) @ D ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.25/5.54 = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ D ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % double_arith_series
% 5.25/5.54 thf(fact_6693_double__arith__series,axiom,
% 5.25/5.54 ! [A: int,D: int,N: nat] :
% 5.25/5.54 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.25/5.54 @ ( groups3539618377306564664at_int
% 5.25/5.54 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.25/5.54 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % double_arith_series
% 5.25/5.54 thf(fact_6694_double__arith__series,axiom,
% 5.25/5.54 ! [A: rat,D: rat,N: nat] :
% 5.25/5.54 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.25/5.54 @ ( groups2906978787729119204at_rat
% 5.25/5.54 @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I3 ) @ D ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.25/5.54 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % double_arith_series
% 5.25/5.54 thf(fact_6695_double__arith__series,axiom,
% 5.25/5.54 ! [A: nat,D: nat,N: nat] :
% 5.25/5.54 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.25/5.54 @ ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.25/5.54 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % double_arith_series
% 5.25/5.54 thf(fact_6696_double__arith__series,axiom,
% 5.25/5.54 ! [A: real,D: real,N: nat] :
% 5.25/5.54 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.25/5.54 @ ( groups6591440286371151544t_real
% 5.25/5.54 @ ^ [I3: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I3 ) @ D ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.25/5.54 = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ D ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % double_arith_series
% 5.25/5.54 thf(fact_6697_gauss__sum,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.25/5.54 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % gauss_sum
% 5.25/5.54 thf(fact_6698_gauss__sum,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.25/5.54 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % gauss_sum
% 5.25/5.54 thf(fact_6699_arith__series,axiom,
% 5.25/5.54 ! [A: int,D: int,N: nat] :
% 5.25/5.54 ( ( groups3539618377306564664at_int
% 5.25/5.54 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.25/5.54 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % arith_series
% 5.25/5.54 thf(fact_6700_arith__series,axiom,
% 5.25/5.54 ! [A: nat,D: nat,N: nat] :
% 5.25/5.54 ( ( groups3542108847815614940at_nat
% 5.25/5.54 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D ) )
% 5.25/5.54 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.25/5.54 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.54
% 5.25/5.54 % arith_series
% 5.25/5.54 thf(fact_6701_double__gauss__sum__from__Suc__0,axiom,
% 5.25/5.54 ! [N: nat] :
% 5.25/5.54 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.25/5.55 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % double_gauss_sum_from_Suc_0
% 5.25/5.55 thf(fact_6702_double__gauss__sum__from__Suc__0,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.25/5.55 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % double_gauss_sum_from_Suc_0
% 5.25/5.55 thf(fact_6703_double__gauss__sum__from__Suc__0,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.25/5.55 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % double_gauss_sum_from_Suc_0
% 5.25/5.55 thf(fact_6704_double__gauss__sum__from__Suc__0,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.25/5.55 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % double_gauss_sum_from_Suc_0
% 5.25/5.55 thf(fact_6705_double__gauss__sum__from__Suc__0,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.25/5.55 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % double_gauss_sum_from_Suc_0
% 5.25/5.55 thf(fact_6706_Bernoulli__inequality__even,axiom,
% 5.25/5.55 ! [N: nat,X3: real] :
% 5.25/5.55 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.55 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X3 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X3 ) @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % Bernoulli_inequality_even
% 5.25/5.55 thf(fact_6707_sum__gp__offset,axiom,
% 5.25/5.55 ! [X3: complex,M: nat,N: nat] :
% 5.25/5.55 ( ( ( X3 = one_one_complex )
% 5.25/5.55 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.25/5.55 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 5.25/5.55 & ( ( X3 != one_one_complex )
% 5.25/5.55 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.25/5.55 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_gp_offset
% 5.25/5.55 thf(fact_6708_sum__gp__offset,axiom,
% 5.25/5.55 ! [X3: rat,M: nat,N: nat] :
% 5.25/5.55 ( ( ( X3 = one_one_rat )
% 5.25/5.55 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.25/5.55 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 5.25/5.55 & ( ( X3 != one_one_rat )
% 5.25/5.55 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.25/5.55 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_gp_offset
% 5.25/5.55 thf(fact_6709_sum__gp__offset,axiom,
% 5.25/5.55 ! [X3: real,M: nat,N: nat] :
% 5.25/5.55 ( ( ( X3 = one_one_real )
% 5.25/5.55 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.25/5.55 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 5.25/5.55 & ( ( X3 != one_one_real )
% 5.25/5.55 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.25/5.55 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_gp_offset
% 5.25/5.55 thf(fact_6710_of__nat__code__if,axiom,
% 5.25/5.55 ( semiri8010041392384452111omplex
% 5.25/5.55 = ( ^ [N2: nat] :
% 5.25/5.55 ( if_complex @ ( N2 = zero_zero_nat ) @ zero_zero_complex
% 5.25/5.55 @ ( produc1917071388513777916omplex
% 5.25/5.55 @ ^ [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 ) )
% 5.25/5.55 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % of_nat_code_if
% 5.25/5.55 thf(fact_6711_of__nat__code__if,axiom,
% 5.25/5.55 ( semiri1314217659103216013at_int
% 5.25/5.55 = ( ^ [N2: nat] :
% 5.25/5.55 ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int
% 5.25/5.55 @ ( produc6840382203811409530at_int
% 5.25/5.55 @ ^ [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 ) )
% 5.25/5.55 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % of_nat_code_if
% 5.25/5.55 thf(fact_6712_of__nat__code__if,axiom,
% 5.25/5.55 ( semiri5074537144036343181t_real
% 5.25/5.55 = ( ^ [N2: nat] :
% 5.25/5.55 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 5.25/5.55 @ ( produc1703576794950452218t_real
% 5.25/5.55 @ ^ [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 ) )
% 5.25/5.55 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % of_nat_code_if
% 5.25/5.55 thf(fact_6713_of__nat__code__if,axiom,
% 5.25/5.55 ( semiri1316708129612266289at_nat
% 5.25/5.55 = ( ^ [N2: nat] :
% 5.25/5.55 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 5.25/5.55 @ ( produc6842872674320459806at_nat
% 5.25/5.55 @ ^ [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 ) )
% 5.25/5.55 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % of_nat_code_if
% 5.25/5.55 thf(fact_6714_of__nat__code__if,axiom,
% 5.25/5.55 ( semiri681578069525770553at_rat
% 5.25/5.55 = ( ^ [N2: nat] :
% 5.25/5.55 ( if_rat @ ( N2 = zero_zero_nat ) @ zero_zero_rat
% 5.25/5.55 @ ( produc6207742614233964070at_rat
% 5.25/5.55 @ ^ [M6: nat,Q4: nat] : ( if_rat @ ( Q4 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M6 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M6 ) ) @ one_one_rat ) )
% 5.25/5.55 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % of_nat_code_if
% 5.25/5.55 thf(fact_6715_lemma__termdiff3,axiom,
% 5.25/5.55 ! [H2: real,Z: real,K5: real,N: nat] :
% 5.25/5.55 ( ( H2 != zero_zero_real )
% 5.25/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 5.25/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lemma_termdiff3
% 5.25/5.55 thf(fact_6716_lemma__termdiff3,axiom,
% 5.25/5.55 ! [H2: complex,Z: complex,K5: real,N: nat] :
% 5.25/5.55 ( ( H2 != zero_zero_complex )
% 5.25/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 5.25/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lemma_termdiff3
% 5.25/5.55 thf(fact_6717_pochhammer__double,axiom,
% 5.25/5.55 ! [Z: complex,N: nat] :
% 5.25/5.55 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.55 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_double
% 5.25/5.55 thf(fact_6718_pochhammer__double,axiom,
% 5.25/5.55 ! [Z: real,N: nat] :
% 5.25/5.55 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.55 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_double
% 5.25/5.55 thf(fact_6719_pochhammer__double,axiom,
% 5.25/5.55 ! [Z: rat,N: nat] :
% 5.25/5.55 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.55 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_double
% 5.25/5.55 thf(fact_6720_of__nat__code,axiom,
% 5.25/5.55 ( semiri8010041392384452111omplex
% 5.25/5.55 = ( ^ [N2: nat] :
% 5.25/5.55 ( semiri2816024913162550771omplex
% 5.25/5.55 @ ^ [I3: complex] : ( plus_plus_complex @ I3 @ one_one_complex )
% 5.25/5.55 @ N2
% 5.25/5.55 @ zero_zero_complex ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % of_nat_code
% 5.25/5.55 thf(fact_6721_of__nat__code,axiom,
% 5.25/5.55 ( semiri1314217659103216013at_int
% 5.25/5.55 = ( ^ [N2: nat] :
% 5.25/5.55 ( semiri8420488043553186161ux_int
% 5.25/5.55 @ ^ [I3: int] : ( plus_plus_int @ I3 @ one_one_int )
% 5.25/5.55 @ N2
% 5.25/5.55 @ zero_zero_int ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % of_nat_code
% 5.25/5.55 thf(fact_6722_of__nat__code,axiom,
% 5.25/5.55 ( semiri5074537144036343181t_real
% 5.25/5.55 = ( ^ [N2: nat] :
% 5.25/5.55 ( semiri7260567687927622513x_real
% 5.25/5.55 @ ^ [I3: real] : ( plus_plus_real @ I3 @ one_one_real )
% 5.25/5.55 @ N2
% 5.25/5.55 @ zero_zero_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % of_nat_code
% 5.25/5.55 thf(fact_6723_of__nat__code,axiom,
% 5.25/5.55 ( semiri1316708129612266289at_nat
% 5.25/5.55 = ( ^ [N2: nat] :
% 5.25/5.55 ( semiri8422978514062236437ux_nat
% 5.25/5.55 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ one_one_nat )
% 5.25/5.55 @ N2
% 5.25/5.55 @ zero_zero_nat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % of_nat_code
% 5.25/5.55 thf(fact_6724_of__nat__code,axiom,
% 5.25/5.55 ( semiri681578069525770553at_rat
% 5.25/5.55 = ( ^ [N2: nat] :
% 5.25/5.55 ( semiri7787848453975740701ux_rat
% 5.25/5.55 @ ^ [I3: rat] : ( plus_plus_rat @ I3 @ one_one_rat )
% 5.25/5.55 @ N2
% 5.25/5.55 @ zero_zero_rat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % of_nat_code
% 5.25/5.55 thf(fact_6725_lemma__termdiff2,axiom,
% 5.25/5.55 ! [H2: complex,Z: complex,N: nat] :
% 5.25/5.55 ( ( H2 != zero_zero_complex )
% 5.25/5.55 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.25/5.55 = ( times_times_complex @ H2
% 5.25/5.55 @ ( groups2073611262835488442omplex
% 5.25/5.55 @ ^ [P4: nat] :
% 5.25/5.55 ( groups2073611262835488442omplex
% 5.25/5.55 @ ^ [Q4: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q4 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lemma_termdiff2
% 5.25/5.55 thf(fact_6726_lemma__termdiff2,axiom,
% 5.25/5.55 ! [H2: rat,Z: rat,N: nat] :
% 5.25/5.55 ( ( H2 != zero_zero_rat )
% 5.25/5.55 => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ N ) @ ( power_power_rat @ Z @ N ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.25/5.55 = ( times_times_rat @ H2
% 5.25/5.55 @ ( groups2906978787729119204at_rat
% 5.25/5.55 @ ^ [P4: nat] :
% 5.25/5.55 ( groups2906978787729119204at_rat
% 5.25/5.55 @ ^ [Q4: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ Q4 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lemma_termdiff2
% 5.25/5.55 thf(fact_6727_lemma__termdiff2,axiom,
% 5.25/5.55 ! [H2: real,Z: real,N: nat] :
% 5.25/5.55 ( ( H2 != zero_zero_real )
% 5.25/5.55 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.25/5.55 = ( times_times_real @ H2
% 5.25/5.55 @ ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [P4: nat] :
% 5.25/5.55 ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [Q4: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q4 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lemma_termdiff2
% 5.25/5.55 thf(fact_6728_signed__take__bit__eq__take__bit__minus,axiom,
% 5.25/5.55 ( bit_ri631733984087533419it_int
% 5.25/5.55 = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % signed_take_bit_eq_take_bit_minus
% 5.25/5.55 thf(fact_6729_lessThan__eq__iff,axiom,
% 5.25/5.55 ! [X3: nat,Y: nat] :
% 5.25/5.55 ( ( ( set_ord_lessThan_nat @ X3 )
% 5.25/5.55 = ( set_ord_lessThan_nat @ Y ) )
% 5.25/5.55 = ( X3 = Y ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_eq_iff
% 5.25/5.55 thf(fact_6730_lessThan__eq__iff,axiom,
% 5.25/5.55 ! [X3: int,Y: int] :
% 5.25/5.55 ( ( ( set_ord_lessThan_int @ X3 )
% 5.25/5.55 = ( set_ord_lessThan_int @ Y ) )
% 5.25/5.55 = ( X3 = Y ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_eq_iff
% 5.25/5.55 thf(fact_6731_lessThan__eq__iff,axiom,
% 5.25/5.55 ! [X3: real,Y: real] :
% 5.25/5.55 ( ( ( set_or5984915006950818249n_real @ X3 )
% 5.25/5.55 = ( set_or5984915006950818249n_real @ Y ) )
% 5.25/5.55 = ( X3 = Y ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_eq_iff
% 5.25/5.55 thf(fact_6732_lessThan__iff,axiom,
% 5.25/5.55 ! [I2: rat,K: rat] :
% 5.25/5.55 ( ( member_rat @ I2 @ ( set_ord_lessThan_rat @ K ) )
% 5.25/5.55 = ( ord_less_rat @ I2 @ K ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_iff
% 5.25/5.55 thf(fact_6733_lessThan__iff,axiom,
% 5.25/5.55 ! [I2: num,K: num] :
% 5.25/5.55 ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K ) )
% 5.25/5.55 = ( ord_less_num @ I2 @ K ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_iff
% 5.25/5.55 thf(fact_6734_lessThan__iff,axiom,
% 5.25/5.55 ! [I2: nat,K: nat] :
% 5.25/5.55 ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K ) )
% 5.25/5.55 = ( ord_less_nat @ I2 @ K ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_iff
% 5.25/5.55 thf(fact_6735_lessThan__iff,axiom,
% 5.25/5.55 ! [I2: int,K: int] :
% 5.25/5.55 ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K ) )
% 5.25/5.55 = ( ord_less_int @ I2 @ K ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_iff
% 5.25/5.55 thf(fact_6736_lessThan__iff,axiom,
% 5.25/5.55 ! [I2: real,K: real] :
% 5.25/5.55 ( ( member_real @ I2 @ ( set_or5984915006950818249n_real @ K ) )
% 5.25/5.55 = ( ord_less_real @ I2 @ K ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_iff
% 5.25/5.55 thf(fact_6737_bit__0__eq,axiom,
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ zero_zero_int )
% 5.25/5.55 = bot_bot_nat_o ) ).
% 5.25/5.55
% 5.25/5.55 % bit_0_eq
% 5.25/5.55 thf(fact_6738_bit__0__eq,axiom,
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ zero_zero_nat )
% 5.25/5.55 = bot_bot_nat_o ) ).
% 5.25/5.55
% 5.25/5.55 % bit_0_eq
% 5.25/5.55 thf(fact_6739_lessThan__subset__iff,axiom,
% 5.25/5.55 ! [X3: rat,Y: rat] :
% 5.25/5.55 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X3 ) @ ( set_ord_lessThan_rat @ Y ) )
% 5.25/5.55 = ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_subset_iff
% 5.25/5.55 thf(fact_6740_lessThan__subset__iff,axiom,
% 5.25/5.55 ! [X3: num,Y: num] :
% 5.25/5.55 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X3 ) @ ( set_ord_lessThan_num @ Y ) )
% 5.25/5.55 = ( ord_less_eq_num @ X3 @ Y ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_subset_iff
% 5.25/5.55 thf(fact_6741_lessThan__subset__iff,axiom,
% 5.25/5.55 ! [X3: nat,Y: nat] :
% 5.25/5.55 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X3 ) @ ( set_ord_lessThan_nat @ Y ) )
% 5.25/5.55 = ( ord_less_eq_nat @ X3 @ Y ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_subset_iff
% 5.25/5.55 thf(fact_6742_lessThan__subset__iff,axiom,
% 5.25/5.55 ! [X3: int,Y: int] :
% 5.25/5.55 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X3 ) @ ( set_ord_lessThan_int @ Y ) )
% 5.25/5.55 = ( ord_less_eq_int @ X3 @ Y ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_subset_iff
% 5.25/5.55 thf(fact_6743_lessThan__subset__iff,axiom,
% 5.25/5.55 ! [X3: real,Y: real] :
% 5.25/5.55 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X3 ) @ ( set_or5984915006950818249n_real @ Y ) )
% 5.25/5.55 = ( ord_less_eq_real @ X3 @ Y ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_subset_iff
% 5.25/5.55 thf(fact_6744_pochhammer__0,axiom,
% 5.25/5.55 ! [A: complex] :
% 5.25/5.55 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.25/5.55 = one_one_complex ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_0
% 5.25/5.55 thf(fact_6745_pochhammer__0,axiom,
% 5.25/5.55 ! [A: real] :
% 5.25/5.55 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.25/5.55 = one_one_real ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_0
% 5.25/5.55 thf(fact_6746_pochhammer__0,axiom,
% 5.25/5.55 ! [A: rat] :
% 5.25/5.55 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 5.25/5.55 = one_one_rat ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_0
% 5.25/5.55 thf(fact_6747_pochhammer__0,axiom,
% 5.25/5.55 ! [A: nat] :
% 5.25/5.55 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.25/5.55 = one_one_nat ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_0
% 5.25/5.55 thf(fact_6748_pochhammer__0,axiom,
% 5.25/5.55 ! [A: int] :
% 5.25/5.55 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.25/5.55 = one_one_int ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_0
% 5.25/5.55 thf(fact_6749_lessThan__0,axiom,
% 5.25/5.55 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 5.25/5.55 = bot_bot_set_nat ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_0
% 5.25/5.55 thf(fact_6750_bit__numeral__Bit0__Suc__iff,axiom,
% 5.25/5.55 ! [M: num,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( suc @ N ) )
% 5.25/5.55 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_numeral_Bit0_Suc_iff
% 5.25/5.55 thf(fact_6751_bit__numeral__Bit0__Suc__iff,axiom,
% 5.25/5.55 ! [M: num,N: nat] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( suc @ N ) )
% 5.25/5.55 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_numeral_Bit0_Suc_iff
% 5.25/5.55 thf(fact_6752_bit__numeral__Bit1__Suc__iff,axiom,
% 5.25/5.55 ! [M: num,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( suc @ N ) )
% 5.25/5.55 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_numeral_Bit1_Suc_iff
% 5.25/5.55 thf(fact_6753_bit__numeral__Bit1__Suc__iff,axiom,
% 5.25/5.55 ! [M: num,N: nat] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( suc @ N ) )
% 5.25/5.55 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_numeral_Bit1_Suc_iff
% 5.25/5.55 thf(fact_6754_sum_OlessThan__Suc,axiom,
% 5.25/5.55 ! [G: nat > rat,N: nat] :
% 5.25/5.55 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum.lessThan_Suc
% 5.25/5.55 thf(fact_6755_sum_OlessThan__Suc,axiom,
% 5.25/5.55 ! [G: nat > int,N: nat] :
% 5.25/5.55 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum.lessThan_Suc
% 5.25/5.55 thf(fact_6756_sum_OlessThan__Suc,axiom,
% 5.25/5.55 ! [G: nat > nat,N: nat] :
% 5.25/5.55 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum.lessThan_Suc
% 5.25/5.55 thf(fact_6757_sum_OlessThan__Suc,axiom,
% 5.25/5.55 ! [G: nat > real,N: nat] :
% 5.25/5.55 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum.lessThan_Suc
% 5.25/5.55 thf(fact_6758_signed__take__bit__nonnegative__iff,axiom,
% 5.25/5.55 ! [N: nat,K: int] :
% 5.25/5.55 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.25/5.55 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % signed_take_bit_nonnegative_iff
% 5.25/5.55 thf(fact_6759_signed__take__bit__negative__iff,axiom,
% 5.25/5.55 ! [N: nat,K: int] :
% 5.25/5.55 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 5.25/5.55 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % signed_take_bit_negative_iff
% 5.25/5.55 thf(fact_6760_bit__numeral__simps_I2_J,axiom,
% 5.25/5.55 ! [W: num,N: num] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.55 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_numeral_simps(2)
% 5.25/5.55 thf(fact_6761_bit__numeral__simps_I2_J,axiom,
% 5.25/5.55 ! [W: num,N: num] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.55 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_numeral_simps(2)
% 5.25/5.55 thf(fact_6762_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.25/5.55 ! [W: num,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 5.25/5.55 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_minus_numeral_Bit0_Suc_iff
% 5.25/5.55 thf(fact_6763_bit__numeral__simps_I3_J,axiom,
% 5.25/5.55 ! [W: num,N: num] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.55 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_numeral_simps(3)
% 5.25/5.55 thf(fact_6764_bit__numeral__simps_I3_J,axiom,
% 5.25/5.55 ! [W: num,N: num] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.55 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_numeral_simps(3)
% 5.25/5.55 thf(fact_6765_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.25/5.55 ! [W: num,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 5.25/5.55 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_minus_numeral_Bit1_Suc_iff
% 5.25/5.55 thf(fact_6766_and__nat__numerals_I1_J,axiom,
% 5.25/5.55 ! [Y: num] :
% 5.25/5.55 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.25/5.55 = zero_zero_nat ) ).
% 5.25/5.55
% 5.25/5.55 % and_nat_numerals(1)
% 5.25/5.55 thf(fact_6767_and__nat__numerals_I3_J,axiom,
% 5.25/5.55 ! [X3: num] :
% 5.25/5.55 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 5.25/5.55 = zero_zero_nat ) ).
% 5.25/5.55
% 5.25/5.55 % and_nat_numerals(3)
% 5.25/5.55 thf(fact_6768_bit__0,axiom,
% 5.25/5.55 ! [A: code_integer] :
% 5.25/5.55 ( ( bit_se9216721137139052372nteger @ A @ zero_zero_nat )
% 5.25/5.55 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_0
% 5.25/5.55 thf(fact_6769_bit__0,axiom,
% 5.25/5.55 ! [A: int] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ A @ zero_zero_nat )
% 5.25/5.55 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_0
% 5.25/5.55 thf(fact_6770_bit__0,axiom,
% 5.25/5.55 ! [A: nat] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ A @ zero_zero_nat )
% 5.25/5.55 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_0
% 5.25/5.55 thf(fact_6771_and__nat__numerals_I2_J,axiom,
% 5.25/5.55 ! [Y: num] :
% 5.25/5.55 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.25/5.55 = one_one_nat ) ).
% 5.25/5.55
% 5.25/5.55 % and_nat_numerals(2)
% 5.25/5.55 thf(fact_6772_and__nat__numerals_I4_J,axiom,
% 5.25/5.55 ! [X3: num] :
% 5.25/5.55 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 5.25/5.55 = one_one_nat ) ).
% 5.25/5.55
% 5.25/5.55 % and_nat_numerals(4)
% 5.25/5.55 thf(fact_6773_bit__minus__numeral__int_I1_J,axiom,
% 5.25/5.55 ! [W: num,N: num] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.55 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_minus_numeral_int(1)
% 5.25/5.55 thf(fact_6774_bit__minus__numeral__int_I2_J,axiom,
% 5.25/5.55 ! [W: num,N: num] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.55 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_minus_numeral_int(2)
% 5.25/5.55 thf(fact_6775_bit__mod__2__iff,axiom,
% 5.25/5.55 ! [A: code_integer,N: nat] :
% 5.25/5.55 ( ( bit_se9216721137139052372nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N )
% 5.25/5.55 = ( ( N = zero_zero_nat )
% 5.25/5.55 & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_mod_2_iff
% 5.25/5.55 thf(fact_6776_bit__mod__2__iff,axiom,
% 5.25/5.55 ! [A: int,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N )
% 5.25/5.55 = ( ( N = zero_zero_nat )
% 5.25/5.55 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_mod_2_iff
% 5.25/5.55 thf(fact_6777_bit__mod__2__iff,axiom,
% 5.25/5.55 ! [A: nat,N: nat] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.25/5.55 = ( ( N = zero_zero_nat )
% 5.25/5.55 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_mod_2_iff
% 5.25/5.55 thf(fact_6778_and__Suc__0__eq,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.25/5.55 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % and_Suc_0_eq
% 5.25/5.55 thf(fact_6779_Suc__0__and__eq,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.25/5.55 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % Suc_0_and_eq
% 5.25/5.55 thf(fact_6780_bit__of__nat__iff__bit,axiom,
% 5.25/5.55 ! [M: nat,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( semiri1314217659103216013at_int @ M ) @ N )
% 5.25/5.55 = ( bit_se1148574629649215175it_nat @ M @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_of_nat_iff_bit
% 5.25/5.55 thf(fact_6781_bit__of__nat__iff__bit,axiom,
% 5.25/5.55 ! [M: nat,N: nat] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ ( semiri1316708129612266289at_nat @ M ) @ N )
% 5.25/5.55 = ( bit_se1148574629649215175it_nat @ M @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_of_nat_iff_bit
% 5.25/5.55 thf(fact_6782_bit__numeral__iff,axiom,
% 5.25/5.55 ! [M: num,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N )
% 5.25/5.55 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_numeral_iff
% 5.25/5.55 thf(fact_6783_bit__numeral__iff,axiom,
% 5.25/5.55 ! [M: num,N: nat] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N )
% 5.25/5.55 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_numeral_iff
% 5.25/5.55 thf(fact_6784_bit__disjunctive__add__iff,axiom,
% 5.25/5.55 ! [A: int,B: int,N: nat] :
% 5.25/5.55 ( ! [N3: nat] :
% 5.25/5.55 ( ~ ( bit_se1146084159140164899it_int @ A @ N3 )
% 5.25/5.55 | ~ ( bit_se1146084159140164899it_int @ B @ N3 ) )
% 5.25/5.55 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ B ) @ N )
% 5.25/5.55 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.25/5.55 | ( bit_se1146084159140164899it_int @ B @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_disjunctive_add_iff
% 5.25/5.55 thf(fact_6785_bit__disjunctive__add__iff,axiom,
% 5.25/5.55 ! [A: nat,B: nat,N: nat] :
% 5.25/5.55 ( ! [N3: nat] :
% 5.25/5.55 ( ~ ( bit_se1148574629649215175it_nat @ A @ N3 )
% 5.25/5.55 | ~ ( bit_se1148574629649215175it_nat @ B @ N3 ) )
% 5.25/5.55 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.25/5.55 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.25/5.55 | ( bit_se1148574629649215175it_nat @ B @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_disjunctive_add_iff
% 5.25/5.55 thf(fact_6786_bot__nat__def,axiom,
% 5.25/5.55 bot_bot_nat = zero_zero_nat ).
% 5.25/5.55
% 5.25/5.55 % bot_nat_def
% 5.25/5.55 thf(fact_6787_lessThan__non__empty,axiom,
% 5.25/5.55 ! [X3: int] :
% 5.25/5.55 ( ( set_ord_lessThan_int @ X3 )
% 5.25/5.55 != bot_bot_set_int ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_non_empty
% 5.25/5.55 thf(fact_6788_lessThan__non__empty,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( set_or5984915006950818249n_real @ X3 )
% 5.25/5.55 != bot_bot_set_real ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_non_empty
% 5.25/5.55 thf(fact_6789_bit__and__iff,axiom,
% 5.25/5.55 ! [A: int,B: int,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ N )
% 5.25/5.55 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.25/5.55 & ( bit_se1146084159140164899it_int @ B @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_and_iff
% 5.25/5.55 thf(fact_6790_bit__and__iff,axiom,
% 5.25/5.55 ! [A: nat,B: nat,N: nat] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ N )
% 5.25/5.55 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.25/5.55 & ( bit_se1148574629649215175it_nat @ B @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_and_iff
% 5.25/5.55 thf(fact_6791_bit__and__int__iff,axiom,
% 5.25/5.55 ! [K: int,L2: int,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ N )
% 5.25/5.55 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.25/5.55 & ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_and_int_iff
% 5.25/5.55 thf(fact_6792_bit__unset__bit__iff,axiom,
% 5.25/5.55 ! [M: nat,A: int,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( bit_se4203085406695923979it_int @ M @ A ) @ N )
% 5.25/5.55 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.25/5.55 & ( M != N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_unset_bit_iff
% 5.25/5.55 thf(fact_6793_bit__unset__bit__iff,axiom,
% 5.25/5.55 ! [M: nat,A: nat,N: nat] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ ( bit_se4205575877204974255it_nat @ M @ A ) @ N )
% 5.25/5.55 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.25/5.55 & ( M != N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_unset_bit_iff
% 5.25/5.55 thf(fact_6794_bot__enat__def,axiom,
% 5.25/5.55 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.25/5.55
% 5.25/5.55 % bot_enat_def
% 5.25/5.55 thf(fact_6795_lessThan__def,axiom,
% 5.25/5.55 ( set_ord_lessThan_rat
% 5.25/5.55 = ( ^ [U2: rat] :
% 5.25/5.55 ( collect_rat
% 5.25/5.55 @ ^ [X2: rat] : ( ord_less_rat @ X2 @ U2 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_def
% 5.25/5.55 thf(fact_6796_lessThan__def,axiom,
% 5.25/5.55 ( set_ord_lessThan_num
% 5.25/5.55 = ( ^ [U2: num] :
% 5.25/5.55 ( collect_num
% 5.25/5.55 @ ^ [X2: num] : ( ord_less_num @ X2 @ U2 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_def
% 5.25/5.55 thf(fact_6797_lessThan__def,axiom,
% 5.25/5.55 ( set_ord_lessThan_nat
% 5.25/5.55 = ( ^ [U2: nat] :
% 5.25/5.55 ( collect_nat
% 5.25/5.55 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ U2 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_def
% 5.25/5.55 thf(fact_6798_lessThan__def,axiom,
% 5.25/5.55 ( set_ord_lessThan_int
% 5.25/5.55 = ( ^ [U2: int] :
% 5.25/5.55 ( collect_int
% 5.25/5.55 @ ^ [X2: int] : ( ord_less_int @ X2 @ U2 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_def
% 5.25/5.55 thf(fact_6799_lessThan__def,axiom,
% 5.25/5.55 ( set_or5984915006950818249n_real
% 5.25/5.55 = ( ^ [U2: real] :
% 5.25/5.55 ( collect_real
% 5.25/5.55 @ ^ [X2: real] : ( ord_less_real @ X2 @ U2 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_def
% 5.25/5.55 thf(fact_6800_not__bit__1__Suc,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % not_bit_1_Suc
% 5.25/5.55 thf(fact_6801_not__bit__1__Suc,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % not_bit_1_Suc
% 5.25/5.55 thf(fact_6802_bit__1__iff,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ one_one_int @ N )
% 5.25/5.55 = ( N = zero_zero_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_1_iff
% 5.25/5.55 thf(fact_6803_bit__1__iff,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N )
% 5.25/5.55 = ( N = zero_zero_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_1_iff
% 5.25/5.55 thf(fact_6804_bit__numeral__simps_I1_J,axiom,
% 5.25/5.55 ! [N: num] :
% 5.25/5.55 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( numeral_numeral_nat @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_numeral_simps(1)
% 5.25/5.55 thf(fact_6805_bit__numeral__simps_I1_J,axiom,
% 5.25/5.55 ! [N: num] :
% 5.25/5.55 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_numeral_simps(1)
% 5.25/5.55 thf(fact_6806_bit__take__bit__iff,axiom,
% 5.25/5.55 ! [M: nat,A: int,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ M @ A ) @ N )
% 5.25/5.55 = ( ( ord_less_nat @ N @ M )
% 5.25/5.55 & ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_take_bit_iff
% 5.25/5.55 thf(fact_6807_bit__take__bit__iff,axiom,
% 5.25/5.55 ! [M: nat,A: nat,N: nat] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ ( bit_se2925701944663578781it_nat @ M @ A ) @ N )
% 5.25/5.55 = ( ( ord_less_nat @ N @ M )
% 5.25/5.55 & ( bit_se1148574629649215175it_nat @ A @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_take_bit_iff
% 5.25/5.55 thf(fact_6808_bit__of__bool__iff,axiom,
% 5.25/5.55 ! [B: $o,N: nat] :
% 5.25/5.55 ( ( bit_se9216721137139052372nteger @ ( zero_n356916108424825756nteger @ B ) @ N )
% 5.25/5.55 = ( B
% 5.25/5.55 & ( N = zero_zero_nat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_of_bool_iff
% 5.25/5.55 thf(fact_6809_bit__of__bool__iff,axiom,
% 5.25/5.55 ! [B: $o,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( zero_n2684676970156552555ol_int @ B ) @ N )
% 5.25/5.55 = ( B
% 5.25/5.55 & ( N = zero_zero_nat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_of_bool_iff
% 5.25/5.55 thf(fact_6810_bit__of__bool__iff,axiom,
% 5.25/5.55 ! [B: $o,N: nat] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ N )
% 5.25/5.55 = ( B
% 5.25/5.55 & ( N = zero_zero_nat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_of_bool_iff
% 5.25/5.55 thf(fact_6811_Iio__eq__empty__iff,axiom,
% 5.25/5.55 ! [N: extended_enat] :
% 5.25/5.55 ( ( ( set_or8419480210114673929d_enat @ N )
% 5.25/5.55 = bot_bo7653980558646680370d_enat )
% 5.25/5.55 = ( N = bot_bo4199563552545308370d_enat ) ) ).
% 5.25/5.55
% 5.25/5.55 % Iio_eq_empty_iff
% 5.25/5.55 thf(fact_6812_Iio__eq__empty__iff,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( ( set_ord_lessThan_nat @ N )
% 5.25/5.55 = bot_bot_set_nat )
% 5.25/5.55 = ( N = bot_bot_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % Iio_eq_empty_iff
% 5.25/5.55 thf(fact_6813_lessThan__strict__subset__iff,axiom,
% 5.25/5.55 ! [M: rat,N: rat] :
% 5.25/5.55 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 5.25/5.55 = ( ord_less_rat @ M @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_strict_subset_iff
% 5.25/5.55 thf(fact_6814_lessThan__strict__subset__iff,axiom,
% 5.25/5.55 ! [M: num,N: num] :
% 5.25/5.55 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 5.25/5.55 = ( ord_less_num @ M @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_strict_subset_iff
% 5.25/5.55 thf(fact_6815_lessThan__strict__subset__iff,axiom,
% 5.25/5.55 ! [M: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 = ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_strict_subset_iff
% 5.25/5.55 thf(fact_6816_lessThan__strict__subset__iff,axiom,
% 5.25/5.55 ! [M: int,N: int] :
% 5.25/5.55 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 5.25/5.55 = ( ord_less_int @ M @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_strict_subset_iff
% 5.25/5.55 thf(fact_6817_lessThan__strict__subset__iff,axiom,
% 5.25/5.55 ! [M: real,N: real] :
% 5.25/5.55 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 5.25/5.55 = ( ord_less_real @ M @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_strict_subset_iff
% 5.25/5.55 thf(fact_6818_signed__take__bit__eq__if__positive,axiom,
% 5.25/5.55 ! [A: int,N: nat] :
% 5.25/5.55 ( ~ ( bit_se1146084159140164899it_int @ A @ N )
% 5.25/5.55 => ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.25/5.55 = ( bit_se2923211474154528505it_int @ N @ A ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % signed_take_bit_eq_if_positive
% 5.25/5.55 thf(fact_6819_pochhammer__pos,axiom,
% 5.25/5.55 ! [X3: real,N: nat] :
% 5.25/5.55 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X3 @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_pos
% 5.25/5.55 thf(fact_6820_pochhammer__pos,axiom,
% 5.25/5.55 ! [X3: rat,N: nat] :
% 5.25/5.55 ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 5.25/5.55 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X3 @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_pos
% 5.25/5.55 thf(fact_6821_pochhammer__pos,axiom,
% 5.25/5.55 ! [X3: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 5.25/5.55 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_pos
% 5.25/5.55 thf(fact_6822_pochhammer__pos,axiom,
% 5.25/5.55 ! [X3: int,N: nat] :
% 5.25/5.55 ( ( ord_less_int @ zero_zero_int @ X3 )
% 5.25/5.55 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X3 @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_pos
% 5.25/5.55 thf(fact_6823_pochhammer__neq__0__mono,axiom,
% 5.25/5.55 ! [A: complex,M: nat,N: nat] :
% 5.25/5.55 ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.25/5.55 != zero_zero_complex )
% 5.25/5.55 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.55 => ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.25/5.55 != zero_zero_complex ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_neq_0_mono
% 5.25/5.55 thf(fact_6824_pochhammer__neq__0__mono,axiom,
% 5.25/5.55 ! [A: real,M: nat,N: nat] :
% 5.25/5.55 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.25/5.55 != zero_zero_real )
% 5.25/5.55 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.55 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.25/5.55 != zero_zero_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_neq_0_mono
% 5.25/5.55 thf(fact_6825_pochhammer__neq__0__mono,axiom,
% 5.25/5.55 ! [A: rat,M: nat,N: nat] :
% 5.25/5.55 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.25/5.55 != zero_zero_rat )
% 5.25/5.55 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.55 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.25/5.55 != zero_zero_rat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_neq_0_mono
% 5.25/5.55 thf(fact_6826_pochhammer__eq__0__mono,axiom,
% 5.25/5.55 ! [A: complex,N: nat,M: nat] :
% 5.25/5.55 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.25/5.55 = zero_zero_complex )
% 5.25/5.55 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.55 => ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.25/5.55 = zero_zero_complex ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_eq_0_mono
% 5.25/5.55 thf(fact_6827_pochhammer__eq__0__mono,axiom,
% 5.25/5.55 ! [A: real,N: nat,M: nat] :
% 5.25/5.55 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.25/5.55 = zero_zero_real )
% 5.25/5.55 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.55 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.25/5.55 = zero_zero_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_eq_0_mono
% 5.25/5.55 thf(fact_6828_pochhammer__eq__0__mono,axiom,
% 5.25/5.55 ! [A: rat,N: nat,M: nat] :
% 5.25/5.55 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.25/5.55 = zero_zero_rat )
% 5.25/5.55 => ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.55 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.25/5.55 = zero_zero_rat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_eq_0_mono
% 5.25/5.55 thf(fact_6829_lessThan__empty__iff,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( ( set_ord_lessThan_nat @ N )
% 5.25/5.55 = bot_bot_set_nat )
% 5.25/5.55 = ( N = zero_zero_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_empty_iff
% 5.25/5.55 thf(fact_6830_sumr__diff__mult__const2,axiom,
% 5.25/5.55 ! [F: nat > int,N: nat,R2: int] :
% 5.25/5.55 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R2 ) )
% 5.25/5.55 = ( groups3539618377306564664at_int
% 5.25/5.55 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ I3 ) @ R2 )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sumr_diff_mult_const2
% 5.25/5.55 thf(fact_6831_sumr__diff__mult__const2,axiom,
% 5.25/5.55 ! [F: nat > rat,N: nat,R2: rat] :
% 5.25/5.55 ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R2 ) )
% 5.25/5.55 = ( groups2906978787729119204at_rat
% 5.25/5.55 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ I3 ) @ R2 )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sumr_diff_mult_const2
% 5.25/5.55 thf(fact_6832_sumr__diff__mult__const2,axiom,
% 5.25/5.55 ! [F: nat > real,N: nat,R2: real] :
% 5.25/5.55 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R2 ) )
% 5.25/5.55 = ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [I3: nat] : ( minus_minus_real @ ( F @ I3 ) @ R2 )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sumr_diff_mult_const2
% 5.25/5.55 thf(fact_6833_bit__not__int__iff_H,axiom,
% 5.25/5.55 ! [K: int,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 5.25/5.55 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_not_int_iff'
% 5.25/5.55 thf(fact_6834_pochhammer__nonneg,axiom,
% 5.25/5.55 ! [X3: real,N: nat] :
% 5.25/5.55 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X3 @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_nonneg
% 5.25/5.55 thf(fact_6835_pochhammer__nonneg,axiom,
% 5.25/5.55 ! [X3: rat,N: nat] :
% 5.25/5.55 ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 5.25/5.55 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X3 @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_nonneg
% 5.25/5.55 thf(fact_6836_pochhammer__nonneg,axiom,
% 5.25/5.55 ! [X3: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_nat @ zero_zero_nat @ X3 )
% 5.25/5.55 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X3 @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_nonneg
% 5.25/5.55 thf(fact_6837_pochhammer__nonneg,axiom,
% 5.25/5.55 ! [X3: int,N: nat] :
% 5.25/5.55 ( ( ord_less_int @ zero_zero_int @ X3 )
% 5.25/5.55 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X3 @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_nonneg
% 5.25/5.55 thf(fact_6838_pochhammer__0__left,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( ( N = zero_zero_nat )
% 5.25/5.55 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.25/5.55 = one_one_complex ) )
% 5.25/5.55 & ( ( N != zero_zero_nat )
% 5.25/5.55 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.25/5.55 = zero_zero_complex ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_0_left
% 5.25/5.55 thf(fact_6839_pochhammer__0__left,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( ( N = zero_zero_nat )
% 5.25/5.55 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.25/5.55 = one_one_real ) )
% 5.25/5.55 & ( ( N != zero_zero_nat )
% 5.25/5.55 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.25/5.55 = zero_zero_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_0_left
% 5.25/5.55 thf(fact_6840_pochhammer__0__left,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( ( N = zero_zero_nat )
% 5.25/5.55 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.25/5.55 = one_one_rat ) )
% 5.25/5.55 & ( ( N != zero_zero_nat )
% 5.25/5.55 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.25/5.55 = zero_zero_rat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_0_left
% 5.25/5.55 thf(fact_6841_pochhammer__0__left,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( ( N = zero_zero_nat )
% 5.25/5.55 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.25/5.55 = one_one_nat ) )
% 5.25/5.55 & ( ( N != zero_zero_nat )
% 5.25/5.55 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.25/5.55 = zero_zero_nat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_0_left
% 5.25/5.55 thf(fact_6842_pochhammer__0__left,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( ( N = zero_zero_nat )
% 5.25/5.55 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.25/5.55 = one_one_int ) )
% 5.25/5.55 & ( ( N != zero_zero_nat )
% 5.25/5.55 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.25/5.55 = zero_zero_int ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_0_left
% 5.25/5.55 thf(fact_6843_sum_Onat__diff__reindex,axiom,
% 5.25/5.55 ! [G: nat > nat,N: nat] :
% 5.25/5.55 ( ( groups3542108847815614940at_nat
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum.nat_diff_reindex
% 5.25/5.55 thf(fact_6844_sum_Onat__diff__reindex,axiom,
% 5.25/5.55 ! [G: nat > real,N: nat] :
% 5.25/5.55 ( ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum.nat_diff_reindex
% 5.25/5.55 thf(fact_6845_flip__bit__eq__if,axiom,
% 5.25/5.55 ( bit_se2159334234014336723it_int
% 5.25/5.55 = ( ^ [N2: nat,A3: int] : ( if_nat_int_int @ ( bit_se1146084159140164899it_int @ A3 @ N2 ) @ bit_se4203085406695923979it_int @ bit_se7879613467334960850it_int @ N2 @ A3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % flip_bit_eq_if
% 5.25/5.55 thf(fact_6846_flip__bit__eq__if,axiom,
% 5.25/5.55 ( bit_se2161824704523386999it_nat
% 5.25/5.55 = ( ^ [N2: nat,A3: nat] : ( if_nat_nat_nat @ ( bit_se1148574629649215175it_nat @ A3 @ N2 ) @ bit_se4205575877204974255it_nat @ bit_se7882103937844011126it_nat @ N2 @ A3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % flip_bit_eq_if
% 5.25/5.55 thf(fact_6847_sum__diff__distrib,axiom,
% 5.25/5.55 ! [Q: int > nat,P: int > nat,N: int] :
% 5.25/5.55 ( ! [X5: int] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 5.25/5.55 => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N ) ) )
% 5.25/5.55 = ( groups4541462559716669496nt_nat
% 5.25/5.55 @ ^ [X2: int] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.25/5.55 @ ( set_ord_lessThan_int @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_diff_distrib
% 5.25/5.55 thf(fact_6848_sum__diff__distrib,axiom,
% 5.25/5.55 ! [Q: real > nat,P: real > nat,N: real] :
% 5.25/5.55 ( ! [X5: real] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 5.25/5.55 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 5.25/5.55 = ( groups1935376822645274424al_nat
% 5.25/5.55 @ ^ [X2: real] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.25/5.55 @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_diff_distrib
% 5.25/5.55 thf(fact_6849_sum__diff__distrib,axiom,
% 5.25/5.55 ! [Q: nat > nat,P: nat > nat,N: nat] :
% 5.25/5.55 ( ! [X5: nat] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 5.25/5.55 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 5.25/5.55 = ( groups3542108847815614940at_nat
% 5.25/5.55 @ ^ [X2: nat] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_diff_distrib
% 5.25/5.55 thf(fact_6850_bit__imp__take__bit__positive,axiom,
% 5.25/5.55 ! [N: nat,M: nat,K: int] :
% 5.25/5.55 ( ( ord_less_nat @ N @ M )
% 5.25/5.55 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.25/5.55 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_imp_take_bit_positive
% 5.25/5.55 thf(fact_6851_bit__concat__bit__iff,axiom,
% 5.25/5.55 ! [M: nat,K: int,L2: int,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L2 ) @ N )
% 5.25/5.55 = ( ( ( ord_less_nat @ N @ M )
% 5.25/5.55 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 5.25/5.55 | ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 & ( bit_se1146084159140164899it_int @ L2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_concat_bit_iff
% 5.25/5.55 thf(fact_6852_pochhammer__rec,axiom,
% 5.25/5.55 ! [A: complex,N: nat] :
% 5.25/5.55 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.25/5.55 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_rec
% 5.25/5.55 thf(fact_6853_pochhammer__rec,axiom,
% 5.25/5.55 ! [A: real,N: nat] :
% 5.25/5.55 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.25/5.55 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_rec
% 5.25/5.55 thf(fact_6854_pochhammer__rec,axiom,
% 5.25/5.55 ! [A: rat,N: nat] :
% 5.25/5.55 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.25/5.55 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_rec
% 5.25/5.55 thf(fact_6855_pochhammer__rec,axiom,
% 5.25/5.55 ! [A: nat,N: nat] :
% 5.25/5.55 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.25/5.55 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_rec
% 5.25/5.55 thf(fact_6856_pochhammer__rec,axiom,
% 5.25/5.55 ! [A: int,N: nat] :
% 5.25/5.55 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.25/5.55 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_rec
% 5.25/5.55 thf(fact_6857_pochhammer__Suc,axiom,
% 5.25/5.55 ! [A: int,N: nat] :
% 5.25/5.55 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.25/5.55 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_Suc
% 5.25/5.55 thf(fact_6858_pochhammer__Suc,axiom,
% 5.25/5.55 ! [A: real,N: nat] :
% 5.25/5.55 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.25/5.55 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_Suc
% 5.25/5.55 thf(fact_6859_pochhammer__Suc,axiom,
% 5.25/5.55 ! [A: nat,N: nat] :
% 5.25/5.55 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.25/5.55 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_Suc
% 5.25/5.55 thf(fact_6860_pochhammer__Suc,axiom,
% 5.25/5.55 ! [A: rat,N: nat] :
% 5.25/5.55 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.25/5.55 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_Suc
% 5.25/5.55 thf(fact_6861_pochhammer__rec_H,axiom,
% 5.25/5.55 ! [Z: int,N: nat] :
% 5.25/5.55 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 5.25/5.55 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_rec'
% 5.25/5.55 thf(fact_6862_pochhammer__rec_H,axiom,
% 5.25/5.55 ! [Z: real,N: nat] :
% 5.25/5.55 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) )
% 5.25/5.55 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_rec'
% 5.25/5.55 thf(fact_6863_pochhammer__rec_H,axiom,
% 5.25/5.55 ! [Z: nat,N: nat] :
% 5.25/5.55 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 5.25/5.55 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_rec'
% 5.25/5.55 thf(fact_6864_pochhammer__rec_H,axiom,
% 5.25/5.55 ! [Z: rat,N: nat] :
% 5.25/5.55 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 5.25/5.55 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_rec'
% 5.25/5.55 thf(fact_6865_pochhammer__eq__0__iff,axiom,
% 5.25/5.55 ! [A: complex,N: nat] :
% 5.25/5.55 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.25/5.55 = zero_zero_complex )
% 5.25/5.55 = ( ? [K3: nat] :
% 5.25/5.55 ( ( ord_less_nat @ K3 @ N )
% 5.25/5.55 & ( A
% 5.25/5.55 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_eq_0_iff
% 5.25/5.55 thf(fact_6866_pochhammer__eq__0__iff,axiom,
% 5.25/5.55 ! [A: real,N: nat] :
% 5.25/5.55 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.25/5.55 = zero_zero_real )
% 5.25/5.55 = ( ? [K3: nat] :
% 5.25/5.55 ( ( ord_less_nat @ K3 @ N )
% 5.25/5.55 & ( A
% 5.25/5.55 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_eq_0_iff
% 5.25/5.55 thf(fact_6867_pochhammer__eq__0__iff,axiom,
% 5.25/5.55 ! [A: rat,N: nat] :
% 5.25/5.55 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.25/5.55 = zero_zero_rat )
% 5.25/5.55 = ( ? [K3: nat] :
% 5.25/5.55 ( ( ord_less_nat @ K3 @ N )
% 5.25/5.55 & ( A
% 5.25/5.55 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_eq_0_iff
% 5.25/5.55 thf(fact_6868_pochhammer__of__nat__eq__0__iff,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.25/5.55 = zero_zero_complex )
% 5.25/5.55 = ( ord_less_nat @ N @ K ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_iff
% 5.25/5.55 thf(fact_6869_pochhammer__of__nat__eq__0__iff,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.25/5.55 = zero_z3403309356797280102nteger )
% 5.25/5.55 = ( ord_less_nat @ N @ K ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_iff
% 5.25/5.55 thf(fact_6870_pochhammer__of__nat__eq__0__iff,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.25/5.55 = zero_zero_int )
% 5.25/5.55 = ( ord_less_nat @ N @ K ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_iff
% 5.25/5.55 thf(fact_6871_pochhammer__of__nat__eq__0__iff,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.25/5.55 = zero_zero_real )
% 5.25/5.55 = ( ord_less_nat @ N @ K ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_iff
% 5.25/5.55 thf(fact_6872_pochhammer__of__nat__eq__0__iff,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.25/5.55 = zero_zero_rat )
% 5.25/5.55 = ( ord_less_nat @ N @ K ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_iff
% 5.25/5.55 thf(fact_6873_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( ord_less_nat @ N @ K )
% 5.25/5.55 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.25/5.55 = zero_zero_complex ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_lemma
% 5.25/5.55 thf(fact_6874_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( ord_less_nat @ N @ K )
% 5.25/5.55 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.25/5.55 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_lemma
% 5.25/5.55 thf(fact_6875_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( ord_less_nat @ N @ K )
% 5.25/5.55 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.25/5.55 = zero_zero_int ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_lemma
% 5.25/5.55 thf(fact_6876_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( ord_less_nat @ N @ K )
% 5.25/5.55 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.25/5.55 = zero_zero_real ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_lemma
% 5.25/5.55 thf(fact_6877_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( ord_less_nat @ N @ K )
% 5.25/5.55 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.25/5.55 = zero_zero_rat ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_lemma
% 5.25/5.55 thf(fact_6878_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.25/5.55 ! [K: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.55 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.25/5.55 != zero_zero_complex ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_lemma'
% 5.25/5.55 thf(fact_6879_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.25/5.55 ! [K: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.55 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.25/5.55 != zero_z3403309356797280102nteger ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_lemma'
% 5.25/5.55 thf(fact_6880_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.25/5.55 ! [K: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.55 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.25/5.55 != zero_zero_int ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_lemma'
% 5.25/5.55 thf(fact_6881_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.25/5.55 ! [K: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.55 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.25/5.55 != zero_zero_real ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_lemma'
% 5.25/5.55 thf(fact_6882_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.25/5.55 ! [K: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.55 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.25/5.55 != zero_zero_rat ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_of_nat_eq_0_lemma'
% 5.25/5.55 thf(fact_6883_pochhammer__product_H,axiom,
% 5.25/5.55 ! [Z: int,N: nat,M: nat] :
% 5.25/5.55 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.25/5.55 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_product'
% 5.25/5.55 thf(fact_6884_pochhammer__product_H,axiom,
% 5.25/5.55 ! [Z: real,N: nat,M: nat] :
% 5.25/5.55 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.25/5.55 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_product'
% 5.25/5.55 thf(fact_6885_pochhammer__product_H,axiom,
% 5.25/5.55 ! [Z: nat,N: nat,M: nat] :
% 5.25/5.55 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.25/5.55 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_product'
% 5.25/5.55 thf(fact_6886_pochhammer__product_H,axiom,
% 5.25/5.55 ! [Z: rat,N: nat,M: nat] :
% 5.25/5.55 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.25/5.55 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_product'
% 5.25/5.55 thf(fact_6887_sum_OlessThan__Suc__shift,axiom,
% 5.25/5.55 ! [G: nat > rat,N: nat] :
% 5.25/5.55 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.25/5.55 @ ( groups2906978787729119204at_rat
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum.lessThan_Suc_shift
% 5.25/5.55 thf(fact_6888_sum_OlessThan__Suc__shift,axiom,
% 5.25/5.55 ! [G: nat > int,N: nat] :
% 5.25/5.55 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.25/5.55 @ ( groups3539618377306564664at_int
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum.lessThan_Suc_shift
% 5.25/5.55 thf(fact_6889_sum_OlessThan__Suc__shift,axiom,
% 5.25/5.55 ! [G: nat > nat,N: nat] :
% 5.25/5.55 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.25/5.55 @ ( groups3542108847815614940at_nat
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum.lessThan_Suc_shift
% 5.25/5.55 thf(fact_6890_sum_OlessThan__Suc__shift,axiom,
% 5.25/5.55 ! [G: nat > real,N: nat] :
% 5.25/5.55 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.25/5.55 @ ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum.lessThan_Suc_shift
% 5.25/5.55 thf(fact_6891_sum__lessThan__telescope_H,axiom,
% 5.25/5.55 ! [F: nat > rat,M: nat] :
% 5.25/5.55 ( ( groups2906978787729119204at_rat
% 5.25/5.55 @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.25/5.55 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_lessThan_telescope'
% 5.25/5.55 thf(fact_6892_sum__lessThan__telescope_H,axiom,
% 5.25/5.55 ! [F: nat > int,M: nat] :
% 5.25/5.55 ( ( groups3539618377306564664at_int
% 5.25/5.55 @ ^ [N2: nat] : ( minus_minus_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.25/5.55 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_lessThan_telescope'
% 5.25/5.55 thf(fact_6893_sum__lessThan__telescope_H,axiom,
% 5.25/5.55 ! [F: nat > real,M: nat] :
% 5.25/5.55 ( ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.25/5.55 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_lessThan_telescope'
% 5.25/5.55 thf(fact_6894_sum__lessThan__telescope,axiom,
% 5.25/5.55 ! [F: nat > rat,M: nat] :
% 5.25/5.55 ( ( groups2906978787729119204at_rat
% 5.25/5.55 @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.25/5.55 = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_lessThan_telescope
% 5.25/5.55 thf(fact_6895_sum__lessThan__telescope,axiom,
% 5.25/5.55 ! [F: nat > int,M: nat] :
% 5.25/5.55 ( ( groups3539618377306564664at_int
% 5.25/5.55 @ ^ [N2: nat] : ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.25/5.55 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_lessThan_telescope
% 5.25/5.55 thf(fact_6896_sum__lessThan__telescope,axiom,
% 5.25/5.55 ! [F: nat > real,M: nat] :
% 5.25/5.55 ( ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.25/5.55 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_lessThan_telescope
% 5.25/5.55 thf(fact_6897_sum_OatLeast1__atMost__eq,axiom,
% 5.25/5.55 ! [G: nat > nat,N: nat] :
% 5.25/5.55 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.25/5.55 = ( groups3542108847815614940at_nat
% 5.25/5.55 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum.atLeast1_atMost_eq
% 5.25/5.55 thf(fact_6898_sum_OatLeast1__atMost__eq,axiom,
% 5.25/5.55 ! [G: nat > real,N: nat] :
% 5.25/5.55 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.25/5.55 = ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum.atLeast1_atMost_eq
% 5.25/5.55 thf(fact_6899_signed__take__bit__eq__concat__bit,axiom,
% 5.25/5.55 ( bit_ri631733984087533419it_int
% 5.25/5.55 = ( ^ [N2: nat,K3: int] : ( bit_concat_bit @ N2 @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % signed_take_bit_eq_concat_bit
% 5.25/5.55 thf(fact_6900_exp__eq__0__imp__not__bit,axiom,
% 5.25/5.55 ! [N: nat,A: int] :
% 5.25/5.55 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.25/5.55 = zero_zero_int )
% 5.25/5.55 => ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % exp_eq_0_imp_not_bit
% 5.25/5.55 thf(fact_6901_exp__eq__0__imp__not__bit,axiom,
% 5.25/5.55 ! [N: nat,A: nat] :
% 5.25/5.55 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.55 = zero_zero_nat )
% 5.25/5.55 => ~ ( bit_se1148574629649215175it_nat @ A @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % exp_eq_0_imp_not_bit
% 5.25/5.55 thf(fact_6902_lemma__termdiff1,axiom,
% 5.25/5.55 ! [Z: complex,H2: complex,M: nat] :
% 5.25/5.55 ( ( groups2073611262835488442omplex
% 5.25/5.55 @ ^ [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 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.25/5.55 = ( groups2073611262835488442omplex
% 5.25/5.55 @ ^ [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 ) ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lemma_termdiff1
% 5.25/5.55 thf(fact_6903_lemma__termdiff1,axiom,
% 5.25/5.55 ! [Z: rat,H2: rat,M: nat] :
% 5.25/5.55 ( ( groups2906978787729119204at_rat
% 5.25/5.55 @ ^ [P4: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_rat @ Z @ P4 ) ) @ ( power_power_rat @ Z @ M ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.25/5.55 = ( groups2906978787729119204at_rat
% 5.25/5.55 @ ^ [P4: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P4 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lemma_termdiff1
% 5.25/5.55 thf(fact_6904_lemma__termdiff1,axiom,
% 5.25/5.55 ! [Z: int,H2: int,M: nat] :
% 5.25/5.55 ( ( groups3539618377306564664at_int
% 5.25/5.55 @ ^ [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 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.25/5.55 = ( groups3539618377306564664at_int
% 5.25/5.55 @ ^ [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 ) ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lemma_termdiff1
% 5.25/5.55 thf(fact_6905_lemma__termdiff1,axiom,
% 5.25/5.55 ! [Z: real,H2: real,M: nat] :
% 5.25/5.55 ( ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [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 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ M ) )
% 5.25/5.55 = ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [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 ) ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lemma_termdiff1
% 5.25/5.55 thf(fact_6906_bit__Suc,axiom,
% 5.25/5.55 ! [A: int,N: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ A @ ( suc @ N ) )
% 5.25/5.55 = ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_Suc
% 5.25/5.55 thf(fact_6907_bit__Suc,axiom,
% 5.25/5.55 ! [A: nat,N: nat] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ A @ ( suc @ N ) )
% 5.25/5.55 = ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_Suc
% 5.25/5.55 thf(fact_6908_stable__imp__bit__iff__odd,axiom,
% 5.25/5.55 ! [A: code_integer,N: nat] :
% 5.25/5.55 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.55 = A )
% 5.25/5.55 => ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.25/5.55 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % stable_imp_bit_iff_odd
% 5.25/5.55 thf(fact_6909_stable__imp__bit__iff__odd,axiom,
% 5.25/5.55 ! [A: int,N: nat] :
% 5.25/5.55 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.55 = A )
% 5.25/5.55 => ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.25/5.55 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % stable_imp_bit_iff_odd
% 5.25/5.55 thf(fact_6910_stable__imp__bit__iff__odd,axiom,
% 5.25/5.55 ! [A: nat,N: nat] :
% 5.25/5.55 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.55 = A )
% 5.25/5.55 => ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.25/5.55 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % stable_imp_bit_iff_odd
% 5.25/5.55 thf(fact_6911_bit__iff__idd__imp__stable,axiom,
% 5.25/5.55 ! [A: code_integer] :
% 5.25/5.55 ( ! [N3: nat] :
% 5.25/5.55 ( ( bit_se9216721137139052372nteger @ A @ N3 )
% 5.25/5.55 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.25/5.55 => ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.55 = A ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_iff_idd_imp_stable
% 5.25/5.55 thf(fact_6912_bit__iff__idd__imp__stable,axiom,
% 5.25/5.55 ! [A: int] :
% 5.25/5.55 ( ! [N3: nat] :
% 5.25/5.55 ( ( bit_se1146084159140164899it_int @ A @ N3 )
% 5.25/5.55 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.25/5.55 => ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.55 = A ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_iff_idd_imp_stable
% 5.25/5.55 thf(fact_6913_bit__iff__idd__imp__stable,axiom,
% 5.25/5.55 ! [A: nat] :
% 5.25/5.55 ( ! [N3: nat] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ A @ N3 )
% 5.25/5.55 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.25/5.55 => ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.55 = A ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_iff_idd_imp_stable
% 5.25/5.55 thf(fact_6914_int__bit__bound,axiom,
% 5.25/5.55 ! [K: int] :
% 5.25/5.55 ~ ! [N3: nat] :
% 5.25/5.55 ( ! [M2: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ N3 @ M2 )
% 5.25/5.55 => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 5.25/5.55 = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 5.25/5.55 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.25/5.55 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 5.25/5.55 = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % int_bit_bound
% 5.25/5.55 thf(fact_6915_real__sum__nat__ivl__bounded2,axiom,
% 5.25/5.55 ! [N: nat,F: nat > rat,K5: rat,K: nat] :
% 5.25/5.55 ( ! [P7: nat] :
% 5.25/5.55 ( ( ord_less_nat @ P7 @ N )
% 5.25/5.55 => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 5.25/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 5.25/5.55 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % real_sum_nat_ivl_bounded2
% 5.25/5.55 thf(fact_6916_real__sum__nat__ivl__bounded2,axiom,
% 5.25/5.55 ! [N: nat,F: nat > int,K5: int,K: nat] :
% 5.25/5.55 ( ! [P7: nat] :
% 5.25/5.55 ( ( ord_less_nat @ P7 @ N )
% 5.25/5.55 => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 5.25/5.55 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 5.25/5.55 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % real_sum_nat_ivl_bounded2
% 5.25/5.55 thf(fact_6917_real__sum__nat__ivl__bounded2,axiom,
% 5.25/5.55 ! [N: nat,F: nat > nat,K5: nat,K: nat] :
% 5.25/5.55 ( ! [P7: nat] :
% 5.25/5.55 ( ( ord_less_nat @ P7 @ N )
% 5.25/5.55 => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 5.25/5.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 5.25/5.55 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % real_sum_nat_ivl_bounded2
% 5.25/5.55 thf(fact_6918_real__sum__nat__ivl__bounded2,axiom,
% 5.25/5.55 ! [N: nat,F: nat > real,K5: real,K: nat] :
% 5.25/5.55 ( ! [P7: nat] :
% 5.25/5.55 ( ( ord_less_nat @ P7 @ N )
% 5.25/5.55 => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 5.25/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 5.25/5.55 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % real_sum_nat_ivl_bounded2
% 5.25/5.55 thf(fact_6919_one__diff__power__eq,axiom,
% 5.25/5.55 ! [X3: complex,N: nat] :
% 5.25/5.55 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N ) )
% 5.25/5.55 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % one_diff_power_eq
% 5.25/5.55 thf(fact_6920_one__diff__power__eq,axiom,
% 5.25/5.55 ! [X3: rat,N: nat] :
% 5.25/5.55 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N ) )
% 5.25/5.55 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % one_diff_power_eq
% 5.25/5.55 thf(fact_6921_one__diff__power__eq,axiom,
% 5.25/5.55 ! [X3: int,N: nat] :
% 5.25/5.55 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ N ) )
% 5.25/5.55 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % one_diff_power_eq
% 5.25/5.55 thf(fact_6922_one__diff__power__eq,axiom,
% 5.25/5.55 ! [X3: real,N: nat] :
% 5.25/5.55 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N ) )
% 5.25/5.55 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % one_diff_power_eq
% 5.25/5.55 thf(fact_6923_power__diff__1__eq,axiom,
% 5.25/5.55 ! [X3: complex,N: nat] :
% 5.25/5.55 ( ( minus_minus_complex @ ( power_power_complex @ X3 @ N ) @ one_one_complex )
% 5.25/5.55 = ( times_times_complex @ ( minus_minus_complex @ X3 @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_diff_1_eq
% 5.25/5.55 thf(fact_6924_power__diff__1__eq,axiom,
% 5.25/5.55 ! [X3: rat,N: nat] :
% 5.25/5.55 ( ( minus_minus_rat @ ( power_power_rat @ X3 @ N ) @ one_one_rat )
% 5.25/5.55 = ( times_times_rat @ ( minus_minus_rat @ X3 @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_diff_1_eq
% 5.25/5.55 thf(fact_6925_power__diff__1__eq,axiom,
% 5.25/5.55 ! [X3: int,N: nat] :
% 5.25/5.55 ( ( minus_minus_int @ ( power_power_int @ X3 @ N ) @ one_one_int )
% 5.25/5.55 = ( times_times_int @ ( minus_minus_int @ X3 @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_diff_1_eq
% 5.25/5.55 thf(fact_6926_power__diff__1__eq,axiom,
% 5.25/5.55 ! [X3: real,N: nat] :
% 5.25/5.55 ( ( minus_minus_real @ ( power_power_real @ X3 @ N ) @ one_one_real )
% 5.25/5.55 = ( times_times_real @ ( minus_minus_real @ X3 @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_diff_1_eq
% 5.25/5.55 thf(fact_6927_geometric__sum,axiom,
% 5.25/5.55 ! [X3: complex,N: nat] :
% 5.25/5.55 ( ( X3 != one_one_complex )
% 5.25/5.55 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X3 @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X3 @ one_one_complex ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % geometric_sum
% 5.25/5.55 thf(fact_6928_geometric__sum,axiom,
% 5.25/5.55 ! [X3: rat,N: nat] :
% 5.25/5.55 ( ( X3 != one_one_rat )
% 5.25/5.55 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X3 @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X3 @ one_one_rat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % geometric_sum
% 5.25/5.55 thf(fact_6929_geometric__sum,axiom,
% 5.25/5.55 ! [X3: real,N: nat] :
% 5.25/5.55 ( ( X3 != one_one_real )
% 5.25/5.55 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X3 @ N ) @ one_one_real ) @ ( minus_minus_real @ X3 @ one_one_real ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % geometric_sum
% 5.25/5.55 thf(fact_6930_pochhammer__product,axiom,
% 5.25/5.55 ! [M: nat,N: nat,Z: int] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 5.25/5.55 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_product
% 5.25/5.55 thf(fact_6931_pochhammer__product,axiom,
% 5.25/5.55 ! [M: nat,N: nat,Z: real] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 5.25/5.55 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_product
% 5.25/5.55 thf(fact_6932_pochhammer__product,axiom,
% 5.25/5.55 ! [M: nat,N: nat,Z: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 5.25/5.55 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_product
% 5.25/5.55 thf(fact_6933_pochhammer__product,axiom,
% 5.25/5.55 ! [M: nat,N: nat,Z: rat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 5.25/5.55 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_product
% 5.25/5.55 thf(fact_6934_bit__iff__odd,axiom,
% 5.25/5.55 ( bit_se9216721137139052372nteger
% 5.25/5.55 = ( ^ [A3: code_integer,N2: nat] :
% 5.25/5.55 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_iff_odd
% 5.25/5.55 thf(fact_6935_bit__iff__odd,axiom,
% 5.25/5.55 ( bit_se1146084159140164899it_int
% 5.25/5.55 = ( ^ [A3: int,N2: nat] :
% 5.25/5.55 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_iff_odd
% 5.25/5.55 thf(fact_6936_bit__iff__odd,axiom,
% 5.25/5.55 ( bit_se1148574629649215175it_nat
% 5.25/5.55 = ( ^ [A3: nat,N2: nat] :
% 5.25/5.55 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_iff_odd
% 5.25/5.55 thf(fact_6937_and__exp__eq__0__iff__not__bit,axiom,
% 5.25/5.55 ! [A: int,N: nat] :
% 5.25/5.55 ( ( ( bit_se725231765392027082nd_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.55 = zero_zero_int )
% 5.25/5.55 = ( ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % and_exp_eq_0_iff_not_bit
% 5.25/5.55 thf(fact_6938_and__exp__eq__0__iff__not__bit,axiom,
% 5.25/5.55 ! [A: nat,N: nat] :
% 5.25/5.55 ( ( ( bit_se727722235901077358nd_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.55 = zero_zero_nat )
% 5.25/5.55 = ( ~ ( bit_se1148574629649215175it_nat @ A @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % and_exp_eq_0_iff_not_bit
% 5.25/5.55 thf(fact_6939_bit__int__def,axiom,
% 5.25/5.55 ( bit_se1146084159140164899it_int
% 5.25/5.55 = ( ^ [K3: int,N2: nat] :
% 5.25/5.55 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_int_def
% 5.25/5.55 thf(fact_6940_sum__gp__strict,axiom,
% 5.25/5.55 ! [X3: complex,N: nat] :
% 5.25/5.55 ( ( ( X3 = one_one_complex )
% 5.25/5.55 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 = ( semiri8010041392384452111omplex @ N ) ) )
% 5.25/5.55 & ( ( X3 != one_one_complex )
% 5.25/5.55 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_gp_strict
% 5.25/5.55 thf(fact_6941_sum__gp__strict,axiom,
% 5.25/5.55 ! [X3: rat,N: nat] :
% 5.25/5.55 ( ( ( X3 = one_one_rat )
% 5.25/5.55 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 = ( semiri681578069525770553at_rat @ N ) ) )
% 5.25/5.55 & ( ( X3 != one_one_rat )
% 5.25/5.55 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_gp_strict
% 5.25/5.55 thf(fact_6942_sum__gp__strict,axiom,
% 5.25/5.55 ! [X3: real,N: nat] :
% 5.25/5.55 ( ( ( X3 = one_one_real )
% 5.25/5.55 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 = ( semiri5074537144036343181t_real @ N ) ) )
% 5.25/5.55 & ( ( X3 != one_one_real )
% 5.25/5.55 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_gp_strict
% 5.25/5.55 thf(fact_6943_sum__split__even__odd,axiom,
% 5.25/5.55 ! [F: nat > real,G: nat > real,N: nat] :
% 5.25/5.55 ( ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( F @ I3 ) @ ( G @ I3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.55 = ( plus_plus_real
% 5.25/5.55 @ ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [I3: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 @ ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ one_one_nat ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_split_even_odd
% 5.25/5.55 thf(fact_6944_power__diff__sumr2,axiom,
% 5.25/5.55 ! [X3: complex,N: nat,Y: complex] :
% 5.25/5.55 ( ( minus_minus_complex @ ( power_power_complex @ X3 @ N ) @ ( power_power_complex @ Y @ N ) )
% 5.25/5.55 = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y )
% 5.25/5.55 @ ( groups2073611262835488442omplex
% 5.25/5.55 @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_complex @ X3 @ I3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_diff_sumr2
% 5.25/5.55 thf(fact_6945_power__diff__sumr2,axiom,
% 5.25/5.55 ! [X3: rat,N: nat,Y: rat] :
% 5.25/5.55 ( ( minus_minus_rat @ ( power_power_rat @ X3 @ N ) @ ( power_power_rat @ Y @ N ) )
% 5.25/5.55 = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y )
% 5.25/5.55 @ ( groups2906978787729119204at_rat
% 5.25/5.55 @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_rat @ X3 @ I3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_diff_sumr2
% 5.25/5.55 thf(fact_6946_power__diff__sumr2,axiom,
% 5.25/5.55 ! [X3: int,N: nat,Y: int] :
% 5.25/5.55 ( ( minus_minus_int @ ( power_power_int @ X3 @ N ) @ ( power_power_int @ Y @ N ) )
% 5.25/5.55 = ( times_times_int @ ( minus_minus_int @ X3 @ Y )
% 5.25/5.55 @ ( groups3539618377306564664at_int
% 5.25/5.55 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_int @ X3 @ I3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_diff_sumr2
% 5.25/5.55 thf(fact_6947_power__diff__sumr2,axiom,
% 5.25/5.55 ! [X3: real,N: nat,Y: real] :
% 5.25/5.55 ( ( minus_minus_real @ ( power_power_real @ X3 @ N ) @ ( power_power_real @ Y @ N ) )
% 5.25/5.55 = ( times_times_real @ ( minus_minus_real @ X3 @ Y )
% 5.25/5.55 @ ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_real @ X3 @ I3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_diff_sumr2
% 5.25/5.55 thf(fact_6948_diff__power__eq__sum,axiom,
% 5.25/5.55 ! [X3: complex,N: nat,Y: complex] :
% 5.25/5.55 ( ( minus_minus_complex @ ( power_power_complex @ X3 @ ( suc @ N ) ) @ ( power_power_complex @ Y @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y )
% 5.25/5.55 @ ( groups2073611262835488442omplex
% 5.25/5.55 @ ^ [P4: nat] : ( times_times_complex @ ( power_power_complex @ X3 @ P4 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % diff_power_eq_sum
% 5.25/5.55 thf(fact_6949_diff__power__eq__sum,axiom,
% 5.25/5.55 ! [X3: rat,N: nat,Y: rat] :
% 5.25/5.55 ( ( minus_minus_rat @ ( power_power_rat @ X3 @ ( suc @ N ) ) @ ( power_power_rat @ Y @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y )
% 5.25/5.55 @ ( groups2906978787729119204at_rat
% 5.25/5.55 @ ^ [P4: nat] : ( times_times_rat @ ( power_power_rat @ X3 @ P4 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % diff_power_eq_sum
% 5.25/5.55 thf(fact_6950_diff__power__eq__sum,axiom,
% 5.25/5.55 ! [X3: int,N: nat,Y: int] :
% 5.25/5.55 ( ( minus_minus_int @ ( power_power_int @ X3 @ ( suc @ N ) ) @ ( power_power_int @ Y @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_int @ ( minus_minus_int @ X3 @ Y )
% 5.25/5.55 @ ( groups3539618377306564664at_int
% 5.25/5.55 @ ^ [P4: nat] : ( times_times_int @ ( power_power_int @ X3 @ P4 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % diff_power_eq_sum
% 5.25/5.55 thf(fact_6951_diff__power__eq__sum,axiom,
% 5.25/5.55 ! [X3: real,N: nat,Y: real] :
% 5.25/5.55 ( ( minus_minus_real @ ( power_power_real @ X3 @ ( suc @ N ) ) @ ( power_power_real @ Y @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_real @ ( minus_minus_real @ X3 @ Y )
% 5.25/5.55 @ ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [P4: nat] : ( times_times_real @ ( power_power_real @ X3 @ P4 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % diff_power_eq_sum
% 5.25/5.55 thf(fact_6952_pochhammer__absorb__comp,axiom,
% 5.25/5.55 ! [R2: complex,K: nat] :
% 5.25/5.55 ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 5.25/5.55 = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_absorb_comp
% 5.25/5.55 thf(fact_6953_pochhammer__absorb__comp,axiom,
% 5.25/5.55 ! [R2: code_integer,K: nat] :
% 5.25/5.55 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 5.25/5.55 = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_absorb_comp
% 5.25/5.55 thf(fact_6954_pochhammer__absorb__comp,axiom,
% 5.25/5.55 ! [R2: int,K: nat] :
% 5.25/5.55 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 5.25/5.55 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_absorb_comp
% 5.25/5.55 thf(fact_6955_pochhammer__absorb__comp,axiom,
% 5.25/5.55 ! [R2: real,K: nat] :
% 5.25/5.55 ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 5.25/5.55 = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_absorb_comp
% 5.25/5.55 thf(fact_6956_pochhammer__absorb__comp,axiom,
% 5.25/5.55 ! [R2: rat,K: nat] :
% 5.25/5.55 ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 5.25/5.55 = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_absorb_comp
% 5.25/5.55 thf(fact_6957_even__bit__succ__iff,axiom,
% 5.25/5.55 ! [A: code_integer,N: nat] :
% 5.25/5.55 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.55 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ N )
% 5.25/5.55 = ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.25/5.55 | ( N = zero_zero_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % even_bit_succ_iff
% 5.25/5.55 thf(fact_6958_even__bit__succ__iff,axiom,
% 5.25/5.55 ! [A: int,N: nat] :
% 5.25/5.55 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.55 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N )
% 5.25/5.55 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.25/5.55 | ( N = zero_zero_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % even_bit_succ_iff
% 5.25/5.55 thf(fact_6959_even__bit__succ__iff,axiom,
% 5.25/5.55 ! [A: nat,N: nat] :
% 5.25/5.55 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.55 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N )
% 5.25/5.55 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.25/5.55 | ( N = zero_zero_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % even_bit_succ_iff
% 5.25/5.55 thf(fact_6960_odd__bit__iff__bit__pred,axiom,
% 5.25/5.55 ! [A: code_integer,N: nat] :
% 5.25/5.55 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.55 => ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.25/5.55 = ( ( bit_se9216721137139052372nteger @ ( minus_8373710615458151222nteger @ A @ one_one_Code_integer ) @ N )
% 5.25/5.55 | ( N = zero_zero_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % odd_bit_iff_bit_pred
% 5.25/5.55 thf(fact_6961_odd__bit__iff__bit__pred,axiom,
% 5.25/5.55 ! [A: int,N: nat] :
% 5.25/5.55 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.55 => ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.25/5.55 = ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ A @ one_one_int ) @ N )
% 5.25/5.55 | ( N = zero_zero_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % odd_bit_iff_bit_pred
% 5.25/5.55 thf(fact_6962_odd__bit__iff__bit__pred,axiom,
% 5.25/5.55 ! [A: nat,N: nat] :
% 5.25/5.55 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.55 => ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.25/5.55 = ( ( bit_se1148574629649215175it_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ N )
% 5.25/5.55 | ( N = zero_zero_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % odd_bit_iff_bit_pred
% 5.25/5.55 thf(fact_6963_one__diff__power__eq_H,axiom,
% 5.25/5.55 ! [X3: complex,N: nat] :
% 5.25/5.55 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ N ) )
% 5.25/5.55 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 )
% 5.25/5.55 @ ( groups2073611262835488442omplex
% 5.25/5.55 @ ^ [I3: nat] : ( power_power_complex @ X3 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % one_diff_power_eq'
% 5.25/5.55 thf(fact_6964_one__diff__power__eq_H,axiom,
% 5.25/5.55 ! [X3: rat,N: nat] :
% 5.25/5.55 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ N ) )
% 5.25/5.55 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 )
% 5.25/5.55 @ ( groups2906978787729119204at_rat
% 5.25/5.55 @ ^ [I3: nat] : ( power_power_rat @ X3 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % one_diff_power_eq'
% 5.25/5.55 thf(fact_6965_one__diff__power__eq_H,axiom,
% 5.25/5.55 ! [X3: int,N: nat] :
% 5.25/5.55 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ N ) )
% 5.25/5.55 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 )
% 5.25/5.55 @ ( groups3539618377306564664at_int
% 5.25/5.55 @ ^ [I3: nat] : ( power_power_int @ X3 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % one_diff_power_eq'
% 5.25/5.55 thf(fact_6966_one__diff__power__eq_H,axiom,
% 5.25/5.55 ! [X3: real,N: nat] :
% 5.25/5.55 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ N ) )
% 5.25/5.55 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 )
% 5.25/5.55 @ ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [I3: nat] : ( power_power_real @ X3 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % one_diff_power_eq'
% 5.25/5.55 thf(fact_6967_pochhammer__minus_H,axiom,
% 5.25/5.55 ! [B: complex,K: nat] :
% 5.25/5.55 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.25/5.55 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_minus'
% 5.25/5.55 thf(fact_6968_pochhammer__minus_H,axiom,
% 5.25/5.55 ! [B: code_integer,K: nat] :
% 5.25/5.55 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.25/5.55 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_minus'
% 5.25/5.55 thf(fact_6969_pochhammer__minus_H,axiom,
% 5.25/5.55 ! [B: int,K: nat] :
% 5.25/5.55 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.25/5.55 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_minus'
% 5.25/5.55 thf(fact_6970_pochhammer__minus_H,axiom,
% 5.25/5.55 ! [B: real,K: nat] :
% 5.25/5.55 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.25/5.55 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_minus'
% 5.25/5.55 thf(fact_6971_pochhammer__minus_H,axiom,
% 5.25/5.55 ! [B: rat,K: nat] :
% 5.25/5.55 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.25/5.55 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_minus'
% 5.25/5.55 thf(fact_6972_pochhammer__minus,axiom,
% 5.25/5.55 ! [B: complex,K: nat] :
% 5.25/5.55 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 5.25/5.55 = ( 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 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_minus
% 5.25/5.55 thf(fact_6973_pochhammer__minus,axiom,
% 5.25/5.55 ! [B: code_integer,K: nat] :
% 5.25/5.55 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.25/5.55 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_minus
% 5.25/5.55 thf(fact_6974_pochhammer__minus,axiom,
% 5.25/5.55 ! [B: int,K: nat] :
% 5.25/5.55 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.25/5.55 = ( 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 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_minus
% 5.25/5.55 thf(fact_6975_pochhammer__minus,axiom,
% 5.25/5.55 ! [B: real,K: nat] :
% 5.25/5.55 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 5.25/5.55 = ( 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 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_minus
% 5.25/5.55 thf(fact_6976_pochhammer__minus,axiom,
% 5.25/5.55 ! [B: rat,K: nat] :
% 5.25/5.55 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 5.25/5.55 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_minus
% 5.25/5.55 thf(fact_6977_bit__sum__mult__2__cases,axiom,
% 5.25/5.55 ! [A: code_integer,B: code_integer,N: nat] :
% 5.25/5.55 ( ! [J: nat] :
% 5.25/5.55 ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J ) )
% 5.25/5.55 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.25/5.55 = ( ( ( N = zero_zero_nat )
% 5.25/5.55 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.55 & ( ( N != zero_zero_nat )
% 5.25/5.55 => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_sum_mult_2_cases
% 5.25/5.55 thf(fact_6978_bit__sum__mult__2__cases,axiom,
% 5.25/5.55 ! [A: int,B: int,N: nat] :
% 5.25/5.55 ( ! [J: nat] :
% 5.25/5.55 ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J ) )
% 5.25/5.55 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.25/5.55 = ( ( ( N = zero_zero_nat )
% 5.25/5.55 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.55 & ( ( N != zero_zero_nat )
% 5.25/5.55 => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_sum_mult_2_cases
% 5.25/5.55 thf(fact_6979_bit__sum__mult__2__cases,axiom,
% 5.25/5.55 ! [A: nat,B: nat,N: nat] :
% 5.25/5.55 ( ! [J: nat] :
% 5.25/5.55 ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J ) )
% 5.25/5.55 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.25/5.55 = ( ( ( N = zero_zero_nat )
% 5.25/5.55 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.55 & ( ( N != zero_zero_nat )
% 5.25/5.55 => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_sum_mult_2_cases
% 5.25/5.55 thf(fact_6980_bit__rec,axiom,
% 5.25/5.55 ( bit_se9216721137139052372nteger
% 5.25/5.55 = ( ^ [A3: code_integer,N2: nat] :
% 5.25/5.55 ( ( ( N2 = zero_zero_nat )
% 5.25/5.55 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) )
% 5.25/5.55 & ( ( N2 != zero_zero_nat )
% 5.25/5.55 => ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_rec
% 5.25/5.55 thf(fact_6981_bit__rec,axiom,
% 5.25/5.55 ( bit_se1146084159140164899it_int
% 5.25/5.55 = ( ^ [A3: int,N2: nat] :
% 5.25/5.55 ( ( ( N2 = zero_zero_nat )
% 5.25/5.55 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) )
% 5.25/5.55 & ( ( N2 != zero_zero_nat )
% 5.25/5.55 => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_rec
% 5.25/5.55 thf(fact_6982_bit__rec,axiom,
% 5.25/5.55 ( bit_se1148574629649215175it_nat
% 5.25/5.55 = ( ^ [A3: nat,N2: nat] :
% 5.25/5.55 ( ( ( N2 = zero_zero_nat )
% 5.25/5.55 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) )
% 5.25/5.55 & ( ( N2 != zero_zero_nat )
% 5.25/5.55 => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_rec
% 5.25/5.55 thf(fact_6983_and__nat__unfold,axiom,
% 5.25/5.55 ( bit_se727722235901077358nd_nat
% 5.25/5.55 = ( ^ [M6: nat,N2: nat] :
% 5.25/5.55 ( if_nat
% 5.25/5.55 @ ( ( M6 = zero_zero_nat )
% 5.25/5.55 | ( N2 = zero_zero_nat ) )
% 5.25/5.55 @ zero_zero_nat
% 5.25/5.55 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % and_nat_unfold
% 5.25/5.55 thf(fact_6984_and__nat__rec,axiom,
% 5.25/5.55 ( bit_se727722235901077358nd_nat
% 5.25/5.55 = ( ^ [M6: nat,N2: nat] :
% 5.25/5.55 ( plus_plus_nat
% 5.25/5.55 @ ( zero_n2687167440665602831ol_nat
% 5.25/5.55 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.25/5.55 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.25/5.55 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % and_nat_rec
% 5.25/5.55 thf(fact_6985_set__bit__eq,axiom,
% 5.25/5.55 ( bit_se7879613467334960850it_int
% 5.25/5.55 = ( ^ [N2: nat,K3: int] :
% 5.25/5.55 ( plus_plus_int @ K3
% 5.25/5.55 @ ( times_times_int
% 5.25/5.55 @ ( zero_n2684676970156552555ol_int
% 5.25/5.55 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N2 ) )
% 5.25/5.55 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_bit_eq
% 5.25/5.55 thf(fact_6986_unset__bit__eq,axiom,
% 5.25/5.55 ( bit_se4203085406695923979it_int
% 5.25/5.55 = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % unset_bit_eq
% 5.25/5.55 thf(fact_6987_take__bit__Suc__from__most,axiom,
% 5.25/5.55 ! [N: nat,K: int] :
% 5.25/5.55 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 5.25/5.55 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % take_bit_Suc_from_most
% 5.25/5.55 thf(fact_6988_norm__divide__numeral,axiom,
% 5.25/5.55 ! [A: real,W: num] :
% 5.25/5.55 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.55 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_divide_numeral
% 5.25/5.55 thf(fact_6989_norm__divide__numeral,axiom,
% 5.25/5.55 ! [A: complex,W: num] :
% 5.25/5.55 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.25/5.55 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_divide_numeral
% 5.25/5.55 thf(fact_6990_norm__mult__numeral2,axiom,
% 5.25/5.55 ! [A: real,W: num] :
% 5.25/5.55 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.55 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_mult_numeral2
% 5.25/5.55 thf(fact_6991_norm__mult__numeral2,axiom,
% 5.25/5.55 ! [A: complex,W: num] :
% 5.25/5.55 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.25/5.55 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_mult_numeral2
% 5.25/5.55 thf(fact_6992_norm__mult__numeral1,axiom,
% 5.25/5.55 ! [W: num,A: real] :
% 5.25/5.55 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.25/5.55 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_mult_numeral1
% 5.25/5.55 thf(fact_6993_norm__mult__numeral1,axiom,
% 5.25/5.55 ! [W: num,A: complex] :
% 5.25/5.55 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.25/5.55 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_mult_numeral1
% 5.25/5.55 thf(fact_6994_norm__neg__numeral,axiom,
% 5.25/5.55 ! [W: num] :
% 5.25/5.55 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.55 = ( numeral_numeral_real @ W ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_neg_numeral
% 5.25/5.55 thf(fact_6995_norm__neg__numeral,axiom,
% 5.25/5.55 ! [W: num] :
% 5.25/5.55 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.25/5.55 = ( numeral_numeral_real @ W ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_neg_numeral
% 5.25/5.55 thf(fact_6996_norm__le__zero__iff,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X3 ) @ zero_zero_real )
% 5.25/5.55 = ( X3 = zero_zero_real ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_le_zero_iff
% 5.25/5.55 thf(fact_6997_norm__le__zero__iff,axiom,
% 5.25/5.55 ! [X3: complex] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X3 ) @ zero_zero_real )
% 5.25/5.55 = ( X3 = zero_zero_complex ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_le_zero_iff
% 5.25/5.55 thf(fact_6998_norm__numeral,axiom,
% 5.25/5.55 ! [W: num] :
% 5.25/5.55 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.25/5.55 = ( numeral_numeral_real @ W ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_numeral
% 5.25/5.55 thf(fact_6999_norm__numeral,axiom,
% 5.25/5.55 ! [W: num] :
% 5.25/5.55 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.25/5.55 = ( numeral_numeral_real @ W ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_numeral
% 5.25/5.55 thf(fact_7000_norm__one,axiom,
% 5.25/5.55 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.25/5.55 = one_one_real ) ).
% 5.25/5.55
% 5.25/5.55 % norm_one
% 5.25/5.55 thf(fact_7001_norm__one,axiom,
% 5.25/5.55 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.25/5.55 = one_one_real ) ).
% 5.25/5.55
% 5.25/5.55 % norm_one
% 5.25/5.55 thf(fact_7002_bit__Suc__0__iff,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.25/5.55 = ( N = zero_zero_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_Suc_0_iff
% 5.25/5.55 thf(fact_7003_not__bit__Suc__0__Suc,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % not_bit_Suc_0_Suc
% 5.25/5.55 thf(fact_7004_not__bit__Suc__0__numeral,axiom,
% 5.25/5.55 ! [N: num] :
% 5.25/5.55 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % not_bit_Suc_0_numeral
% 5.25/5.55 thf(fact_7005_bit__nat__def,axiom,
% 5.25/5.55 ( bit_se1148574629649215175it_nat
% 5.25/5.55 = ( ^ [M6: nat,N2: nat] :
% 5.25/5.55 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % bit_nat_def
% 5.25/5.55 thf(fact_7006_norm__ge__zero,axiom,
% 5.25/5.55 ! [X3: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_ge_zero
% 5.25/5.55 thf(fact_7007_norm__mult,axiom,
% 5.25/5.55 ! [X3: real,Y: real] :
% 5.25/5.55 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X3 @ Y ) )
% 5.25/5.55 = ( times_times_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_mult
% 5.25/5.55 thf(fact_7008_norm__mult,axiom,
% 5.25/5.55 ! [X3: complex,Y: complex] :
% 5.25/5.55 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X3 @ Y ) )
% 5.25/5.55 = ( times_times_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_mult
% 5.25/5.55 thf(fact_7009_sum__norm__le,axiom,
% 5.25/5.55 ! [S3: set_real,F: real > complex,G: real > real] :
% 5.25/5.55 ( ! [X5: real] :
% 5.25/5.55 ( ( member_real @ X5 @ S3 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S3 ) ) @ ( groups8097168146408367636l_real @ G @ S3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_norm_le
% 5.25/5.55 thf(fact_7010_sum__norm__le,axiom,
% 5.25/5.55 ! [S3: set_int,F: int > complex,G: int > real] :
% 5.25/5.55 ( ! [X5: int] :
% 5.25/5.55 ( ( member_int @ X5 @ S3 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S3 ) ) @ ( groups8778361861064173332t_real @ G @ S3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_norm_le
% 5.25/5.55 thf(fact_7011_sum__norm__le,axiom,
% 5.25/5.55 ! [S3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > complex,G: product_prod_nat_nat > real] :
% 5.25/5.55 ( ! [X5: product_prod_nat_nat] :
% 5.25/5.55 ( ( member8440522571783428010at_nat @ X5 @ S3 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups6381953495645901045omplex @ F @ S3 ) ) @ ( groups4567486121110086003t_real @ G @ S3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_norm_le
% 5.25/5.55 thf(fact_7012_sum__norm__le,axiom,
% 5.25/5.55 ! [S3: set_nat,F: nat > complex,G: nat > real] :
% 5.25/5.55 ( ! [X5: nat] :
% 5.25/5.55 ( ( member_nat @ X5 @ S3 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S3 ) ) @ ( groups6591440286371151544t_real @ G @ S3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_norm_le
% 5.25/5.55 thf(fact_7013_sum__norm__le,axiom,
% 5.25/5.55 ! [S3: set_nat,F: nat > real,G: nat > real] :
% 5.25/5.55 ( ! [X5: nat] :
% 5.25/5.55 ( ( member_nat @ X5 @ S3 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S3 ) ) @ ( groups6591440286371151544t_real @ G @ S3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_norm_le
% 5.25/5.55 thf(fact_7014_sum__norm__le,axiom,
% 5.25/5.55 ! [S3: set_complex,F: complex > complex,G: complex > real] :
% 5.25/5.55 ( ! [X5: complex] :
% 5.25/5.55 ( ( member_complex @ X5 @ S3 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S3 ) ) @ ( groups5808333547571424918x_real @ G @ S3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_norm_le
% 5.25/5.55 thf(fact_7015_norm__divide,axiom,
% 5.25/5.55 ! [A: real,B: real] :
% 5.25/5.55 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.25/5.55 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_divide
% 5.25/5.55 thf(fact_7016_norm__divide,axiom,
% 5.25/5.55 ! [A: complex,B: complex] :
% 5.25/5.55 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.25/5.55 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_divide
% 5.25/5.55 thf(fact_7017_norm__power,axiom,
% 5.25/5.55 ! [X3: real,N: nat] :
% 5.25/5.55 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X3 @ N ) )
% 5.25/5.55 = ( power_power_real @ ( real_V7735802525324610683m_real @ X3 ) @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_power
% 5.25/5.55 thf(fact_7018_norm__power,axiom,
% 5.25/5.55 ! [X3: complex,N: nat] :
% 5.25/5.55 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X3 @ N ) )
% 5.25/5.55 = ( power_power_real @ ( real_V1022390504157884413omplex @ X3 ) @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_power
% 5.25/5.55 thf(fact_7019_norm__sum,axiom,
% 5.25/5.55 ! [F: nat > complex,A2: set_nat] :
% 5.25/5.55 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 5.25/5.55 @ ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [I3: nat] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 5.25/5.55 @ A2 ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_sum
% 5.25/5.55 thf(fact_7020_norm__sum,axiom,
% 5.25/5.55 ! [F: nat > real,A2: set_nat] :
% 5.25/5.55 ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.25/5.55 @ ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [I3: nat] : ( real_V7735802525324610683m_real @ ( F @ I3 ) )
% 5.25/5.55 @ A2 ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_sum
% 5.25/5.55 thf(fact_7021_norm__sum,axiom,
% 5.25/5.55 ! [F: complex > complex,A2: set_complex] :
% 5.25/5.55 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.25/5.55 @ ( groups5808333547571424918x_real
% 5.25/5.55 @ ^ [I3: complex] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 5.25/5.55 @ A2 ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_sum
% 5.25/5.55 thf(fact_7022_norm__uminus__minus,axiom,
% 5.25/5.55 ! [X3: real,Y: real] :
% 5.25/5.55 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X3 ) @ Y ) )
% 5.25/5.55 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_uminus_minus
% 5.25/5.55 thf(fact_7023_norm__uminus__minus,axiom,
% 5.25/5.55 ! [X3: complex,Y: complex] :
% 5.25/5.55 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X3 ) @ Y ) )
% 5.25/5.55 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_uminus_minus
% 5.25/5.55 thf(fact_7024_nonzero__norm__divide,axiom,
% 5.25/5.55 ! [B: real,A: real] :
% 5.25/5.55 ( ( B != zero_zero_real )
% 5.25/5.55 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.25/5.55 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % nonzero_norm_divide
% 5.25/5.55 thf(fact_7025_nonzero__norm__divide,axiom,
% 5.25/5.55 ! [B: complex,A: complex] :
% 5.25/5.55 ( ( B != zero_zero_complex )
% 5.25/5.55 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.25/5.55 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % nonzero_norm_divide
% 5.25/5.55 thf(fact_7026_power__eq__imp__eq__norm,axiom,
% 5.25/5.55 ! [W: real,N: nat,Z: real] :
% 5.25/5.55 ( ( ( power_power_real @ W @ N )
% 5.25/5.55 = ( power_power_real @ Z @ N ) )
% 5.25/5.55 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.55 => ( ( real_V7735802525324610683m_real @ W )
% 5.25/5.55 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_eq_imp_eq_norm
% 5.25/5.55 thf(fact_7027_power__eq__imp__eq__norm,axiom,
% 5.25/5.55 ! [W: complex,N: nat,Z: complex] :
% 5.25/5.55 ( ( ( power_power_complex @ W @ N )
% 5.25/5.55 = ( power_power_complex @ Z @ N ) )
% 5.25/5.55 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.55 => ( ( real_V1022390504157884413omplex @ W )
% 5.25/5.55 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_eq_imp_eq_norm
% 5.25/5.55 thf(fact_7028_norm__mult__less,axiom,
% 5.25/5.55 ! [X3: real,R2: real,Y: real,S: real] :
% 5.25/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ R2 )
% 5.25/5.55 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 5.25/5.55 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X3 @ Y ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_mult_less
% 5.25/5.55 thf(fact_7029_norm__mult__less,axiom,
% 5.25/5.55 ! [X3: complex,R2: real,Y: complex,S: real] :
% 5.25/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ R2 )
% 5.25/5.55 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 5.25/5.55 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X3 @ Y ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_mult_less
% 5.25/5.55 thf(fact_7030_norm__mult__ineq,axiom,
% 5.25/5.55 ! [X3: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X3 @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_mult_ineq
% 5.25/5.55 thf(fact_7031_norm__mult__ineq,axiom,
% 5.25/5.55 ! [X3: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X3 @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_mult_ineq
% 5.25/5.55 thf(fact_7032_norm__triangle__lt,axiom,
% 5.25/5.55 ! [X3: real,Y: real,E: real] :
% 5.25/5.55 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.25/5.55 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) @ E ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_lt
% 5.25/5.55 thf(fact_7033_norm__triangle__lt,axiom,
% 5.25/5.55 ! [X3: complex,Y: complex,E: real] :
% 5.25/5.55 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.25/5.55 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) @ E ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_lt
% 5.25/5.55 thf(fact_7034_norm__add__less,axiom,
% 5.25/5.55 ! [X3: real,R2: real,Y: real,S: real] :
% 5.25/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ R2 )
% 5.25/5.55 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 5.25/5.55 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_add_less
% 5.25/5.55 thf(fact_7035_norm__add__less,axiom,
% 5.25/5.55 ! [X3: complex,R2: real,Y: complex,S: real] :
% 5.25/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ R2 )
% 5.25/5.55 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 5.25/5.55 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_add_less
% 5.25/5.55 thf(fact_7036_norm__triangle__mono,axiom,
% 5.25/5.55 ! [A: real,R2: real,B: real,S: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 5.25/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_mono
% 5.25/5.55 thf(fact_7037_norm__triangle__mono,axiom,
% 5.25/5.55 ! [A: complex,R2: real,B: complex,S: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 5.25/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_mono
% 5.25/5.55 thf(fact_7038_norm__triangle__ineq,axiom,
% 5.25/5.55 ! [X3: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_ineq
% 5.25/5.55 thf(fact_7039_norm__triangle__ineq,axiom,
% 5.25/5.55 ! [X3: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_ineq
% 5.25/5.55 thf(fact_7040_norm__triangle__le,axiom,
% 5.25/5.55 ! [X3: real,Y: real,E: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X3 @ Y ) ) @ E ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_le
% 5.25/5.55 thf(fact_7041_norm__triangle__le,axiom,
% 5.25/5.55 ! [X3: complex,Y: complex,E: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X3 @ Y ) ) @ E ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_le
% 5.25/5.55 thf(fact_7042_norm__add__leD,axiom,
% 5.25/5.55 ! [A: real,B: real,C: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_add_leD
% 5.25/5.55 thf(fact_7043_norm__add__leD,axiom,
% 5.25/5.55 ! [A: complex,B: complex,C: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_add_leD
% 5.25/5.55 thf(fact_7044_norm__power__ineq,axiom,
% 5.25/5.55 ! [X3: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X3 @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X3 ) @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_power_ineq
% 5.25/5.55 thf(fact_7045_norm__power__ineq,axiom,
% 5.25/5.55 ! [X3: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X3 @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X3 ) @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_power_ineq
% 5.25/5.55 thf(fact_7046_norm__diff__triangle__less,axiom,
% 5.25/5.55 ! [X3: real,Y: real,E1: real,Z: real,E22: real] :
% 5.25/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Y ) ) @ E1 )
% 5.25/5.55 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.25/5.55 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_diff_triangle_less
% 5.25/5.55 thf(fact_7047_norm__diff__triangle__less,axiom,
% 5.25/5.55 ! [X3: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.25/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y ) ) @ E1 )
% 5.25/5.55 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.25/5.55 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_diff_triangle_less
% 5.25/5.55 thf(fact_7048_norm__triangle__le__diff,axiom,
% 5.25/5.55 ! [X3: real,Y: real,E: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Y ) ) @ E ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_le_diff
% 5.25/5.55 thf(fact_7049_norm__triangle__le__diff,axiom,
% 5.25/5.55 ! [X3: complex,Y: complex,E: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y ) ) @ E ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_le_diff
% 5.25/5.55 thf(fact_7050_norm__diff__triangle__le,axiom,
% 5.25/5.55 ! [X3: real,Y: real,E1: real,Z: real,E22: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Y ) ) @ E1 )
% 5.25/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_diff_triangle_le
% 5.25/5.55 thf(fact_7051_norm__diff__triangle__le,axiom,
% 5.25/5.55 ! [X3: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y ) ) @ E1 )
% 5.25/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_diff_triangle_le
% 5.25/5.55 thf(fact_7052_norm__triangle__ineq4,axiom,
% 5.25/5.55 ! [A: real,B: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_ineq4
% 5.25/5.55 thf(fact_7053_norm__triangle__ineq4,axiom,
% 5.25/5.55 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_ineq4
% 5.25/5.55 thf(fact_7054_norm__triangle__sub,axiom,
% 5.25/5.55 ! [X3: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X3 ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_sub
% 5.25/5.55 thf(fact_7055_norm__triangle__sub,axiom,
% 5.25/5.55 ! [X3: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_sub
% 5.25/5.55 thf(fact_7056_norm__diff__ineq,axiom,
% 5.25/5.55 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_diff_ineq
% 5.25/5.55 thf(fact_7057_norm__diff__ineq,axiom,
% 5.25/5.55 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_diff_ineq
% 5.25/5.55 thf(fact_7058_norm__triangle__ineq2,axiom,
% 5.25/5.55 ! [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 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_ineq2
% 5.25/5.55 thf(fact_7059_norm__triangle__ineq2,axiom,
% 5.25/5.55 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_triangle_ineq2
% 5.25/5.55 thf(fact_7060_power__eq__1__iff,axiom,
% 5.25/5.55 ! [W: real,N: nat] :
% 5.25/5.55 ( ( ( power_power_real @ W @ N )
% 5.25/5.55 = one_one_real )
% 5.25/5.55 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.25/5.55 = one_one_real )
% 5.25/5.55 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_eq_1_iff
% 5.25/5.55 thf(fact_7061_power__eq__1__iff,axiom,
% 5.25/5.55 ! [W: complex,N: nat] :
% 5.25/5.55 ( ( ( power_power_complex @ W @ N )
% 5.25/5.55 = one_one_complex )
% 5.25/5.55 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.25/5.55 = one_one_real )
% 5.25/5.55 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_eq_1_iff
% 5.25/5.55 thf(fact_7062_norm__diff__triangle__ineq,axiom,
% 5.25/5.55 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_diff_triangle_ineq
% 5.25/5.55 thf(fact_7063_norm__diff__triangle__ineq,axiom,
% 5.25/5.55 ! [A: complex,B: complex,C: complex,D: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_diff_triangle_ineq
% 5.25/5.55 thf(fact_7064_square__norm__one,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.55 = one_one_real )
% 5.25/5.55 => ( ( real_V7735802525324610683m_real @ X3 )
% 5.25/5.55 = one_one_real ) ) ).
% 5.25/5.55
% 5.25/5.55 % square_norm_one
% 5.25/5.55 thf(fact_7065_square__norm__one,axiom,
% 5.25/5.55 ! [X3: complex] :
% 5.25/5.55 ( ( ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.55 = one_one_complex )
% 5.25/5.55 => ( ( real_V1022390504157884413omplex @ X3 )
% 5.25/5.55 = one_one_real ) ) ).
% 5.25/5.55
% 5.25/5.55 % square_norm_one
% 5.25/5.55 thf(fact_7066_norm__power__diff,axiom,
% 5.25/5.55 ! [Z: real,W: real,M: nat] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.25/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.25/5.55 => ( 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 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_power_diff
% 5.25/5.55 thf(fact_7067_norm__power__diff,axiom,
% 5.25/5.55 ! [Z: complex,W: complex,M: nat] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.25/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.25/5.55 => ( 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 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_power_diff
% 5.25/5.55 thf(fact_7068_arcosh__1,axiom,
% 5.25/5.55 ( ( arcosh_real @ one_one_real )
% 5.25/5.55 = zero_zero_real ) ).
% 5.25/5.55
% 5.25/5.55 % arcosh_1
% 5.25/5.55 thf(fact_7069_sum__bounds__lt__plus1,axiom,
% 5.25/5.55 ! [F: nat > nat,Mm: nat] :
% 5.25/5.55 ( ( groups3542108847815614940at_nat
% 5.25/5.55 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.25/5.55 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_bounds_lt_plus1
% 5.25/5.55 thf(fact_7070_sum__bounds__lt__plus1,axiom,
% 5.25/5.55 ! [F: nat > real,Mm: nat] :
% 5.25/5.55 ( ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.25/5.55 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_bounds_lt_plus1
% 5.25/5.55 thf(fact_7071_sumr__cos__zero__one,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = one_one_real ) ).
% 5.25/5.55
% 5.25/5.55 % sumr_cos_zero_one
% 5.25/5.55 thf(fact_7072_pochhammer__times__pochhammer__half,axiom,
% 5.25/5.55 ! [Z: complex,N: nat] :
% 5.25/5.55 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.25/5.55 = ( groups6464643781859351333omplex
% 5.25/5.55 @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_times_pochhammer_half
% 5.25/5.55 thf(fact_7073_pochhammer__times__pochhammer__half,axiom,
% 5.25/5.55 ! [Z: real,N: nat] :
% 5.25/5.55 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.25/5.55 = ( groups129246275422532515t_real
% 5.25/5.55 @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_times_pochhammer_half
% 5.25/5.55 thf(fact_7074_pochhammer__times__pochhammer__half,axiom,
% 5.25/5.55 ! [Z: rat,N: nat] :
% 5.25/5.55 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.25/5.55 = ( groups73079841787564623at_rat
% 5.25/5.55 @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_times_pochhammer_half
% 5.25/5.55 thf(fact_7075_pochhammer__code,axiom,
% 5.25/5.55 ( comm_s2602460028002588243omplex
% 5.25/5.55 = ( ^ [A3: complex,N2: nat] :
% 5.25/5.55 ( if_complex @ ( N2 = zero_zero_nat ) @ one_one_complex
% 5.25/5.55 @ ( set_fo1517530859248394432omplex
% 5.25/5.55 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.25/5.55 @ zero_zero_nat
% 5.25/5.55 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.25/5.55 @ one_one_complex ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_code
% 5.25/5.55 thf(fact_7076_pochhammer__code,axiom,
% 5.25/5.55 ( comm_s4660882817536571857er_int
% 5.25/5.55 = ( ^ [A3: int,N2: nat] :
% 5.25/5.55 ( if_int @ ( N2 = zero_zero_nat ) @ one_one_int
% 5.25/5.55 @ ( set_fo2581907887559384638at_int
% 5.25/5.55 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.25/5.55 @ zero_zero_nat
% 5.25/5.55 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.25/5.55 @ one_one_int ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_code
% 5.25/5.55 thf(fact_7077_pochhammer__code,axiom,
% 5.25/5.55 ( comm_s7457072308508201937r_real
% 5.25/5.55 = ( ^ [A3: real,N2: nat] :
% 5.25/5.55 ( if_real @ ( N2 = zero_zero_nat ) @ one_one_real
% 5.25/5.55 @ ( set_fo3111899725591712190t_real
% 5.25/5.55 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.25/5.55 @ zero_zero_nat
% 5.25/5.55 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.25/5.55 @ one_one_real ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_code
% 5.25/5.55 thf(fact_7078_pochhammer__code,axiom,
% 5.25/5.55 ( comm_s4028243227959126397er_rat
% 5.25/5.55 = ( ^ [A3: rat,N2: nat] :
% 5.25/5.55 ( if_rat @ ( N2 = zero_zero_nat ) @ one_one_rat
% 5.25/5.55 @ ( set_fo1949268297981939178at_rat
% 5.25/5.55 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.25/5.55 @ zero_zero_nat
% 5.25/5.55 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.25/5.55 @ one_one_rat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_code
% 5.25/5.55 thf(fact_7079_pochhammer__code,axiom,
% 5.25/5.55 ( comm_s4663373288045622133er_nat
% 5.25/5.55 = ( ^ [A3: nat,N2: nat] :
% 5.25/5.55 ( if_nat @ ( N2 = zero_zero_nat ) @ one_one_nat
% 5.25/5.55 @ ( set_fo2584398358068434914at_nat
% 5.25/5.55 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.25/5.55 @ zero_zero_nat
% 5.25/5.55 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.25/5.55 @ one_one_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_code
% 5.25/5.55 thf(fact_7080_and__int_Osimps,axiom,
% 5.25/5.55 ( bit_se725231765392027082nd_int
% 5.25/5.55 = ( ^ [K3: int,L: int] :
% 5.25/5.55 ( if_int
% 5.25/5.55 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.25/5.55 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.25/5.55 @ ( uminus_uminus_int
% 5.25/5.55 @ ( zero_n2684676970156552555ol_int
% 5.25/5.55 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.25/5.55 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.25/5.55 @ ( plus_plus_int
% 5.25/5.55 @ ( zero_n2684676970156552555ol_int
% 5.25/5.55 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.25/5.55 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.25/5.55 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % and_int.simps
% 5.25/5.55 thf(fact_7081_insert__subset,axiom,
% 5.25/5.55 ! [X3: nat,A2: set_nat,B3: set_nat] :
% 5.25/5.55 ( ( ord_less_eq_set_nat @ ( insert_nat @ X3 @ A2 ) @ B3 )
% 5.25/5.55 = ( ( member_nat @ X3 @ B3 )
% 5.25/5.55 & ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % insert_subset
% 5.25/5.55 thf(fact_7082_insert__subset,axiom,
% 5.25/5.55 ! [X3: real,A2: set_real,B3: set_real] :
% 5.25/5.55 ( ( ord_less_eq_set_real @ ( insert_real @ X3 @ A2 ) @ B3 )
% 5.25/5.55 = ( ( member_real @ X3 @ B3 )
% 5.25/5.55 & ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % insert_subset
% 5.25/5.55 thf(fact_7083_insert__subset,axiom,
% 5.25/5.55 ! [X3: complex,A2: set_complex,B3: set_complex] :
% 5.25/5.55 ( ( ord_le211207098394363844omplex @ ( insert_complex @ X3 @ A2 ) @ B3 )
% 5.25/5.55 = ( ( member_complex @ X3 @ B3 )
% 5.25/5.55 & ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % insert_subset
% 5.25/5.55 thf(fact_7084_insert__subset,axiom,
% 5.25/5.55 ! [X3: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.25/5.55 ( ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ X3 @ A2 ) @ B3 )
% 5.25/5.55 = ( ( member8440522571783428010at_nat @ X3 @ B3 )
% 5.25/5.55 & ( ord_le3146513528884898305at_nat @ A2 @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % insert_subset
% 5.25/5.55 thf(fact_7085_insert__subset,axiom,
% 5.25/5.55 ! [X3: int,A2: set_int,B3: set_int] :
% 5.25/5.55 ( ( ord_less_eq_set_int @ ( insert_int @ X3 @ A2 ) @ B3 )
% 5.25/5.55 = ( ( member_int @ X3 @ B3 )
% 5.25/5.55 & ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % insert_subset
% 5.25/5.55 thf(fact_7086_prod_Oneutral__const,axiom,
% 5.25/5.55 ! [A2: set_nat] :
% 5.25/5.55 ( ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [Uu3: nat] : one_one_int
% 5.25/5.55 @ A2 )
% 5.25/5.55 = one_one_int ) ).
% 5.25/5.55
% 5.25/5.55 % prod.neutral_const
% 5.25/5.55 thf(fact_7087_prod_Oneutral__const,axiom,
% 5.25/5.55 ! [A2: set_int] :
% 5.25/5.55 ( ( groups1705073143266064639nt_int
% 5.25/5.55 @ ^ [Uu3: int] : one_one_int
% 5.25/5.55 @ A2 )
% 5.25/5.55 = one_one_int ) ).
% 5.25/5.55
% 5.25/5.55 % prod.neutral_const
% 5.25/5.55 thf(fact_7088_prod_Oneutral__const,axiom,
% 5.25/5.55 ! [A2: set_nat] :
% 5.25/5.55 ( ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [Uu3: nat] : one_one_nat
% 5.25/5.55 @ A2 )
% 5.25/5.55 = one_one_nat ) ).
% 5.25/5.55
% 5.25/5.55 % prod.neutral_const
% 5.25/5.55 thf(fact_7089_singleton__insert__inj__eq,axiom,
% 5.25/5.55 ! [B: nat,A: nat,A2: set_nat] :
% 5.25/5.55 ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 5.25/5.55 = ( insert_nat @ A @ A2 ) )
% 5.25/5.55 = ( ( A = B )
% 5.25/5.55 & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % singleton_insert_inj_eq
% 5.25/5.55 thf(fact_7090_singleton__insert__inj__eq,axiom,
% 5.25/5.55 ! [B: real,A: real,A2: set_real] :
% 5.25/5.55 ( ( ( insert_real @ B @ bot_bot_set_real )
% 5.25/5.55 = ( insert_real @ A @ A2 ) )
% 5.25/5.55 = ( ( A = B )
% 5.25/5.55 & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % singleton_insert_inj_eq
% 5.25/5.55 thf(fact_7091_singleton__insert__inj__eq,axiom,
% 5.25/5.55 ! [B: int,A: int,A2: set_int] :
% 5.25/5.55 ( ( ( insert_int @ B @ bot_bot_set_int )
% 5.25/5.55 = ( insert_int @ A @ A2 ) )
% 5.25/5.55 = ( ( A = B )
% 5.25/5.55 & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % singleton_insert_inj_eq
% 5.25/5.55 thf(fact_7092_singleton__insert__inj__eq_H,axiom,
% 5.25/5.55 ! [A: nat,A2: set_nat,B: nat] :
% 5.25/5.55 ( ( ( insert_nat @ A @ A2 )
% 5.25/5.55 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 5.25/5.55 = ( ( A = B )
% 5.25/5.55 & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % singleton_insert_inj_eq'
% 5.25/5.55 thf(fact_7093_singleton__insert__inj__eq_H,axiom,
% 5.25/5.55 ! [A: real,A2: set_real,B: real] :
% 5.25/5.55 ( ( ( insert_real @ A @ A2 )
% 5.25/5.55 = ( insert_real @ B @ bot_bot_set_real ) )
% 5.25/5.55 = ( ( A = B )
% 5.25/5.55 & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % singleton_insert_inj_eq'
% 5.25/5.55 thf(fact_7094_singleton__insert__inj__eq_H,axiom,
% 5.25/5.55 ! [A: int,A2: set_int,B: int] :
% 5.25/5.55 ( ( ( insert_int @ A @ A2 )
% 5.25/5.55 = ( insert_int @ B @ bot_bot_set_int ) )
% 5.25/5.55 = ( ( A = B )
% 5.25/5.55 & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % singleton_insert_inj_eq'
% 5.25/5.55 thf(fact_7095_prod_Oempty,axiom,
% 5.25/5.55 ! [G: nat > complex] :
% 5.25/5.55 ( ( groups6464643781859351333omplex @ G @ bot_bot_set_nat )
% 5.25/5.55 = one_one_complex ) ).
% 5.25/5.55
% 5.25/5.55 % prod.empty
% 5.25/5.55 thf(fact_7096_prod_Oempty,axiom,
% 5.25/5.55 ! [G: nat > real] :
% 5.25/5.55 ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 5.25/5.55 = one_one_real ) ).
% 5.25/5.55
% 5.25/5.55 % prod.empty
% 5.25/5.55 thf(fact_7097_prod_Oempty,axiom,
% 5.25/5.55 ! [G: nat > rat] :
% 5.25/5.55 ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 5.25/5.55 = one_one_rat ) ).
% 5.25/5.55
% 5.25/5.55 % prod.empty
% 5.25/5.55 thf(fact_7098_prod_Oempty,axiom,
% 5.25/5.55 ! [G: int > complex] :
% 5.25/5.55 ( ( groups7440179247065528705omplex @ G @ bot_bot_set_int )
% 5.25/5.55 = one_one_complex ) ).
% 5.25/5.55
% 5.25/5.55 % prod.empty
% 5.25/5.55 thf(fact_7099_prod_Oempty,axiom,
% 5.25/5.55 ! [G: int > real] :
% 5.25/5.55 ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 5.25/5.55 = one_one_real ) ).
% 5.25/5.55
% 5.25/5.55 % prod.empty
% 5.25/5.55 thf(fact_7100_prod_Oempty,axiom,
% 5.25/5.55 ! [G: int > rat] :
% 5.25/5.55 ( ( groups1072433553688619179nt_rat @ G @ bot_bot_set_int )
% 5.25/5.55 = one_one_rat ) ).
% 5.25/5.55
% 5.25/5.55 % prod.empty
% 5.25/5.55 thf(fact_7101_prod_Oempty,axiom,
% 5.25/5.55 ! [G: int > nat] :
% 5.25/5.55 ( ( groups1707563613775114915nt_nat @ G @ bot_bot_set_int )
% 5.25/5.55 = one_one_nat ) ).
% 5.25/5.55
% 5.25/5.55 % prod.empty
% 5.25/5.55 thf(fact_7102_prod_Oempty,axiom,
% 5.25/5.55 ! [G: real > complex] :
% 5.25/5.55 ( ( groups713298508707869441omplex @ G @ bot_bot_set_real )
% 5.25/5.55 = one_one_complex ) ).
% 5.25/5.55
% 5.25/5.55 % prod.empty
% 5.25/5.55 thf(fact_7103_prod_Oempty,axiom,
% 5.25/5.55 ! [G: real > real] :
% 5.25/5.55 ( ( groups1681761925125756287l_real @ G @ bot_bot_set_real )
% 5.25/5.55 = one_one_real ) ).
% 5.25/5.55
% 5.25/5.55 % prod.empty
% 5.25/5.55 thf(fact_7104_prod_Oempty,axiom,
% 5.25/5.55 ! [G: real > rat] :
% 5.25/5.55 ( ( groups4061424788464935467al_rat @ G @ bot_bot_set_real )
% 5.25/5.55 = one_one_rat ) ).
% 5.25/5.55
% 5.25/5.55 % prod.empty
% 5.25/5.55 thf(fact_7105_atLeastAtMost__singleton__iff,axiom,
% 5.25/5.55 ! [A: nat,B: nat,C: nat] :
% 5.25/5.55 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.25/5.55 = ( insert_nat @ C @ bot_bot_set_nat ) )
% 5.25/5.55 = ( ( A = B )
% 5.25/5.55 & ( B = C ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % atLeastAtMost_singleton_iff
% 5.25/5.55 thf(fact_7106_atLeastAtMost__singleton__iff,axiom,
% 5.25/5.55 ! [A: int,B: int,C: int] :
% 5.25/5.55 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.25/5.55 = ( insert_int @ C @ bot_bot_set_int ) )
% 5.25/5.55 = ( ( A = B )
% 5.25/5.55 & ( B = C ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % atLeastAtMost_singleton_iff
% 5.25/5.55 thf(fact_7107_atLeastAtMost__singleton__iff,axiom,
% 5.25/5.55 ! [A: real,B: real,C: real] :
% 5.25/5.55 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.25/5.55 = ( insert_real @ C @ bot_bot_set_real ) )
% 5.25/5.55 = ( ( A = B )
% 5.25/5.55 & ( B = C ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % atLeastAtMost_singleton_iff
% 5.25/5.55 thf(fact_7108_atLeastAtMost__singleton,axiom,
% 5.25/5.55 ! [A: nat] :
% 5.25/5.55 ( ( set_or1269000886237332187st_nat @ A @ A )
% 5.25/5.55 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % atLeastAtMost_singleton
% 5.25/5.55 thf(fact_7109_atLeastAtMost__singleton,axiom,
% 5.25/5.55 ! [A: int] :
% 5.25/5.55 ( ( set_or1266510415728281911st_int @ A @ A )
% 5.25/5.55 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 5.25/5.55
% 5.25/5.55 % atLeastAtMost_singleton
% 5.25/5.55 thf(fact_7110_atLeastAtMost__singleton,axiom,
% 5.25/5.55 ! [A: real] :
% 5.25/5.55 ( ( set_or1222579329274155063t_real @ A @ A )
% 5.25/5.55 = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 5.25/5.55
% 5.25/5.55 % atLeastAtMost_singleton
% 5.25/5.55 thf(fact_7111_cos__coeff__0,axiom,
% 5.25/5.55 ( ( cos_coeff @ zero_zero_nat )
% 5.25/5.55 = one_one_real ) ).
% 5.25/5.55
% 5.25/5.55 % cos_coeff_0
% 5.25/5.55 thf(fact_7112_single__Diff__lessThan,axiom,
% 5.25/5.55 ! [K: nat] :
% 5.25/5.55 ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 5.25/5.55 = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % single_Diff_lessThan
% 5.25/5.55 thf(fact_7113_single__Diff__lessThan,axiom,
% 5.25/5.55 ! [K: int] :
% 5.25/5.55 ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 5.25/5.55 = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 5.25/5.55
% 5.25/5.55 % single_Diff_lessThan
% 5.25/5.55 thf(fact_7114_single__Diff__lessThan,axiom,
% 5.25/5.55 ! [K: real] :
% 5.25/5.55 ( ( minus_minus_set_real @ ( insert_real @ K @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K ) )
% 5.25/5.55 = ( insert_real @ K @ bot_bot_set_real ) ) ).
% 5.25/5.55
% 5.25/5.55 % single_Diff_lessThan
% 5.25/5.55 thf(fact_7115_subset__Compl__singleton,axiom,
% 5.25/5.55 ! [A2: set_complex,B: complex] :
% 5.25/5.55 ( ( ord_le211207098394363844omplex @ A2 @ ( uminus8566677241136511917omplex @ ( insert_complex @ B @ bot_bot_set_complex ) ) )
% 5.25/5.55 = ( ~ ( member_complex @ B @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_Compl_singleton
% 5.25/5.55 thf(fact_7116_subset__Compl__singleton,axiom,
% 5.25/5.55 ! [A2: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 5.25/5.55 ( ( ord_le3146513528884898305at_nat @ A2 @ ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) )
% 5.25/5.55 = ( ~ ( member8440522571783428010at_nat @ B @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_Compl_singleton
% 5.25/5.55 thf(fact_7117_subset__Compl__singleton,axiom,
% 5.25/5.55 ! [A2: set_nat,B: nat] :
% 5.25/5.55 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 5.25/5.55 = ( ~ ( member_nat @ B @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_Compl_singleton
% 5.25/5.55 thf(fact_7118_subset__Compl__singleton,axiom,
% 5.25/5.55 ! [A2: set_real,B: real] :
% 5.25/5.55 ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ ( insert_real @ B @ bot_bot_set_real ) ) )
% 5.25/5.55 = ( ~ ( member_real @ B @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_Compl_singleton
% 5.25/5.55 thf(fact_7119_subset__Compl__singleton,axiom,
% 5.25/5.55 ! [A2: set_int,B: int] :
% 5.25/5.55 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 5.25/5.55 = ( ~ ( member_int @ B @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_Compl_singleton
% 5.25/5.55 thf(fact_7120_prod_OlessThan__Suc,axiom,
% 5.25/5.55 ! [G: nat > real,N: nat] :
% 5.25/5.55 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.lessThan_Suc
% 5.25/5.55 thf(fact_7121_prod_OlessThan__Suc,axiom,
% 5.25/5.55 ! [G: nat > rat,N: nat] :
% 5.25/5.55 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.lessThan_Suc
% 5.25/5.55 thf(fact_7122_prod_OlessThan__Suc,axiom,
% 5.25/5.55 ! [G: nat > int,N: nat] :
% 5.25/5.55 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.lessThan_Suc
% 5.25/5.55 thf(fact_7123_prod_OlessThan__Suc,axiom,
% 5.25/5.55 ! [G: nat > nat,N: nat] :
% 5.25/5.55 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.lessThan_Suc
% 5.25/5.55 thf(fact_7124_set__replicate,axiom,
% 5.25/5.55 ! [N: nat,X3: vEBT_VEBT] :
% 5.25/5.55 ( ( N != zero_zero_nat )
% 5.25/5.55 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X3 ) )
% 5.25/5.55 = ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_replicate
% 5.25/5.55 thf(fact_7125_set__replicate,axiom,
% 5.25/5.55 ! [N: nat,X3: nat] :
% 5.25/5.55 ( ( N != zero_zero_nat )
% 5.25/5.55 => ( ( set_nat2 @ ( replicate_nat @ N @ X3 ) )
% 5.25/5.55 = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_replicate
% 5.25/5.55 thf(fact_7126_set__replicate,axiom,
% 5.25/5.55 ! [N: nat,X3: int] :
% 5.25/5.55 ( ( N != zero_zero_nat )
% 5.25/5.55 => ( ( set_int2 @ ( replicate_int @ N @ X3 ) )
% 5.25/5.55 = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_replicate
% 5.25/5.55 thf(fact_7127_set__replicate,axiom,
% 5.25/5.55 ! [N: nat,X3: real] :
% 5.25/5.55 ( ( N != zero_zero_nat )
% 5.25/5.55 => ( ( set_real2 @ ( replicate_real @ N @ X3 ) )
% 5.25/5.55 = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_replicate
% 5.25/5.55 thf(fact_7128_prod_Ocl__ivl__Suc,axiom,
% 5.25/5.55 ! [N: nat,M: nat,G: nat > complex] :
% 5.25/5.55 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.55 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.55 = one_one_complex ) )
% 5.25/5.55 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.55 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.cl_ivl_Suc
% 5.25/5.55 thf(fact_7129_prod_Ocl__ivl__Suc,axiom,
% 5.25/5.55 ! [N: nat,M: nat,G: nat > real] :
% 5.25/5.55 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.55 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.55 = one_one_real ) )
% 5.25/5.55 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.55 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.cl_ivl_Suc
% 5.25/5.55 thf(fact_7130_prod_Ocl__ivl__Suc,axiom,
% 5.25/5.55 ! [N: nat,M: nat,G: nat > rat] :
% 5.25/5.55 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.55 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.55 = one_one_rat ) )
% 5.25/5.55 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.55 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.cl_ivl_Suc
% 5.25/5.55 thf(fact_7131_prod_Ocl__ivl__Suc,axiom,
% 5.25/5.55 ! [N: nat,M: nat,G: nat > int] :
% 5.25/5.55 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.55 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.55 = one_one_int ) )
% 5.25/5.55 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.55 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.cl_ivl_Suc
% 5.25/5.55 thf(fact_7132_prod_Ocl__ivl__Suc,axiom,
% 5.25/5.55 ! [N: nat,M: nat,G: nat > nat] :
% 5.25/5.55 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.55 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.55 = one_one_nat ) )
% 5.25/5.55 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.25/5.55 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.cl_ivl_Suc
% 5.25/5.55 thf(fact_7133_prod_Oneutral,axiom,
% 5.25/5.55 ! [A2: set_nat,G: nat > int] :
% 5.25/5.55 ( ! [X5: nat] :
% 5.25/5.55 ( ( member_nat @ X5 @ A2 )
% 5.25/5.55 => ( ( G @ X5 )
% 5.25/5.55 = one_one_int ) )
% 5.25/5.55 => ( ( groups705719431365010083at_int @ G @ A2 )
% 5.25/5.55 = one_one_int ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.neutral
% 5.25/5.55 thf(fact_7134_prod_Oneutral,axiom,
% 5.25/5.55 ! [A2: set_int,G: int > int] :
% 5.25/5.55 ( ! [X5: int] :
% 5.25/5.55 ( ( member_int @ X5 @ A2 )
% 5.25/5.55 => ( ( G @ X5 )
% 5.25/5.55 = one_one_int ) )
% 5.25/5.55 => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 5.25/5.55 = one_one_int ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.neutral
% 5.25/5.55 thf(fact_7135_prod_Oneutral,axiom,
% 5.25/5.55 ! [A2: set_nat,G: nat > nat] :
% 5.25/5.55 ( ! [X5: nat] :
% 5.25/5.55 ( ( member_nat @ X5 @ A2 )
% 5.25/5.55 => ( ( G @ X5 )
% 5.25/5.55 = one_one_nat ) )
% 5.25/5.55 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 5.25/5.55 = one_one_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.neutral
% 5.25/5.55 thf(fact_7136_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.25/5.55 ! [G: nat > complex,A2: set_nat] :
% 5.25/5.55 ( ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.25/5.55 != one_one_complex )
% 5.25/5.55 => ~ ! [A5: nat] :
% 5.25/5.55 ( ( member_nat @ A5 @ A2 )
% 5.25/5.55 => ( ( G @ A5 )
% 5.25/5.55 = one_one_complex ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.not_neutral_contains_not_neutral
% 5.25/5.55 thf(fact_7137_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.25/5.55 ! [G: real > complex,A2: set_real] :
% 5.25/5.55 ( ( ( groups713298508707869441omplex @ G @ A2 )
% 5.25/5.55 != one_one_complex )
% 5.25/5.55 => ~ ! [A5: real] :
% 5.25/5.55 ( ( member_real @ A5 @ A2 )
% 5.25/5.55 => ( ( G @ A5 )
% 5.25/5.55 = one_one_complex ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.not_neutral_contains_not_neutral
% 5.25/5.55 thf(fact_7138_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.25/5.55 ! [G: int > complex,A2: set_int] :
% 5.25/5.55 ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.25/5.55 != one_one_complex )
% 5.25/5.55 => ~ ! [A5: int] :
% 5.25/5.55 ( ( member_int @ A5 @ A2 )
% 5.25/5.55 => ( ( G @ A5 )
% 5.25/5.55 = one_one_complex ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.not_neutral_contains_not_neutral
% 5.25/5.55 thf(fact_7139_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.25/5.55 ! [G: complex > complex,A2: set_complex] :
% 5.25/5.55 ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.25/5.55 != one_one_complex )
% 5.25/5.55 => ~ ! [A5: complex] :
% 5.25/5.55 ( ( member_complex @ A5 @ A2 )
% 5.25/5.55 => ( ( G @ A5 )
% 5.25/5.55 = one_one_complex ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.not_neutral_contains_not_neutral
% 5.25/5.55 thf(fact_7140_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.25/5.55 ! [G: nat > real,A2: set_nat] :
% 5.25/5.55 ( ( ( groups129246275422532515t_real @ G @ A2 )
% 5.25/5.55 != one_one_real )
% 5.25/5.55 => ~ ! [A5: nat] :
% 5.25/5.55 ( ( member_nat @ A5 @ A2 )
% 5.25/5.55 => ( ( G @ A5 )
% 5.25/5.55 = one_one_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.not_neutral_contains_not_neutral
% 5.25/5.55 thf(fact_7141_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.25/5.55 ! [G: real > real,A2: set_real] :
% 5.25/5.55 ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.25/5.55 != one_one_real )
% 5.25/5.55 => ~ ! [A5: real] :
% 5.25/5.55 ( ( member_real @ A5 @ A2 )
% 5.25/5.55 => ( ( G @ A5 )
% 5.25/5.55 = one_one_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.not_neutral_contains_not_neutral
% 5.25/5.55 thf(fact_7142_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.25/5.55 ! [G: int > real,A2: set_int] :
% 5.25/5.55 ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.25/5.55 != one_one_real )
% 5.25/5.55 => ~ ! [A5: int] :
% 5.25/5.55 ( ( member_int @ A5 @ A2 )
% 5.25/5.55 => ( ( G @ A5 )
% 5.25/5.55 = one_one_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.not_neutral_contains_not_neutral
% 5.25/5.55 thf(fact_7143_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.25/5.55 ! [G: complex > real,A2: set_complex] :
% 5.25/5.55 ( ( ( groups766887009212190081x_real @ G @ A2 )
% 5.25/5.55 != one_one_real )
% 5.25/5.55 => ~ ! [A5: complex] :
% 5.25/5.55 ( ( member_complex @ A5 @ A2 )
% 5.25/5.55 => ( ( G @ A5 )
% 5.25/5.55 = one_one_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.not_neutral_contains_not_neutral
% 5.25/5.55 thf(fact_7144_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.25/5.55 ! [G: nat > rat,A2: set_nat] :
% 5.25/5.55 ( ( ( groups73079841787564623at_rat @ G @ A2 )
% 5.25/5.55 != one_one_rat )
% 5.25/5.55 => ~ ! [A5: nat] :
% 5.25/5.55 ( ( member_nat @ A5 @ A2 )
% 5.25/5.55 => ( ( G @ A5 )
% 5.25/5.55 = one_one_rat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.not_neutral_contains_not_neutral
% 5.25/5.55 thf(fact_7145_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.25/5.55 ! [G: real > rat,A2: set_real] :
% 5.25/5.55 ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 5.25/5.55 != one_one_rat )
% 5.25/5.55 => ~ ! [A5: real] :
% 5.25/5.55 ( ( member_real @ A5 @ A2 )
% 5.25/5.55 => ( ( G @ A5 )
% 5.25/5.55 = one_one_rat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.not_neutral_contains_not_neutral
% 5.25/5.55 thf(fact_7146_insert__mono,axiom,
% 5.25/5.55 ! [C5: set_nat,D4: set_nat,A: nat] :
% 5.25/5.55 ( ( ord_less_eq_set_nat @ C5 @ D4 )
% 5.25/5.55 => ( ord_less_eq_set_nat @ ( insert_nat @ A @ C5 ) @ ( insert_nat @ A @ D4 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % insert_mono
% 5.25/5.55 thf(fact_7147_insert__mono,axiom,
% 5.25/5.55 ! [C5: set_real,D4: set_real,A: real] :
% 5.25/5.55 ( ( ord_less_eq_set_real @ C5 @ D4 )
% 5.25/5.55 => ( ord_less_eq_set_real @ ( insert_real @ A @ C5 ) @ ( insert_real @ A @ D4 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % insert_mono
% 5.25/5.55 thf(fact_7148_insert__mono,axiom,
% 5.25/5.55 ! [C5: set_int,D4: set_int,A: int] :
% 5.25/5.55 ( ( ord_less_eq_set_int @ C5 @ D4 )
% 5.25/5.55 => ( ord_less_eq_set_int @ ( insert_int @ A @ C5 ) @ ( insert_int @ A @ D4 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % insert_mono
% 5.25/5.55 thf(fact_7149_subset__insert,axiom,
% 5.25/5.55 ! [X3: nat,A2: set_nat,B3: set_nat] :
% 5.25/5.55 ( ~ ( member_nat @ X3 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X3 @ B3 ) )
% 5.25/5.55 = ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insert
% 5.25/5.55 thf(fact_7150_subset__insert,axiom,
% 5.25/5.55 ! [X3: real,A2: set_real,B3: set_real] :
% 5.25/5.55 ( ~ ( member_real @ X3 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X3 @ B3 ) )
% 5.25/5.55 = ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insert
% 5.25/5.55 thf(fact_7151_subset__insert,axiom,
% 5.25/5.55 ! [X3: complex,A2: set_complex,B3: set_complex] :
% 5.25/5.55 ( ~ ( member_complex @ X3 @ A2 )
% 5.25/5.55 => ( ( ord_le211207098394363844omplex @ A2 @ ( insert_complex @ X3 @ B3 ) )
% 5.25/5.55 = ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insert
% 5.25/5.55 thf(fact_7152_subset__insert,axiom,
% 5.25/5.55 ! [X3: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.25/5.55 ( ~ ( member8440522571783428010at_nat @ X3 @ A2 )
% 5.25/5.55 => ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X3 @ B3 ) )
% 5.25/5.55 = ( ord_le3146513528884898305at_nat @ A2 @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insert
% 5.25/5.55 thf(fact_7153_subset__insert,axiom,
% 5.25/5.55 ! [X3: int,A2: set_int,B3: set_int] :
% 5.25/5.55 ( ~ ( member_int @ X3 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X3 @ B3 ) )
% 5.25/5.55 = ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insert
% 5.25/5.55 thf(fact_7154_subset__insertI,axiom,
% 5.25/5.55 ! [B3: set_nat,A: nat] : ( ord_less_eq_set_nat @ B3 @ ( insert_nat @ A @ B3 ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insertI
% 5.25/5.55 thf(fact_7155_subset__insertI,axiom,
% 5.25/5.55 ! [B3: set_real,A: real] : ( ord_less_eq_set_real @ B3 @ ( insert_real @ A @ B3 ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insertI
% 5.25/5.55 thf(fact_7156_subset__insertI,axiom,
% 5.25/5.55 ! [B3: set_int,A: int] : ( ord_less_eq_set_int @ B3 @ ( insert_int @ A @ B3 ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insertI
% 5.25/5.55 thf(fact_7157_subset__insertI2,axiom,
% 5.25/5.55 ! [A2: set_nat,B3: set_nat,B: nat] :
% 5.25/5.55 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.25/5.55 => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insertI2
% 5.25/5.55 thf(fact_7158_subset__insertI2,axiom,
% 5.25/5.55 ! [A2: set_real,B3: set_real,B: real] :
% 5.25/5.55 ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.25/5.55 => ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insertI2
% 5.25/5.55 thf(fact_7159_subset__insertI2,axiom,
% 5.25/5.55 ! [A2: set_int,B3: set_int,B: int] :
% 5.25/5.55 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.55 => ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insertI2
% 5.25/5.55 thf(fact_7160_prod_Odistrib,axiom,
% 5.25/5.55 ! [G: nat > int,H2: nat > int,A2: set_nat] :
% 5.25/5.55 ( ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [X2: nat] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.25/5.55 @ A2 )
% 5.25/5.55 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A2 ) @ ( groups705719431365010083at_int @ H2 @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.distrib
% 5.25/5.55 thf(fact_7161_prod_Odistrib,axiom,
% 5.25/5.55 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.25/5.55 ( ( groups1705073143266064639nt_int
% 5.25/5.55 @ ^ [X2: int] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.25/5.55 @ A2 )
% 5.25/5.55 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A2 ) @ ( groups1705073143266064639nt_int @ H2 @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.distrib
% 5.25/5.55 thf(fact_7162_prod_Odistrib,axiom,
% 5.25/5.55 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.25/5.55 ( ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [X2: nat] : ( times_times_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.25/5.55 @ A2 )
% 5.25/5.55 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A2 ) @ ( groups708209901874060359at_nat @ H2 @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.distrib
% 5.25/5.55 thf(fact_7163_prod__power__distrib,axiom,
% 5.25/5.55 ! [F: nat > int,A2: set_nat,N: nat] :
% 5.25/5.55 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A2 ) @ N )
% 5.25/5.55 = ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [X2: nat] : ( power_power_int @ ( F @ X2 ) @ N )
% 5.25/5.55 @ A2 ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_power_distrib
% 5.25/5.55 thf(fact_7164_prod__power__distrib,axiom,
% 5.25/5.55 ! [F: int > int,A2: set_int,N: nat] :
% 5.25/5.55 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ N )
% 5.25/5.55 = ( groups1705073143266064639nt_int
% 5.25/5.55 @ ^ [X2: int] : ( power_power_int @ ( F @ X2 ) @ N )
% 5.25/5.55 @ A2 ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_power_distrib
% 5.25/5.55 thf(fact_7165_prod__power__distrib,axiom,
% 5.25/5.55 ! [F: nat > nat,A2: set_nat,N: nat] :
% 5.25/5.55 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N )
% 5.25/5.55 = ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [X2: nat] : ( power_power_nat @ ( F @ X2 ) @ N )
% 5.25/5.55 @ A2 ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_power_distrib
% 5.25/5.55 thf(fact_7166_mod__prod__eq,axiom,
% 5.25/5.55 ! [F: nat > int,A: int,A2: set_nat] :
% 5.25/5.55 ( ( modulo_modulo_int
% 5.25/5.55 @ ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [I3: nat] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 5.25/5.55 @ A2 )
% 5.25/5.55 @ A )
% 5.25/5.55 = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A2 ) @ A ) ) ).
% 5.25/5.55
% 5.25/5.55 % mod_prod_eq
% 5.25/5.55 thf(fact_7167_mod__prod__eq,axiom,
% 5.25/5.55 ! [F: int > int,A: int,A2: set_int] :
% 5.25/5.55 ( ( modulo_modulo_int
% 5.25/5.55 @ ( groups1705073143266064639nt_int
% 5.25/5.55 @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 5.25/5.55 @ A2 )
% 5.25/5.55 @ A )
% 5.25/5.55 = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ A ) ) ).
% 5.25/5.55
% 5.25/5.55 % mod_prod_eq
% 5.25/5.55 thf(fact_7168_mod__prod__eq,axiom,
% 5.25/5.55 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.25/5.55 ( ( modulo_modulo_nat
% 5.25/5.55 @ ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 5.25/5.55 @ A2 )
% 5.25/5.55 @ A )
% 5.25/5.55 = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ A ) ) ).
% 5.25/5.55
% 5.25/5.55 % mod_prod_eq
% 5.25/5.55 thf(fact_7169_prod__nonneg,axiom,
% 5.25/5.55 ! [A2: set_nat,F: nat > int] :
% 5.25/5.55 ( ! [X5: nat] :
% 5.25/5.55 ( ( member_nat @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_nonneg
% 5.25/5.55 thf(fact_7170_prod__nonneg,axiom,
% 5.25/5.55 ! [A2: set_int,F: int > int] :
% 5.25/5.55 ( ! [X5: int] :
% 5.25/5.55 ( ( member_int @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_nonneg
% 5.25/5.55 thf(fact_7171_prod__nonneg,axiom,
% 5.25/5.55 ! [A2: set_nat,F: nat > nat] :
% 5.25/5.55 ( ! [X5: nat] :
% 5.25/5.55 ( ( member_nat @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_nonneg
% 5.25/5.55 thf(fact_7172_prod__mono,axiom,
% 5.25/5.55 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.25/5.55 ( ! [I4: nat] :
% 5.25/5.55 ( ( member_nat @ I4 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.25/5.55 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_mono
% 5.25/5.55 thf(fact_7173_prod__mono,axiom,
% 5.25/5.55 ! [A2: set_real,F: real > real,G: real > real] :
% 5.25/5.55 ( ! [I4: real] :
% 5.25/5.55 ( ( member_real @ I4 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.25/5.55 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_mono
% 5.25/5.55 thf(fact_7174_prod__mono,axiom,
% 5.25/5.55 ! [A2: set_int,F: int > real,G: int > real] :
% 5.25/5.55 ( ! [I4: int] :
% 5.25/5.55 ( ( member_int @ I4 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.25/5.55 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_mono
% 5.25/5.55 thf(fact_7175_prod__mono,axiom,
% 5.25/5.55 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.25/5.55 ( ! [I4: complex] :
% 5.25/5.55 ( ( member_complex @ I4 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.25/5.55 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_mono
% 5.25/5.55 thf(fact_7176_prod__mono,axiom,
% 5.25/5.55 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.25/5.55 ( ! [I4: nat] :
% 5.25/5.55 ( ( member_nat @ I4 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 5.25/5.55 & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.25/5.55 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_mono
% 5.25/5.55 thf(fact_7177_prod__mono,axiom,
% 5.25/5.55 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.25/5.55 ( ! [I4: real] :
% 5.25/5.55 ( ( member_real @ I4 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 5.25/5.55 & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.25/5.55 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_mono
% 5.25/5.55 thf(fact_7178_prod__mono,axiom,
% 5.25/5.55 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.25/5.55 ( ! [I4: int] :
% 5.25/5.55 ( ( member_int @ I4 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 5.25/5.55 & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.25/5.55 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_mono
% 5.25/5.55 thf(fact_7179_prod__mono,axiom,
% 5.25/5.55 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.25/5.55 ( ! [I4: complex] :
% 5.25/5.55 ( ( member_complex @ I4 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 5.25/5.55 & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.25/5.55 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_mono
% 5.25/5.55 thf(fact_7180_prod__mono,axiom,
% 5.25/5.55 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.25/5.55 ( ! [I4: real] :
% 5.25/5.55 ( ( member_real @ I4 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 5.25/5.55 & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.25/5.55 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_mono
% 5.25/5.55 thf(fact_7181_prod__mono,axiom,
% 5.25/5.55 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.25/5.55 ( ! [I4: int] :
% 5.25/5.55 ( ( member_int @ I4 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 5.25/5.55 & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.25/5.55 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_mono
% 5.25/5.55 thf(fact_7182_prod__pos,axiom,
% 5.25/5.55 ! [A2: set_nat,F: nat > int] :
% 5.25/5.55 ( ! [X5: nat] :
% 5.25/5.55 ( ( member_nat @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_pos
% 5.25/5.55 thf(fact_7183_prod__pos,axiom,
% 5.25/5.55 ! [A2: set_int,F: int > int] :
% 5.25/5.55 ( ! [X5: int] :
% 5.25/5.55 ( ( member_int @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_pos
% 5.25/5.55 thf(fact_7184_prod__pos,axiom,
% 5.25/5.55 ! [A2: set_nat,F: nat > nat] :
% 5.25/5.55 ( ! [X5: nat] :
% 5.25/5.55 ( ( member_nat @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_pos
% 5.25/5.55 thf(fact_7185_prod__ge__1,axiom,
% 5.25/5.55 ! [A2: set_nat,F: nat > real] :
% 5.25/5.55 ( ! [X5: nat] :
% 5.25/5.55 ( ( member_nat @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_ge_1
% 5.25/5.55 thf(fact_7186_prod__ge__1,axiom,
% 5.25/5.55 ! [A2: set_real,F: real > real] :
% 5.25/5.55 ( ! [X5: real] :
% 5.25/5.55 ( ( member_real @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_ge_1
% 5.25/5.55 thf(fact_7187_prod__ge__1,axiom,
% 5.25/5.55 ! [A2: set_int,F: int > real] :
% 5.25/5.55 ( ! [X5: int] :
% 5.25/5.55 ( ( member_int @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_ge_1
% 5.25/5.55 thf(fact_7188_prod__ge__1,axiom,
% 5.25/5.55 ! [A2: set_complex,F: complex > real] :
% 5.25/5.55 ( ! [X5: complex] :
% 5.25/5.55 ( ( member_complex @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_ge_1
% 5.25/5.55 thf(fact_7189_prod__ge__1,axiom,
% 5.25/5.55 ! [A2: set_nat,F: nat > rat] :
% 5.25/5.55 ( ! [X5: nat] :
% 5.25/5.55 ( ( member_nat @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_ge_1
% 5.25/5.55 thf(fact_7190_prod__ge__1,axiom,
% 5.25/5.55 ! [A2: set_real,F: real > rat] :
% 5.25/5.55 ( ! [X5: real] :
% 5.25/5.55 ( ( member_real @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_ge_1
% 5.25/5.55 thf(fact_7191_prod__ge__1,axiom,
% 5.25/5.55 ! [A2: set_int,F: int > rat] :
% 5.25/5.55 ( ! [X5: int] :
% 5.25/5.55 ( ( member_int @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_ge_1
% 5.25/5.55 thf(fact_7192_prod__ge__1,axiom,
% 5.25/5.55 ! [A2: set_complex,F: complex > rat] :
% 5.25/5.55 ( ! [X5: complex] :
% 5.25/5.55 ( ( member_complex @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_ge_1
% 5.25/5.55 thf(fact_7193_prod__ge__1,axiom,
% 5.25/5.55 ! [A2: set_real,F: real > nat] :
% 5.25/5.55 ( ! [X5: real] :
% 5.25/5.55 ( ( member_real @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_ge_1
% 5.25/5.55 thf(fact_7194_prod__ge__1,axiom,
% 5.25/5.55 ! [A2: set_int,F: int > nat] :
% 5.25/5.55 ( ! [X5: int] :
% 5.25/5.55 ( ( member_int @ X5 @ A2 )
% 5.25/5.55 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X5 ) ) )
% 5.25/5.55 => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_ge_1
% 5.25/5.55 thf(fact_7195_prod__atLeastAtMost__code,axiom,
% 5.25/5.55 ! [F: nat > complex,A: nat,B: nat] :
% 5.25/5.55 ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.25/5.55 = ( set_fo1517530859248394432omplex
% 5.25/5.55 @ ^ [A3: nat] : ( times_times_complex @ ( F @ A3 ) )
% 5.25/5.55 @ A
% 5.25/5.55 @ B
% 5.25/5.55 @ one_one_complex ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_atLeastAtMost_code
% 5.25/5.55 thf(fact_7196_prod__atLeastAtMost__code,axiom,
% 5.25/5.55 ! [F: nat > real,A: nat,B: nat] :
% 5.25/5.55 ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.25/5.55 = ( set_fo3111899725591712190t_real
% 5.25/5.55 @ ^ [A3: nat] : ( times_times_real @ ( F @ A3 ) )
% 5.25/5.55 @ A
% 5.25/5.55 @ B
% 5.25/5.55 @ one_one_real ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_atLeastAtMost_code
% 5.25/5.55 thf(fact_7197_prod__atLeastAtMost__code,axiom,
% 5.25/5.55 ! [F: nat > rat,A: nat,B: nat] :
% 5.25/5.55 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.25/5.55 = ( set_fo1949268297981939178at_rat
% 5.25/5.55 @ ^ [A3: nat] : ( times_times_rat @ ( F @ A3 ) )
% 5.25/5.55 @ A
% 5.25/5.55 @ B
% 5.25/5.55 @ one_one_rat ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_atLeastAtMost_code
% 5.25/5.55 thf(fact_7198_prod__atLeastAtMost__code,axiom,
% 5.25/5.55 ! [F: nat > int,A: nat,B: nat] :
% 5.25/5.55 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.25/5.55 = ( set_fo2581907887559384638at_int
% 5.25/5.55 @ ^ [A3: nat] : ( times_times_int @ ( F @ A3 ) )
% 5.25/5.55 @ A
% 5.25/5.55 @ B
% 5.25/5.55 @ one_one_int ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_atLeastAtMost_code
% 5.25/5.55 thf(fact_7199_prod__atLeastAtMost__code,axiom,
% 5.25/5.55 ! [F: nat > nat,A: nat,B: nat] :
% 5.25/5.55 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.25/5.55 = ( set_fo2584398358068434914at_nat
% 5.25/5.55 @ ^ [A3: nat] : ( times_times_nat @ ( F @ A3 ) )
% 5.25/5.55 @ A
% 5.25/5.55 @ B
% 5.25/5.55 @ one_one_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_atLeastAtMost_code
% 5.25/5.55 thf(fact_7200_subset__singletonD,axiom,
% 5.25/5.55 ! [A2: set_nat,X3: nat] :
% 5.25/5.55 ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 5.25/5.55 => ( ( A2 = bot_bot_set_nat )
% 5.25/5.55 | ( A2
% 5.25/5.55 = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_singletonD
% 5.25/5.55 thf(fact_7201_subset__singletonD,axiom,
% 5.25/5.55 ! [A2: set_real,X3: real] :
% 5.25/5.55 ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) )
% 5.25/5.55 => ( ( A2 = bot_bot_set_real )
% 5.25/5.55 | ( A2
% 5.25/5.55 = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_singletonD
% 5.25/5.55 thf(fact_7202_subset__singletonD,axiom,
% 5.25/5.55 ! [A2: set_int,X3: int] :
% 5.25/5.55 ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) )
% 5.25/5.55 => ( ( A2 = bot_bot_set_int )
% 5.25/5.55 | ( A2
% 5.25/5.55 = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_singletonD
% 5.25/5.55 thf(fact_7203_subset__singleton__iff,axiom,
% 5.25/5.55 ! [X8: set_nat,A: nat] :
% 5.25/5.55 ( ( ord_less_eq_set_nat @ X8 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 5.25/5.55 = ( ( X8 = bot_bot_set_nat )
% 5.25/5.55 | ( X8
% 5.25/5.55 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_singleton_iff
% 5.25/5.55 thf(fact_7204_subset__singleton__iff,axiom,
% 5.25/5.55 ! [X8: set_real,A: real] :
% 5.25/5.55 ( ( ord_less_eq_set_real @ X8 @ ( insert_real @ A @ bot_bot_set_real ) )
% 5.25/5.55 = ( ( X8 = bot_bot_set_real )
% 5.25/5.55 | ( X8
% 5.25/5.55 = ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_singleton_iff
% 5.25/5.55 thf(fact_7205_subset__singleton__iff,axiom,
% 5.25/5.55 ! [X8: set_int,A: int] :
% 5.25/5.55 ( ( ord_less_eq_set_int @ X8 @ ( insert_int @ A @ bot_bot_set_int ) )
% 5.25/5.55 = ( ( X8 = bot_bot_set_int )
% 5.25/5.55 | ( X8
% 5.25/5.55 = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_singleton_iff
% 5.25/5.55 thf(fact_7206_atLeastAtMost__singleton_H,axiom,
% 5.25/5.55 ! [A: nat,B: nat] :
% 5.25/5.55 ( ( A = B )
% 5.25/5.55 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.25/5.55 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % atLeastAtMost_singleton'
% 5.25/5.55 thf(fact_7207_atLeastAtMost__singleton_H,axiom,
% 5.25/5.55 ! [A: int,B: int] :
% 5.25/5.55 ( ( A = B )
% 5.25/5.55 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.25/5.55 = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % atLeastAtMost_singleton'
% 5.25/5.55 thf(fact_7208_atLeastAtMost__singleton_H,axiom,
% 5.25/5.55 ! [A: real,B: real] :
% 5.25/5.55 ( ( A = B )
% 5.25/5.55 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.25/5.55 = ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % atLeastAtMost_singleton'
% 5.25/5.55 thf(fact_7209_subset__Diff__insert,axiom,
% 5.25/5.55 ! [A2: set_real,B3: set_real,X3: real,C5: set_real] :
% 5.25/5.55 ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B3 @ ( insert_real @ X3 @ C5 ) ) )
% 5.25/5.55 = ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B3 @ C5 ) )
% 5.25/5.55 & ~ ( member_real @ X3 @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_Diff_insert
% 5.25/5.55 thf(fact_7210_subset__Diff__insert,axiom,
% 5.25/5.55 ! [A2: set_complex,B3: set_complex,X3: complex,C5: set_complex] :
% 5.25/5.55 ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B3 @ ( insert_complex @ X3 @ C5 ) ) )
% 5.25/5.55 = ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B3 @ C5 ) )
% 5.25/5.55 & ~ ( member_complex @ X3 @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_Diff_insert
% 5.25/5.55 thf(fact_7211_subset__Diff__insert,axiom,
% 5.25/5.55 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,X3: product_prod_nat_nat,C5: set_Pr1261947904930325089at_nat] :
% 5.25/5.55 ( ( ord_le3146513528884898305at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B3 @ ( insert8211810215607154385at_nat @ X3 @ C5 ) ) )
% 5.25/5.55 = ( ( ord_le3146513528884898305at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B3 @ C5 ) )
% 5.25/5.55 & ~ ( member8440522571783428010at_nat @ X3 @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_Diff_insert
% 5.25/5.55 thf(fact_7212_subset__Diff__insert,axiom,
% 5.25/5.55 ! [A2: set_nat,B3: set_nat,X3: nat,C5: set_nat] :
% 5.25/5.55 ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B3 @ ( insert_nat @ X3 @ C5 ) ) )
% 5.25/5.55 = ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B3 @ C5 ) )
% 5.25/5.55 & ~ ( member_nat @ X3 @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_Diff_insert
% 5.25/5.55 thf(fact_7213_subset__Diff__insert,axiom,
% 5.25/5.55 ! [A2: set_int,B3: set_int,X3: int,C5: set_int] :
% 5.25/5.55 ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B3 @ ( insert_int @ X3 @ C5 ) ) )
% 5.25/5.55 = ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B3 @ C5 ) )
% 5.25/5.55 & ~ ( member_int @ X3 @ A2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_Diff_insert
% 5.25/5.55 thf(fact_7214_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.25/5.55 ! [G: nat > int,M: nat,N: nat] :
% 5.25/5.55 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.25/5.55 = ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.shift_bounds_cl_Suc_ivl
% 5.25/5.55 thf(fact_7215_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.25/5.55 ! [G: nat > nat,M: nat,N: nat] :
% 5.25/5.55 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.25/5.55 = ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.shift_bounds_cl_Suc_ivl
% 5.25/5.55 thf(fact_7216_power__sum,axiom,
% 5.25/5.55 ! [C: real,F: nat > nat,A2: set_nat] :
% 5.25/5.55 ( ( power_power_real @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.25/5.55 = ( groups129246275422532515t_real
% 5.25/5.55 @ ^ [A3: nat] : ( power_power_real @ C @ ( F @ A3 ) )
% 5.25/5.55 @ A2 ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_sum
% 5.25/5.55 thf(fact_7217_power__sum,axiom,
% 5.25/5.55 ! [C: complex,F: nat > nat,A2: set_nat] :
% 5.25/5.55 ( ( power_power_complex @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.25/5.55 = ( groups6464643781859351333omplex
% 5.25/5.55 @ ^ [A3: nat] : ( power_power_complex @ C @ ( F @ A3 ) )
% 5.25/5.55 @ A2 ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_sum
% 5.25/5.55 thf(fact_7218_power__sum,axiom,
% 5.25/5.55 ! [C: int,F: nat > nat,A2: set_nat] :
% 5.25/5.55 ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.25/5.55 = ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [A3: nat] : ( power_power_int @ C @ ( F @ A3 ) )
% 5.25/5.55 @ A2 ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_sum
% 5.25/5.55 thf(fact_7219_power__sum,axiom,
% 5.25/5.55 ! [C: int,F: int > nat,A2: set_int] :
% 5.25/5.55 ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 5.25/5.55 = ( groups1705073143266064639nt_int
% 5.25/5.55 @ ^ [A3: int] : ( power_power_int @ C @ ( F @ A3 ) )
% 5.25/5.55 @ A2 ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_sum
% 5.25/5.55 thf(fact_7220_power__sum,axiom,
% 5.25/5.55 ! [C: nat,F: nat > nat,A2: set_nat] :
% 5.25/5.55 ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.25/5.55 = ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [A3: nat] : ( power_power_nat @ C @ ( F @ A3 ) )
% 5.25/5.55 @ A2 ) ) ).
% 5.25/5.55
% 5.25/5.55 % power_sum
% 5.25/5.55 thf(fact_7221_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.25/5.55 ! [G: nat > int,M: nat,K: nat,N: nat] :
% 5.25/5.55 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.25/5.55 = ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.shift_bounds_cl_nat_ivl
% 5.25/5.55 thf(fact_7222_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.25/5.55 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.25/5.55 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.25/5.55 = ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.shift_bounds_cl_nat_ivl
% 5.25/5.55 thf(fact_7223_prod__le__1,axiom,
% 5.25/5.55 ! [A2: set_nat,F: nat > real] :
% 5.25/5.55 ( ! [X5: nat] :
% 5.25/5.55 ( ( member_nat @ X5 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.25/5.55 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_le_1
% 5.25/5.55 thf(fact_7224_prod__le__1,axiom,
% 5.25/5.55 ! [A2: set_real,F: real > real] :
% 5.25/5.55 ( ! [X5: real] :
% 5.25/5.55 ( ( member_real @ X5 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.25/5.55 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_le_1
% 5.25/5.55 thf(fact_7225_prod__le__1,axiom,
% 5.25/5.55 ! [A2: set_int,F: int > real] :
% 5.25/5.55 ( ! [X5: int] :
% 5.25/5.55 ( ( member_int @ X5 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.25/5.55 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_le_1
% 5.25/5.55 thf(fact_7226_prod__le__1,axiom,
% 5.25/5.55 ! [A2: set_complex,F: complex > real] :
% 5.25/5.55 ( ! [X5: complex] :
% 5.25/5.55 ( ( member_complex @ X5 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.25/5.55 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_le_1
% 5.25/5.55 thf(fact_7227_prod__le__1,axiom,
% 5.25/5.55 ! [A2: set_nat,F: nat > rat] :
% 5.25/5.55 ( ! [X5: nat] :
% 5.25/5.55 ( ( member_nat @ X5 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) )
% 5.25/5.55 & ( ord_less_eq_rat @ ( F @ X5 ) @ one_one_rat ) ) )
% 5.25/5.55 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_le_1
% 5.25/5.55 thf(fact_7228_prod__le__1,axiom,
% 5.25/5.55 ! [A2: set_real,F: real > rat] :
% 5.25/5.55 ( ! [X5: real] :
% 5.25/5.55 ( ( member_real @ X5 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) )
% 5.25/5.55 & ( ord_less_eq_rat @ ( F @ X5 ) @ one_one_rat ) ) )
% 5.25/5.55 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_le_1
% 5.25/5.55 thf(fact_7229_prod__le__1,axiom,
% 5.25/5.55 ! [A2: set_int,F: int > rat] :
% 5.25/5.55 ( ! [X5: int] :
% 5.25/5.55 ( ( member_int @ X5 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) )
% 5.25/5.55 & ( ord_less_eq_rat @ ( F @ X5 ) @ one_one_rat ) ) )
% 5.25/5.55 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_le_1
% 5.25/5.55 thf(fact_7230_prod__le__1,axiom,
% 5.25/5.55 ! [A2: set_complex,F: complex > rat] :
% 5.25/5.55 ( ! [X5: complex] :
% 5.25/5.55 ( ( member_complex @ X5 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) )
% 5.25/5.55 & ( ord_less_eq_rat @ ( F @ X5 ) @ one_one_rat ) ) )
% 5.25/5.55 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_le_1
% 5.25/5.55 thf(fact_7231_prod__le__1,axiom,
% 5.25/5.55 ! [A2: set_real,F: real > nat] :
% 5.25/5.55 ( ! [X5: real] :
% 5.25/5.55 ( ( member_real @ X5 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) )
% 5.25/5.55 & ( ord_less_eq_nat @ ( F @ X5 ) @ one_one_nat ) ) )
% 5.25/5.55 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_le_1
% 5.25/5.55 thf(fact_7232_prod__le__1,axiom,
% 5.25/5.55 ! [A2: set_int,F: int > nat] :
% 5.25/5.55 ( ! [X5: int] :
% 5.25/5.55 ( ( member_int @ X5 @ A2 )
% 5.25/5.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) )
% 5.25/5.55 & ( ord_less_eq_nat @ ( F @ X5 ) @ one_one_nat ) ) )
% 5.25/5.55 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_le_1
% 5.25/5.55 thf(fact_7233_Diff__single__insert,axiom,
% 5.25/5.55 ! [A2: set_real,X3: real,B3: set_real] :
% 5.25/5.55 ( ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) @ B3 )
% 5.25/5.55 => ( ord_less_eq_set_real @ A2 @ ( insert_real @ X3 @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % Diff_single_insert
% 5.25/5.55 thf(fact_7234_Diff__single__insert,axiom,
% 5.25/5.55 ! [A2: set_nat,X3: nat,B3: set_nat] :
% 5.25/5.55 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) @ B3 )
% 5.25/5.55 => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X3 @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % Diff_single_insert
% 5.25/5.55 thf(fact_7235_Diff__single__insert,axiom,
% 5.25/5.55 ! [A2: set_int,X3: int,B3: set_int] :
% 5.25/5.55 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) @ B3 )
% 5.25/5.55 => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X3 @ B3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % Diff_single_insert
% 5.25/5.55 thf(fact_7236_subset__insert__iff,axiom,
% 5.25/5.55 ! [A2: set_complex,X3: complex,B3: set_complex] :
% 5.25/5.55 ( ( ord_le211207098394363844omplex @ A2 @ ( insert_complex @ X3 @ B3 ) )
% 5.25/5.55 = ( ( ( member_complex @ X3 @ A2 )
% 5.25/5.55 => ( ord_le211207098394363844omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) @ B3 ) )
% 5.25/5.55 & ( ~ ( member_complex @ X3 @ A2 )
% 5.25/5.55 => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insert_iff
% 5.25/5.55 thf(fact_7237_subset__insert__iff,axiom,
% 5.25/5.55 ! [A2: set_Pr1261947904930325089at_nat,X3: product_prod_nat_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.25/5.55 ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X3 @ B3 ) )
% 5.25/5.55 = ( ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 5.25/5.55 => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) @ B3 ) )
% 5.25/5.55 & ( ~ ( member8440522571783428010at_nat @ X3 @ A2 )
% 5.25/5.55 => ( ord_le3146513528884898305at_nat @ A2 @ B3 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insert_iff
% 5.25/5.55 thf(fact_7238_subset__insert__iff,axiom,
% 5.25/5.55 ! [A2: set_real,X3: real,B3: set_real] :
% 5.25/5.55 ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X3 @ B3 ) )
% 5.25/5.55 = ( ( ( member_real @ X3 @ A2 )
% 5.25/5.55 => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) @ B3 ) )
% 5.25/5.55 & ( ~ ( member_real @ X3 @ A2 )
% 5.25/5.55 => ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insert_iff
% 5.25/5.55 thf(fact_7239_subset__insert__iff,axiom,
% 5.25/5.55 ! [A2: set_nat,X3: nat,B3: set_nat] :
% 5.25/5.55 ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X3 @ B3 ) )
% 5.25/5.55 = ( ( ( member_nat @ X3 @ A2 )
% 5.25/5.55 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) @ B3 ) )
% 5.25/5.55 & ( ~ ( member_nat @ X3 @ A2 )
% 5.25/5.55 => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insert_iff
% 5.25/5.55 thf(fact_7240_subset__insert__iff,axiom,
% 5.25/5.55 ! [A2: set_int,X3: int,B3: set_int] :
% 5.25/5.55 ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X3 @ B3 ) )
% 5.25/5.55 = ( ( ( member_int @ X3 @ A2 )
% 5.25/5.55 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) @ B3 ) )
% 5.25/5.55 & ( ~ ( member_int @ X3 @ A2 )
% 5.25/5.55 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % subset_insert_iff
% 5.25/5.55 thf(fact_7241_set__update__subset__insert,axiom,
% 5.25/5.55 ! [Xs: list_real,I2: nat,X3: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I2 @ X3 ) ) @ ( insert_real @ X3 @ ( set_real2 @ Xs ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_update_subset_insert
% 5.25/5.55 thf(fact_7242_set__update__subset__insert,axiom,
% 5.25/5.55 ! [Xs: list_nat,I2: nat,X3: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I2 @ X3 ) ) @ ( insert_nat @ X3 @ ( set_nat2 @ Xs ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_update_subset_insert
% 5.25/5.55 thf(fact_7243_set__update__subset__insert,axiom,
% 5.25/5.55 ! [Xs: list_VEBT_VEBT,I2: nat,X3: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X3 ) ) @ ( insert_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_update_subset_insert
% 5.25/5.55 thf(fact_7244_set__update__subset__insert,axiom,
% 5.25/5.55 ! [Xs: list_int,I2: nat,X3: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I2 @ X3 ) ) @ ( insert_int @ X3 @ ( set_int2 @ Xs ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_update_subset_insert
% 5.25/5.55 thf(fact_7245_prod_Onat__diff__reindex,axiom,
% 5.25/5.55 ! [G: nat > int,N: nat] :
% 5.25/5.55 ( ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.nat_diff_reindex
% 5.25/5.55 thf(fact_7246_prod_Onat__diff__reindex,axiom,
% 5.25/5.55 ! [G: nat > nat,N: nat] :
% 5.25/5.55 ( ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.55 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.nat_diff_reindex
% 5.25/5.55 thf(fact_7247_prod_OatLeastAtMost__rev,axiom,
% 5.25/5.55 ! [G: nat > int,N: nat,M: nat] :
% 5.25/5.55 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.25/5.55 = ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.atLeastAtMost_rev
% 5.25/5.55 thf(fact_7248_prod_OatLeastAtMost__rev,axiom,
% 5.25/5.55 ! [G: nat > nat,N: nat,M: nat] :
% 5.25/5.55 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.25/5.55 = ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.atLeastAtMost_rev
% 5.25/5.55 thf(fact_7249_prod_OatLeast0__atMost__Suc,axiom,
% 5.25/5.55 ! [G: nat > real,N: nat] :
% 5.25/5.55 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.atLeast0_atMost_Suc
% 5.25/5.55 thf(fact_7250_prod_OatLeast0__atMost__Suc,axiom,
% 5.25/5.55 ! [G: nat > rat,N: nat] :
% 5.25/5.55 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.atLeast0_atMost_Suc
% 5.25/5.55 thf(fact_7251_prod_OatLeast0__atMost__Suc,axiom,
% 5.25/5.55 ! [G: nat > int,N: nat] :
% 5.25/5.55 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.atLeast0_atMost_Suc
% 5.25/5.55 thf(fact_7252_prod_OatLeast0__atMost__Suc,axiom,
% 5.25/5.55 ! [G: nat > nat,N: nat] :
% 5.25/5.55 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.atLeast0_atMost_Suc
% 5.25/5.55 thf(fact_7253_prod_OatLeast__Suc__atMost,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > real] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.55 = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.atLeast_Suc_atMost
% 5.25/5.55 thf(fact_7254_prod_OatLeast__Suc__atMost,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > rat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.55 = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.atLeast_Suc_atMost
% 5.25/5.55 thf(fact_7255_prod_OatLeast__Suc__atMost,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > int] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.55 = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.atLeast_Suc_atMost
% 5.25/5.55 thf(fact_7256_prod_OatLeast__Suc__atMost,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.55 = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.atLeast_Suc_atMost
% 5.25/5.55 thf(fact_7257_prod_Onat__ivl__Suc_H,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > real] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.55 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_real @ ( G @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.nat_ivl_Suc'
% 5.25/5.55 thf(fact_7258_prod_Onat__ivl__Suc_H,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > rat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.55 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_rat @ ( G @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.nat_ivl_Suc'
% 5.25/5.55 thf(fact_7259_prod_Onat__ivl__Suc_H,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > int] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.55 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_int @ ( G @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.nat_ivl_Suc'
% 5.25/5.55 thf(fact_7260_prod_Onat__ivl__Suc_H,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.55 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_nat @ ( G @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.nat_ivl_Suc'
% 5.25/5.55 thf(fact_7261_prod_OlessThan__Suc__shift,axiom,
% 5.25/5.55 ! [G: nat > real,N: nat] :
% 5.25/5.55 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.25/5.55 @ ( groups129246275422532515t_real
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.lessThan_Suc_shift
% 5.25/5.55 thf(fact_7262_prod_OlessThan__Suc__shift,axiom,
% 5.25/5.55 ! [G: nat > rat,N: nat] :
% 5.25/5.55 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.25/5.55 @ ( groups73079841787564623at_rat
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.lessThan_Suc_shift
% 5.25/5.55 thf(fact_7263_prod_OlessThan__Suc__shift,axiom,
% 5.25/5.55 ! [G: nat > int,N: nat] :
% 5.25/5.55 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.25/5.55 @ ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.lessThan_Suc_shift
% 5.25/5.55 thf(fact_7264_prod_OlessThan__Suc__shift,axiom,
% 5.25/5.55 ! [G: nat > nat,N: nat] :
% 5.25/5.55 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.25/5.55 @ ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.lessThan_Suc_shift
% 5.25/5.55 thf(fact_7265_prod_OSuc__reindex__ivl,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > real] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_real @ ( G @ M )
% 5.25/5.55 @ ( groups129246275422532515t_real
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.Suc_reindex_ivl
% 5.25/5.55 thf(fact_7266_prod_OSuc__reindex__ivl,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > rat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_rat @ ( G @ M )
% 5.25/5.55 @ ( groups73079841787564623at_rat
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.Suc_reindex_ivl
% 5.25/5.55 thf(fact_7267_prod_OSuc__reindex__ivl,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > int] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_int @ ( G @ M )
% 5.25/5.55 @ ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.Suc_reindex_ivl
% 5.25/5.55 thf(fact_7268_prod_OSuc__reindex__ivl,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.25/5.55 = ( times_times_nat @ ( G @ M )
% 5.25/5.55 @ ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.Suc_reindex_ivl
% 5.25/5.55 thf(fact_7269_psubset__insert__iff,axiom,
% 5.25/5.55 ! [A2: set_complex,X3: complex,B3: set_complex] :
% 5.25/5.55 ( ( ord_less_set_complex @ A2 @ ( insert_complex @ X3 @ B3 ) )
% 5.25/5.55 = ( ( ( member_complex @ X3 @ B3 )
% 5.25/5.55 => ( ord_less_set_complex @ A2 @ B3 ) )
% 5.25/5.55 & ( ~ ( member_complex @ X3 @ B3 )
% 5.25/5.55 => ( ( ( member_complex @ X3 @ A2 )
% 5.25/5.55 => ( ord_less_set_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) @ B3 ) )
% 5.25/5.55 & ( ~ ( member_complex @ X3 @ A2 )
% 5.25/5.55 => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % psubset_insert_iff
% 5.25/5.55 thf(fact_7270_psubset__insert__iff,axiom,
% 5.25/5.55 ! [A2: set_Pr1261947904930325089at_nat,X3: product_prod_nat_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.25/5.55 ( ( ord_le7866589430770878221at_nat @ A2 @ ( insert8211810215607154385at_nat @ X3 @ B3 ) )
% 5.25/5.55 = ( ( ( member8440522571783428010at_nat @ X3 @ B3 )
% 5.25/5.55 => ( ord_le7866589430770878221at_nat @ A2 @ B3 ) )
% 5.25/5.55 & ( ~ ( member8440522571783428010at_nat @ X3 @ B3 )
% 5.25/5.55 => ( ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 5.25/5.55 => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) @ B3 ) )
% 5.25/5.55 & ( ~ ( member8440522571783428010at_nat @ X3 @ A2 )
% 5.25/5.55 => ( ord_le3146513528884898305at_nat @ A2 @ B3 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % psubset_insert_iff
% 5.25/5.55 thf(fact_7271_psubset__insert__iff,axiom,
% 5.25/5.55 ! [A2: set_real,X3: real,B3: set_real] :
% 5.25/5.55 ( ( ord_less_set_real @ A2 @ ( insert_real @ X3 @ B3 ) )
% 5.25/5.55 = ( ( ( member_real @ X3 @ B3 )
% 5.25/5.55 => ( ord_less_set_real @ A2 @ B3 ) )
% 5.25/5.55 & ( ~ ( member_real @ X3 @ B3 )
% 5.25/5.55 => ( ( ( member_real @ X3 @ A2 )
% 5.25/5.55 => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X3 @ bot_bot_set_real ) ) @ B3 ) )
% 5.25/5.55 & ( ~ ( member_real @ X3 @ A2 )
% 5.25/5.55 => ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % psubset_insert_iff
% 5.25/5.55 thf(fact_7272_psubset__insert__iff,axiom,
% 5.25/5.55 ! [A2: set_nat,X3: nat,B3: set_nat] :
% 5.25/5.55 ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X3 @ B3 ) )
% 5.25/5.55 = ( ( ( member_nat @ X3 @ B3 )
% 5.25/5.55 => ( ord_less_set_nat @ A2 @ B3 ) )
% 5.25/5.55 & ( ~ ( member_nat @ X3 @ B3 )
% 5.25/5.55 => ( ( ( member_nat @ X3 @ A2 )
% 5.25/5.55 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) @ B3 ) )
% 5.25/5.55 & ( ~ ( member_nat @ X3 @ A2 )
% 5.25/5.55 => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % psubset_insert_iff
% 5.25/5.55 thf(fact_7273_psubset__insert__iff,axiom,
% 5.25/5.55 ! [A2: set_int,X3: int,B3: set_int] :
% 5.25/5.55 ( ( ord_less_set_int @ A2 @ ( insert_int @ X3 @ B3 ) )
% 5.25/5.55 = ( ( ( member_int @ X3 @ B3 )
% 5.25/5.55 => ( ord_less_set_int @ A2 @ B3 ) )
% 5.25/5.55 & ( ~ ( member_int @ X3 @ B3 )
% 5.25/5.55 => ( ( ( member_int @ X3 @ A2 )
% 5.25/5.55 => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) @ B3 ) )
% 5.25/5.55 & ( ~ ( member_int @ X3 @ A2 )
% 5.25/5.55 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % psubset_insert_iff
% 5.25/5.55 thf(fact_7274_set__replicate__Suc,axiom,
% 5.25/5.55 ! [N: nat,X3: vEBT_VEBT] :
% 5.25/5.55 ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N ) @ X3 ) )
% 5.25/5.55 = ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_replicate_Suc
% 5.25/5.55 thf(fact_7275_set__replicate__Suc,axiom,
% 5.25/5.55 ! [N: nat,X3: nat] :
% 5.25/5.55 ( ( set_nat2 @ ( replicate_nat @ ( suc @ N ) @ X3 ) )
% 5.25/5.55 = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_replicate_Suc
% 5.25/5.55 thf(fact_7276_set__replicate__Suc,axiom,
% 5.25/5.55 ! [N: nat,X3: int] :
% 5.25/5.55 ( ( set_int2 @ ( replicate_int @ ( suc @ N ) @ X3 ) )
% 5.25/5.55 = ( insert_int @ X3 @ bot_bot_set_int ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_replicate_Suc
% 5.25/5.55 thf(fact_7277_set__replicate__Suc,axiom,
% 5.25/5.55 ! [N: nat,X3: real] :
% 5.25/5.55 ( ( set_real2 @ ( replicate_real @ ( suc @ N ) @ X3 ) )
% 5.25/5.55 = ( insert_real @ X3 @ bot_bot_set_real ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_replicate_Suc
% 5.25/5.55 thf(fact_7278_set__replicate__conv__if,axiom,
% 5.25/5.55 ! [N: nat,X3: vEBT_VEBT] :
% 5.25/5.55 ( ( ( N = zero_zero_nat )
% 5.25/5.55 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X3 ) )
% 5.25/5.55 = bot_bo8194388402131092736T_VEBT ) )
% 5.25/5.55 & ( ( N != zero_zero_nat )
% 5.25/5.55 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X3 ) )
% 5.25/5.55 = ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_replicate_conv_if
% 5.25/5.55 thf(fact_7279_set__replicate__conv__if,axiom,
% 5.25/5.55 ! [N: nat,X3: nat] :
% 5.25/5.55 ( ( ( N = zero_zero_nat )
% 5.25/5.55 => ( ( set_nat2 @ ( replicate_nat @ N @ X3 ) )
% 5.25/5.55 = bot_bot_set_nat ) )
% 5.25/5.55 & ( ( N != zero_zero_nat )
% 5.25/5.55 => ( ( set_nat2 @ ( replicate_nat @ N @ X3 ) )
% 5.25/5.55 = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_replicate_conv_if
% 5.25/5.55 thf(fact_7280_set__replicate__conv__if,axiom,
% 5.25/5.55 ! [N: nat,X3: int] :
% 5.25/5.55 ( ( ( N = zero_zero_nat )
% 5.25/5.55 => ( ( set_int2 @ ( replicate_int @ N @ X3 ) )
% 5.25/5.55 = bot_bot_set_int ) )
% 5.25/5.55 & ( ( N != zero_zero_nat )
% 5.25/5.55 => ( ( set_int2 @ ( replicate_int @ N @ X3 ) )
% 5.25/5.55 = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_replicate_conv_if
% 5.25/5.55 thf(fact_7281_set__replicate__conv__if,axiom,
% 5.25/5.55 ! [N: nat,X3: real] :
% 5.25/5.55 ( ( ( N = zero_zero_nat )
% 5.25/5.55 => ( ( set_real2 @ ( replicate_real @ N @ X3 ) )
% 5.25/5.55 = bot_bot_set_real ) )
% 5.25/5.55 & ( ( N != zero_zero_nat )
% 5.25/5.55 => ( ( set_real2 @ ( replicate_real @ N @ X3 ) )
% 5.25/5.55 = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % set_replicate_conv_if
% 5.25/5.55 thf(fact_7282_prod_OatLeast1__atMost__eq,axiom,
% 5.25/5.55 ! [G: nat > int,N: nat] :
% 5.25/5.55 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.25/5.55 = ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.atLeast1_atMost_eq
% 5.25/5.55 thf(fact_7283_prod_OatLeast1__atMost__eq,axiom,
% 5.25/5.55 ! [G: nat > nat,N: nat] :
% 5.25/5.55 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.25/5.55 = ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.25/5.55 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.atLeast1_atMost_eq
% 5.25/5.55 thf(fact_7284_atLeastAtMostPlus1__int__conv,axiom,
% 5.25/5.55 ! [M: int,N: int] :
% 5.25/5.55 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.25/5.55 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.25/5.55 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % atLeastAtMostPlus1_int_conv
% 5.25/5.55 thf(fact_7285_simp__from__to,axiom,
% 5.25/5.55 ( set_or1266510415728281911st_int
% 5.25/5.55 = ( ^ [I3: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I3 ) @ bot_bot_set_int @ ( insert_int @ I3 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % simp_from_to
% 5.25/5.55 thf(fact_7286_prod_Oub__add__nat,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > real,P2: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.25/5.55 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.25/5.55 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.ub_add_nat
% 5.25/5.55 thf(fact_7287_prod_Oub__add__nat,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > rat,P2: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.25/5.55 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.25/5.55 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.ub_add_nat
% 5.25/5.55 thf(fact_7288_prod_Oub__add__nat,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > int,P2: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.25/5.55 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.25/5.55 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.ub_add_nat
% 5.25/5.55 thf(fact_7289_prod_Oub__add__nat,axiom,
% 5.25/5.55 ! [M: nat,N: nat,G: nat > nat,P2: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.25/5.55 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.25/5.55 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.ub_add_nat
% 5.25/5.55 thf(fact_7290_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.25/5.55 ! [X3: nat > nat > nat,Xa2: nat,Xb3: nat,Xc: nat,Y: nat] :
% 5.25/5.55 ( ( ( set_fo2584398358068434914at_nat @ X3 @ Xa2 @ Xb3 @ Xc )
% 5.25/5.55 = Y )
% 5.25/5.55 => ( ( ( ord_less_nat @ Xb3 @ Xa2 )
% 5.25/5.55 => ( Y = Xc ) )
% 5.25/5.55 & ( ~ ( ord_less_nat @ Xb3 @ Xa2 )
% 5.25/5.55 => ( Y
% 5.25/5.55 = ( set_fo2584398358068434914at_nat @ X3 @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb3 @ ( X3 @ Xa2 @ Xc ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % fold_atLeastAtMost_nat.elims
% 5.25/5.55 thf(fact_7291_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.25/5.55 ( set_fo2584398358068434914at_nat
% 5.25/5.55 = ( ^ [F3: nat > nat > nat,A3: nat,B2: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B2 @ A3 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A3 @ one_one_nat ) @ B2 @ ( F3 @ A3 @ Acc2 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % fold_atLeastAtMost_nat.simps
% 5.25/5.55 thf(fact_7292_norm__prod__diff,axiom,
% 5.25/5.55 ! [I6: set_real,Z: real > real,W: real > real] :
% 5.25/5.55 ( ! [I4: real] :
% 5.25/5.55 ( ( member_real @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ! [I4: real] :
% 5.25/5.55 ( ( member_real @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups1681761925125756287l_real @ Z @ I6 ) @ ( groups1681761925125756287l_real @ W @ I6 ) ) )
% 5.25/5.55 @ ( groups8097168146408367636l_real
% 5.25/5.55 @ ^ [I3: real] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.25/5.55 @ I6 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_prod_diff
% 5.25/5.55 thf(fact_7293_norm__prod__diff,axiom,
% 5.25/5.55 ! [I6: set_int,Z: int > real,W: int > real] :
% 5.25/5.55 ( ! [I4: int] :
% 5.25/5.55 ( ( member_int @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ! [I4: int] :
% 5.25/5.55 ( ( member_int @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups2316167850115554303t_real @ Z @ I6 ) @ ( groups2316167850115554303t_real @ W @ I6 ) ) )
% 5.25/5.55 @ ( groups8778361861064173332t_real
% 5.25/5.55 @ ^ [I3: int] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.25/5.55 @ I6 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_prod_diff
% 5.25/5.55 thf(fact_7294_norm__prod__diff,axiom,
% 5.25/5.55 ! [I6: set_complex,Z: complex > real,W: complex > real] :
% 5.25/5.55 ( ! [I4: complex] :
% 5.25/5.55 ( ( member_complex @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ! [I4: complex] :
% 5.25/5.55 ( ( member_complex @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups766887009212190081x_real @ Z @ I6 ) @ ( groups766887009212190081x_real @ W @ I6 ) ) )
% 5.25/5.55 @ ( groups5808333547571424918x_real
% 5.25/5.55 @ ^ [I3: complex] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.25/5.55 @ I6 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_prod_diff
% 5.25/5.55 thf(fact_7295_norm__prod__diff,axiom,
% 5.25/5.55 ! [I6: set_Pr1261947904930325089at_nat,Z: product_prod_nat_nat > real,W: product_prod_nat_nat > real] :
% 5.25/5.55 ( ! [I4: product_prod_nat_nat] :
% 5.25/5.55 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ! [I4: product_prod_nat_nat] :
% 5.25/5.55 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups6036352826371341000t_real @ Z @ I6 ) @ ( groups6036352826371341000t_real @ W @ I6 ) ) )
% 5.25/5.55 @ ( groups4567486121110086003t_real
% 5.25/5.55 @ ^ [I3: product_prod_nat_nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.25/5.55 @ I6 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_prod_diff
% 5.25/5.55 thf(fact_7296_norm__prod__diff,axiom,
% 5.25/5.55 ! [I6: set_real,Z: real > complex,W: real > complex] :
% 5.25/5.55 ( ! [I4: real] :
% 5.25/5.55 ( ( member_real @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ! [I4: real] :
% 5.25/5.55 ( ( member_real @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups713298508707869441omplex @ Z @ I6 ) @ ( groups713298508707869441omplex @ W @ I6 ) ) )
% 5.25/5.55 @ ( groups8097168146408367636l_real
% 5.25/5.55 @ ^ [I3: real] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.25/5.55 @ I6 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_prod_diff
% 5.25/5.55 thf(fact_7297_norm__prod__diff,axiom,
% 5.25/5.55 ! [I6: set_int,Z: int > complex,W: int > complex] :
% 5.25/5.55 ( ! [I4: int] :
% 5.25/5.55 ( ( member_int @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ! [I4: int] :
% 5.25/5.55 ( ( member_int @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups7440179247065528705omplex @ Z @ I6 ) @ ( groups7440179247065528705omplex @ W @ I6 ) ) )
% 5.25/5.55 @ ( groups8778361861064173332t_real
% 5.25/5.55 @ ^ [I3: int] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.25/5.55 @ I6 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_prod_diff
% 5.25/5.55 thf(fact_7298_norm__prod__diff,axiom,
% 5.25/5.55 ! [I6: set_complex,Z: complex > complex,W: complex > complex] :
% 5.25/5.55 ( ! [I4: complex] :
% 5.25/5.55 ( ( member_complex @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ! [I4: complex] :
% 5.25/5.55 ( ( member_complex @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups3708469109370488835omplex @ Z @ I6 ) @ ( groups3708469109370488835omplex @ W @ I6 ) ) )
% 5.25/5.55 @ ( groups5808333547571424918x_real
% 5.25/5.55 @ ^ [I3: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.25/5.55 @ I6 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_prod_diff
% 5.25/5.55 thf(fact_7299_norm__prod__diff,axiom,
% 5.25/5.55 ! [I6: set_Pr1261947904930325089at_nat,Z: product_prod_nat_nat > complex,W: product_prod_nat_nat > complex] :
% 5.25/5.55 ( ! [I4: product_prod_nat_nat] :
% 5.25/5.55 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ! [I4: product_prod_nat_nat] :
% 5.25/5.55 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups8110221916422527690omplex @ Z @ I6 ) @ ( groups8110221916422527690omplex @ W @ I6 ) ) )
% 5.25/5.55 @ ( groups4567486121110086003t_real
% 5.25/5.55 @ ^ [I3: product_prod_nat_nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.25/5.55 @ I6 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_prod_diff
% 5.25/5.55 thf(fact_7300_norm__prod__diff,axiom,
% 5.25/5.55 ! [I6: set_nat,Z: nat > real,W: nat > real] :
% 5.25/5.55 ( ! [I4: nat] :
% 5.25/5.55 ( ( member_nat @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ! [I4: nat] :
% 5.25/5.55 ( ( member_nat @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups129246275422532515t_real @ Z @ I6 ) @ ( groups129246275422532515t_real @ W @ I6 ) ) )
% 5.25/5.55 @ ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [I3: nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.25/5.55 @ I6 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_prod_diff
% 5.25/5.55 thf(fact_7301_norm__prod__diff,axiom,
% 5.25/5.55 ! [I6: set_nat,Z: nat > complex,W: nat > complex] :
% 5.25/5.55 ( ! [I4: nat] :
% 5.25/5.55 ( ( member_nat @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ! [I4: nat] :
% 5.25/5.55 ( ( member_nat @ I4 @ I6 )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups6464643781859351333omplex @ Z @ I6 ) @ ( groups6464643781859351333omplex @ W @ I6 ) ) )
% 5.25/5.55 @ ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [I3: nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.25/5.55 @ I6 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % norm_prod_diff
% 5.25/5.55 thf(fact_7302_pochhammer__Suc__prod,axiom,
% 5.25/5.55 ! [A: real,N: nat] :
% 5.25/5.55 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.25/5.55 = ( groups129246275422532515t_real
% 5.25/5.55 @ ^ [I3: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I3 ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_Suc_prod
% 5.25/5.55 thf(fact_7303_pochhammer__Suc__prod,axiom,
% 5.25/5.55 ! [A: rat,N: nat] :
% 5.25/5.55 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.25/5.55 = ( groups73079841787564623at_rat
% 5.25/5.55 @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_Suc_prod
% 5.25/5.55 thf(fact_7304_pochhammer__Suc__prod,axiom,
% 5.25/5.55 ! [A: int,N: nat] :
% 5.25/5.55 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.25/5.55 = ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I3 ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_Suc_prod
% 5.25/5.55 thf(fact_7305_pochhammer__Suc__prod,axiom,
% 5.25/5.55 ! [A: nat,N: nat] :
% 5.25/5.55 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.25/5.55 = ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I3 ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_Suc_prod
% 5.25/5.55 thf(fact_7306_pochhammer__prod__rev,axiom,
% 5.25/5.55 ( comm_s7457072308508201937r_real
% 5.25/5.55 = ( ^ [A3: real,N2: nat] :
% 5.25/5.55 ( groups129246275422532515t_real
% 5.25/5.55 @ ^ [I3: nat] : ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_prod_rev
% 5.25/5.55 thf(fact_7307_pochhammer__prod__rev,axiom,
% 5.25/5.55 ( comm_s4028243227959126397er_rat
% 5.25/5.55 = ( ^ [A3: rat,N2: nat] :
% 5.25/5.55 ( groups73079841787564623at_rat
% 5.25/5.55 @ ^ [I3: nat] : ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_prod_rev
% 5.25/5.55 thf(fact_7308_pochhammer__prod__rev,axiom,
% 5.25/5.55 ( comm_s4660882817536571857er_int
% 5.25/5.55 = ( ^ [A3: int,N2: nat] :
% 5.25/5.55 ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [I3: nat] : ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_prod_rev
% 5.25/5.55 thf(fact_7309_pochhammer__prod__rev,axiom,
% 5.25/5.55 ( comm_s4663373288045622133er_nat
% 5.25/5.55 = ( ^ [A3: nat,N2: nat] :
% 5.25/5.55 ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [I3: nat] : ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_prod_rev
% 5.25/5.55 thf(fact_7310_prod_Oin__pairs,axiom,
% 5.25/5.55 ! [G: nat > real,M: nat,N: nat] :
% 5.25/5.55 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.55 = ( groups129246275422532515t_real
% 5.25/5.55 @ ^ [I3: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.in_pairs
% 5.25/5.55 thf(fact_7311_prod_Oin__pairs,axiom,
% 5.25/5.55 ! [G: nat > rat,M: nat,N: nat] :
% 5.25/5.55 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.55 = ( groups73079841787564623at_rat
% 5.25/5.55 @ ^ [I3: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.in_pairs
% 5.25/5.55 thf(fact_7312_prod_Oin__pairs,axiom,
% 5.25/5.55 ! [G: nat > int,M: nat,N: nat] :
% 5.25/5.55 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.55 = ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [I3: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.in_pairs
% 5.25/5.55 thf(fact_7313_prod_Oin__pairs,axiom,
% 5.25/5.55 ! [G: nat > nat,M: nat,N: nat] :
% 5.25/5.55 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.55 = ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [I3: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod.in_pairs
% 5.25/5.55 thf(fact_7314_sum__atLeastAtMost__code,axiom,
% 5.25/5.55 ! [F: nat > complex,A: nat,B: nat] :
% 5.25/5.55 ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.25/5.55 = ( set_fo1517530859248394432omplex
% 5.25/5.55 @ ^ [A3: nat] : ( plus_plus_complex @ ( F @ A3 ) )
% 5.25/5.55 @ A
% 5.25/5.55 @ B
% 5.25/5.55 @ zero_zero_complex ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_atLeastAtMost_code
% 5.25/5.55 thf(fact_7315_sum__atLeastAtMost__code,axiom,
% 5.25/5.55 ! [F: nat > rat,A: nat,B: nat] :
% 5.25/5.55 ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.25/5.55 = ( set_fo1949268297981939178at_rat
% 5.25/5.55 @ ^ [A3: nat] : ( plus_plus_rat @ ( F @ A3 ) )
% 5.25/5.55 @ A
% 5.25/5.55 @ B
% 5.25/5.55 @ zero_zero_rat ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_atLeastAtMost_code
% 5.25/5.55 thf(fact_7316_sum__atLeastAtMost__code,axiom,
% 5.25/5.55 ! [F: nat > int,A: nat,B: nat] :
% 5.25/5.55 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.25/5.55 = ( set_fo2581907887559384638at_int
% 5.25/5.55 @ ^ [A3: nat] : ( plus_plus_int @ ( F @ A3 ) )
% 5.25/5.55 @ A
% 5.25/5.55 @ B
% 5.25/5.55 @ zero_zero_int ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_atLeastAtMost_code
% 5.25/5.55 thf(fact_7317_sum__atLeastAtMost__code,axiom,
% 5.25/5.55 ! [F: nat > nat,A: nat,B: nat] :
% 5.25/5.55 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.25/5.55 = ( set_fo2584398358068434914at_nat
% 5.25/5.55 @ ^ [A3: nat] : ( plus_plus_nat @ ( F @ A3 ) )
% 5.25/5.55 @ A
% 5.25/5.55 @ B
% 5.25/5.55 @ zero_zero_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_atLeastAtMost_code
% 5.25/5.55 thf(fact_7318_sum__atLeastAtMost__code,axiom,
% 5.25/5.55 ! [F: nat > real,A: nat,B: nat] :
% 5.25/5.55 ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.25/5.55 = ( set_fo3111899725591712190t_real
% 5.25/5.55 @ ^ [A3: nat] : ( plus_plus_real @ ( F @ A3 ) )
% 5.25/5.55 @ A
% 5.25/5.55 @ B
% 5.25/5.55 @ zero_zero_real ) ) ).
% 5.25/5.55
% 5.25/5.55 % sum_atLeastAtMost_code
% 5.25/5.55 thf(fact_7319_pochhammer__Suc__prod__rev,axiom,
% 5.25/5.55 ! [A: real,N: nat] :
% 5.25/5.55 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.25/5.55 = ( groups129246275422532515t_real
% 5.25/5.55 @ ^ [I3: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I3 ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_Suc_prod_rev
% 5.25/5.55 thf(fact_7320_pochhammer__Suc__prod__rev,axiom,
% 5.25/5.55 ! [A: rat,N: nat] :
% 5.25/5.55 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.25/5.55 = ( groups73079841787564623at_rat
% 5.25/5.55 @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I3 ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_Suc_prod_rev
% 5.25/5.55 thf(fact_7321_pochhammer__Suc__prod__rev,axiom,
% 5.25/5.55 ! [A: int,N: nat] :
% 5.25/5.55 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.25/5.55 = ( groups705719431365010083at_int
% 5.25/5.55 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I3 ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_Suc_prod_rev
% 5.25/5.55 thf(fact_7322_pochhammer__Suc__prod__rev,axiom,
% 5.25/5.55 ! [A: nat,N: nat] :
% 5.25/5.55 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.25/5.55 = ( groups708209901874060359at_nat
% 5.25/5.55 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I3 ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % pochhammer_Suc_prod_rev
% 5.25/5.55 thf(fact_7323_and__int_Oelims,axiom,
% 5.25/5.55 ! [X3: int,Xa2: int,Y: int] :
% 5.25/5.55 ( ( ( bit_se725231765392027082nd_int @ X3 @ Xa2 )
% 5.25/5.55 = Y )
% 5.25/5.55 => ( ( ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.25/5.55 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.25/5.55 => ( Y
% 5.25/5.55 = ( uminus_uminus_int
% 5.25/5.55 @ ( zero_n2684676970156552555ol_int
% 5.25/5.55 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 5.25/5.55 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.25/5.55 & ( ~ ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.25/5.55 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.25/5.55 => ( Y
% 5.25/5.55 = ( plus_plus_int
% 5.25/5.55 @ ( zero_n2684676970156552555ol_int
% 5.25/5.55 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 5.25/5.55 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.25/5.55 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % and_int.elims
% 5.25/5.55 thf(fact_7324_and__int_Opsimps,axiom,
% 5.25/5.55 ! [K: int,L2: int] :
% 5.25/5.55 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L2 ) )
% 5.25/5.55 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.25/5.55 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.25/5.55 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.25/5.55 = ( uminus_uminus_int
% 5.25/5.55 @ ( zero_n2684676970156552555ol_int
% 5.25/5.55 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.25/5.55 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ) ) )
% 5.25/5.55 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.25/5.55 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.25/5.55 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.25/5.55 = ( plus_plus_int
% 5.25/5.55 @ ( zero_n2684676970156552555ol_int
% 5.25/5.55 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.25/5.55 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.25/5.55 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % and_int.psimps
% 5.25/5.55 thf(fact_7325_and__int_Opelims,axiom,
% 5.25/5.55 ! [X3: int,Xa2: int,Y: int] :
% 5.25/5.55 ( ( ( bit_se725231765392027082nd_int @ X3 @ Xa2 )
% 5.25/5.55 = Y )
% 5.25/5.55 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X3 @ Xa2 ) )
% 5.25/5.55 => ~ ( ( ( ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.25/5.55 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.25/5.55 => ( Y
% 5.25/5.55 = ( uminus_uminus_int
% 5.25/5.55 @ ( zero_n2684676970156552555ol_int
% 5.25/5.55 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 5.25/5.55 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.25/5.55 & ( ~ ( ( member_int @ X3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.25/5.55 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.25/5.55 => ( Y
% 5.25/5.55 = ( plus_plus_int
% 5.25/5.55 @ ( zero_n2684676970156552555ol_int
% 5.25/5.55 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X3 )
% 5.25/5.55 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.25/5.55 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.25/5.55 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X3 @ Xa2 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % and_int.pelims
% 5.25/5.55 thf(fact_7326_geometric__deriv__sums,axiom,
% 5.25/5.55 ! [Z: real] :
% 5.25/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.25/5.55 => ( sums_real
% 5.25/5.55 @ ^ [N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) )
% 5.25/5.55 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % geometric_deriv_sums
% 5.25/5.55 thf(fact_7327_geometric__deriv__sums,axiom,
% 5.25/5.55 ! [Z: complex] :
% 5.25/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.25/5.55 => ( sums_complex
% 5.25/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) )
% 5.25/5.55 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % geometric_deriv_sums
% 5.25/5.55 thf(fact_7328_gchoose__row__sum__weighted,axiom,
% 5.25/5.55 ! [R2: complex,M: nat] :
% 5.25/5.55 ( ( groups2073611262835488442omplex
% 5.25/5.55 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R2 @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R2 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.25/5.55 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R2 @ ( suc @ M ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gchoose_row_sum_weighted
% 5.25/5.55 thf(fact_7329_gchoose__row__sum__weighted,axiom,
% 5.25/5.55 ! [R2: rat,M: nat] :
% 5.25/5.55 ( ( groups2906978787729119204at_rat
% 5.25/5.55 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R2 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.25/5.55 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R2 @ ( suc @ M ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gchoose_row_sum_weighted
% 5.25/5.55 thf(fact_7330_gchoose__row__sum__weighted,axiom,
% 5.25/5.55 ! [R2: real,M: nat] :
% 5.25/5.55 ( ( groups6591440286371151544t_real
% 5.25/5.55 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R2 @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.25/5.55 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.25/5.55 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R2 @ ( suc @ M ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gchoose_row_sum_weighted
% 5.25/5.55 thf(fact_7331_ln__one__minus__pos__lower__bound,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.55 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X3 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_one_minus_pos_lower_bound
% 5.25/5.55 thf(fact_7332_central__binomial__lower__bound,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.55 => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % central_binomial_lower_bound
% 5.25/5.55 thf(fact_7333_binomial__Suc__n,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( binomial @ ( suc @ N ) @ N )
% 5.25/5.55 = ( suc @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % binomial_Suc_n
% 5.25/5.55 thf(fact_7334_binomial__n__n,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( binomial @ N @ N )
% 5.25/5.55 = one_one_nat ) ).
% 5.25/5.55
% 5.25/5.55 % binomial_n_n
% 5.25/5.55 thf(fact_7335_ln__one,axiom,
% 5.25/5.55 ( ( ln_ln_real @ one_one_real )
% 5.25/5.55 = zero_zero_real ) ).
% 5.25/5.55
% 5.25/5.55 % ln_one
% 5.25/5.55 thf(fact_7336_gbinomial__0_I2_J,axiom,
% 5.25/5.55 ! [K: nat] :
% 5.25/5.55 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 5.25/5.55 = zero_zero_complex ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_0(2)
% 5.25/5.55 thf(fact_7337_gbinomial__0_I2_J,axiom,
% 5.25/5.55 ! [K: nat] :
% 5.25/5.55 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.25/5.55 = zero_zero_real ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_0(2)
% 5.25/5.55 thf(fact_7338_gbinomial__0_I2_J,axiom,
% 5.25/5.55 ! [K: nat] :
% 5.25/5.55 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 5.25/5.55 = zero_zero_rat ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_0(2)
% 5.25/5.55 thf(fact_7339_gbinomial__0_I2_J,axiom,
% 5.25/5.55 ! [K: nat] :
% 5.25/5.55 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.25/5.55 = zero_zero_nat ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_0(2)
% 5.25/5.55 thf(fact_7340_gbinomial__0_I2_J,axiom,
% 5.25/5.55 ! [K: nat] :
% 5.25/5.55 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.25/5.55 = zero_zero_int ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_0(2)
% 5.25/5.55 thf(fact_7341_binomial__0__Suc,axiom,
% 5.25/5.55 ! [K: nat] :
% 5.25/5.55 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.25/5.55 = zero_zero_nat ) ).
% 5.25/5.55
% 5.25/5.55 % binomial_0_Suc
% 5.25/5.55 thf(fact_7342_binomial__1,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 5.25/5.55 = N ) ).
% 5.25/5.55
% 5.25/5.55 % binomial_1
% 5.25/5.55 thf(fact_7343_binomial__eq__0__iff,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( ( binomial @ N @ K )
% 5.25/5.55 = zero_zero_nat )
% 5.25/5.55 = ( ord_less_nat @ N @ K ) ) ).
% 5.25/5.55
% 5.25/5.55 % binomial_eq_0_iff
% 5.25/5.55 thf(fact_7344_gbinomial__0_I1_J,axiom,
% 5.25/5.55 ! [A: complex] :
% 5.25/5.55 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 5.25/5.55 = one_one_complex ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_0(1)
% 5.25/5.55 thf(fact_7345_gbinomial__0_I1_J,axiom,
% 5.25/5.55 ! [A: real] :
% 5.25/5.55 ( ( gbinomial_real @ A @ zero_zero_nat )
% 5.25/5.55 = one_one_real ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_0(1)
% 5.25/5.55 thf(fact_7346_gbinomial__0_I1_J,axiom,
% 5.25/5.55 ! [A: rat] :
% 5.25/5.55 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 5.25/5.55 = one_one_rat ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_0(1)
% 5.25/5.55 thf(fact_7347_gbinomial__0_I1_J,axiom,
% 5.25/5.55 ! [A: nat] :
% 5.25/5.55 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 5.25/5.55 = one_one_nat ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_0(1)
% 5.25/5.55 thf(fact_7348_gbinomial__0_I1_J,axiom,
% 5.25/5.55 ! [A: int] :
% 5.25/5.55 ( ( gbinomial_int @ A @ zero_zero_nat )
% 5.25/5.55 = one_one_int ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_0(1)
% 5.25/5.55 thf(fact_7349_binomial__Suc__Suc,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.25/5.55 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % binomial_Suc_Suc
% 5.25/5.55 thf(fact_7350_binomial__n__0,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( binomial @ N @ zero_zero_nat )
% 5.25/5.55 = one_one_nat ) ).
% 5.25/5.55
% 5.25/5.55 % binomial_n_0
% 5.25/5.55 thf(fact_7351_zero__less__binomial__iff,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 5.25/5.55 = ( ord_less_eq_nat @ K @ N ) ) ).
% 5.25/5.55
% 5.25/5.55 % zero_less_binomial_iff
% 5.25/5.55 thf(fact_7352_ln__le__cancel__iff,axiom,
% 5.25/5.55 ! [X3: real,Y: real] :
% 5.25/5.55 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.55 => ( ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y ) )
% 5.25/5.55 = ( ord_less_eq_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_le_cancel_iff
% 5.25/5.55 thf(fact_7353_ln__less__zero__iff,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ( ord_less_real @ ( ln_ln_real @ X3 ) @ zero_zero_real )
% 5.25/5.55 = ( ord_less_real @ X3 @ one_one_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_less_zero_iff
% 5.25/5.55 thf(fact_7354_ln__gt__zero__iff,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 5.25/5.55 = ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_gt_zero_iff
% 5.25/5.55 thf(fact_7355_ln__eq__zero__iff,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ( ( ln_ln_real @ X3 )
% 5.25/5.55 = zero_zero_real )
% 5.25/5.55 = ( X3 = one_one_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_eq_zero_iff
% 5.25/5.55 thf(fact_7356_ln__ge__zero__iff,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 5.25/5.55 = ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_ge_zero_iff
% 5.25/5.55 thf(fact_7357_ln__le__zero__iff,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ zero_zero_real )
% 5.25/5.55 = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_le_zero_iff
% 5.25/5.55 thf(fact_7358_powser__sums__zero__iff,axiom,
% 5.25/5.55 ! [A: nat > complex,X3: complex] :
% 5.25/5.55 ( ( sums_complex
% 5.25/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( A @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 5.25/5.55 @ X3 )
% 5.25/5.55 = ( ( A @ zero_zero_nat )
% 5.25/5.55 = X3 ) ) ).
% 5.25/5.55
% 5.25/5.55 % powser_sums_zero_iff
% 5.25/5.55 thf(fact_7359_powser__sums__zero__iff,axiom,
% 5.25/5.55 ! [A: nat > real,X3: real] :
% 5.25/5.55 ( ( sums_real
% 5.25/5.55 @ ^ [N2: nat] : ( times_times_real @ ( A @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 5.25/5.55 @ X3 )
% 5.25/5.55 = ( ( A @ zero_zero_nat )
% 5.25/5.55 = X3 ) ) ).
% 5.25/5.55
% 5.25/5.55 % powser_sums_zero_iff
% 5.25/5.55 thf(fact_7360_choose__one,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( binomial @ N @ one_one_nat )
% 5.25/5.55 = N ) ).
% 5.25/5.55
% 5.25/5.55 % choose_one
% 5.25/5.55 thf(fact_7361_binomial__eq__0,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( ord_less_nat @ N @ K )
% 5.25/5.55 => ( ( binomial @ N @ K )
% 5.25/5.55 = zero_zero_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % binomial_eq_0
% 5.25/5.55 thf(fact_7362_Suc__times__binomial,axiom,
% 5.25/5.55 ! [K: nat,N: nat] :
% 5.25/5.55 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 5.25/5.55 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % Suc_times_binomial
% 5.25/5.55 thf(fact_7363_Suc__times__binomial__eq,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 5.25/5.55 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % Suc_times_binomial_eq
% 5.25/5.55 thf(fact_7364_binomial__symmetric,axiom,
% 5.25/5.55 ! [K: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.55 => ( ( binomial @ N @ K )
% 5.25/5.55 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % binomial_symmetric
% 5.25/5.55 thf(fact_7365_choose__mult__lemma,axiom,
% 5.25/5.55 ! [M: nat,R2: nat,K: nat] :
% 5.25/5.55 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 5.25/5.55 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % choose_mult_lemma
% 5.25/5.55 thf(fact_7366_binomial__le__pow,axiom,
% 5.25/5.55 ! [R2: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ R2 @ N )
% 5.25/5.55 => ( ord_less_eq_nat @ ( binomial @ N @ R2 ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % binomial_le_pow
% 5.25/5.55 thf(fact_7367_lessThan__Suc,axiom,
% 5.25/5.55 ! [K: nat] :
% 5.25/5.55 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.25/5.55 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_Suc
% 5.25/5.55 thf(fact_7368_ln__bound,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ X3 ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_bound
% 5.25/5.55 thf(fact_7369_zero__less__binomial,axiom,
% 5.25/5.55 ! [K: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.55 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % zero_less_binomial
% 5.25/5.55 thf(fact_7370_ln__gt__zero__imp__gt__one,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 5.25/5.55 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_gt_zero_imp_gt_one
% 5.25/5.55 thf(fact_7371_ln__less__zero,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ( ord_less_real @ X3 @ one_one_real )
% 5.25/5.55 => ( ord_less_real @ ( ln_ln_real @ X3 ) @ zero_zero_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_less_zero
% 5.25/5.55 thf(fact_7372_ln__gt__zero,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_real @ one_one_real @ X3 )
% 5.25/5.55 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_gt_zero
% 5.25/5.55 thf(fact_7373_ln__ge__zero,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ one_one_real @ X3 )
% 5.25/5.55 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_ge_zero
% 5.25/5.55 thf(fact_7374_Suc__times__binomial__add,axiom,
% 5.25/5.55 ! [A: nat,B: nat] :
% 5.25/5.55 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.25/5.55 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % Suc_times_binomial_add
% 5.25/5.55 thf(fact_7375_choose__mult,axiom,
% 5.25/5.55 ! [K: nat,M: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ K @ M )
% 5.25/5.55 => ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 5.25/5.55 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % choose_mult
% 5.25/5.55 thf(fact_7376_binomial__Suc__Suc__eq__times,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.25/5.55 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % binomial_Suc_Suc_eq_times
% 5.25/5.55 thf(fact_7377_binomial__absorb__comp,axiom,
% 5.25/5.55 ! [N: nat,K: nat] :
% 5.25/5.55 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 5.25/5.55 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % binomial_absorb_comp
% 5.25/5.55 thf(fact_7378_gbinomial__Suc__Suc,axiom,
% 5.25/5.55 ! [A: complex,K: nat] :
% 5.25/5.55 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.25/5.55 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_Suc_Suc
% 5.25/5.55 thf(fact_7379_gbinomial__Suc__Suc,axiom,
% 5.25/5.55 ! [A: real,K: nat] :
% 5.25/5.55 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.25/5.55 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_Suc_Suc
% 5.25/5.55 thf(fact_7380_gbinomial__Suc__Suc,axiom,
% 5.25/5.55 ! [A: rat,K: nat] :
% 5.25/5.55 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.25/5.55 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_Suc_Suc
% 5.25/5.55 thf(fact_7381_gbinomial__of__nat__symmetric,axiom,
% 5.25/5.55 ! [K: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.55 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 5.25/5.55 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_of_nat_symmetric
% 5.25/5.55 thf(fact_7382_gbinomial__of__nat__symmetric,axiom,
% 5.25/5.55 ! [K: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.55 => ( ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K )
% 5.25/5.55 = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_of_nat_symmetric
% 5.25/5.55 thf(fact_7383_atLeast0__atMost__Suc,axiom,
% 5.25/5.55 ! [N: nat] :
% 5.25/5.55 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.25/5.55 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % atLeast0_atMost_Suc
% 5.25/5.55 thf(fact_7384_Icc__eq__insert__lb__nat,axiom,
% 5.25/5.55 ! [M: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 5.25/5.55 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % Icc_eq_insert_lb_nat
% 5.25/5.55 thf(fact_7385_atLeastAtMostSuc__conv,axiom,
% 5.25/5.55 ! [M: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.25/5.55 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 5.25/5.55 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % atLeastAtMostSuc_conv
% 5.25/5.55 thf(fact_7386_atLeastAtMost__insertL,axiom,
% 5.25/5.55 ! [M: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.55 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.25/5.55 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % atLeastAtMost_insertL
% 5.25/5.55 thf(fact_7387_lessThan__nat__numeral,axiom,
% 5.25/5.55 ! [K: num] :
% 5.25/5.55 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.25/5.55 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % lessThan_nat_numeral
% 5.25/5.55 thf(fact_7388_prod__int__eq,axiom,
% 5.25/5.55 ! [I2: nat,J2: nat] :
% 5.25/5.55 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ J2 ) )
% 5.25/5.55 = ( groups1705073143266064639nt_int
% 5.25/5.55 @ ^ [X2: int] : X2
% 5.25/5.55 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J2 ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_int_eq
% 5.25/5.55 thf(fact_7389_ln__ge__zero__imp__ge__one,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X3 ) )
% 5.25/5.55 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_ge_zero_imp_ge_one
% 5.25/5.55 thf(fact_7390_powser__sums__zero,axiom,
% 5.25/5.55 ! [A: nat > complex] :
% 5.25/5.55 ( sums_complex
% 5.25/5.55 @ ^ [N2: nat] : ( times_times_complex @ ( A @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 5.25/5.55 @ ( A @ zero_zero_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % powser_sums_zero
% 5.25/5.55 thf(fact_7391_powser__sums__zero,axiom,
% 5.25/5.55 ! [A: nat > real] :
% 5.25/5.55 ( sums_real
% 5.25/5.55 @ ^ [N2: nat] : ( times_times_real @ ( A @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 5.25/5.55 @ ( A @ zero_zero_nat ) ) ).
% 5.25/5.55
% 5.25/5.55 % powser_sums_zero
% 5.25/5.55 thf(fact_7392_ln__add__one__self__le__self,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_add_one_self_le_self
% 5.25/5.55 thf(fact_7393_ln__mult,axiom,
% 5.25/5.55 ! [X3: real,Y: real] :
% 5.25/5.55 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.55 => ( ( ln_ln_real @ ( times_times_real @ X3 @ Y ) )
% 5.25/5.55 = ( plus_plus_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_mult
% 5.25/5.55 thf(fact_7394_binomial__absorption,axiom,
% 5.25/5.55 ! [K: nat,N: nat] :
% 5.25/5.55 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 5.25/5.55 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % binomial_absorption
% 5.25/5.55 thf(fact_7395_ln__eq__minus__one,axiom,
% 5.25/5.55 ! [X3: real] :
% 5.25/5.55 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.55 => ( ( ( ln_ln_real @ X3 )
% 5.25/5.55 = ( minus_minus_real @ X3 @ one_one_real ) )
% 5.25/5.55 => ( X3 = one_one_real ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % ln_eq_minus_one
% 5.25/5.55 thf(fact_7396_gbinomial__addition__formula,axiom,
% 5.25/5.55 ! [A: complex,K: nat] :
% 5.25/5.55 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.25/5.55 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_addition_formula
% 5.25/5.55 thf(fact_7397_gbinomial__addition__formula,axiom,
% 5.25/5.55 ! [A: real,K: nat] :
% 5.25/5.55 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.25/5.55 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_addition_formula
% 5.25/5.55 thf(fact_7398_gbinomial__addition__formula,axiom,
% 5.25/5.55 ! [A: rat,K: nat] :
% 5.25/5.55 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.25/5.55 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_addition_formula
% 5.25/5.55 thf(fact_7399_gbinomial__absorb__comp,axiom,
% 5.25/5.55 ! [A: complex,K: nat] :
% 5.25/5.55 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 5.25/5.55 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_absorb_comp
% 5.25/5.55 thf(fact_7400_gbinomial__absorb__comp,axiom,
% 5.25/5.55 ! [A: real,K: nat] :
% 5.25/5.55 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 5.25/5.55 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_absorb_comp
% 5.25/5.55 thf(fact_7401_gbinomial__absorb__comp,axiom,
% 5.25/5.55 ! [A: rat,K: nat] :
% 5.25/5.55 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 5.25/5.55 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_absorb_comp
% 5.25/5.55 thf(fact_7402_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.25/5.55 ! [K: nat,A: real] :
% 5.25/5.55 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 5.25/5.55 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_ge_n_over_k_pow_k
% 5.25/5.55 thf(fact_7403_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.25/5.55 ! [K: nat,A: rat] :
% 5.25/5.55 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 5.25/5.55 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_ge_n_over_k_pow_k
% 5.25/5.55 thf(fact_7404_gbinomial__mult__1_H,axiom,
% 5.25/5.55 ! [A: real,K: nat] :
% 5.25/5.55 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 5.25/5.55 = ( 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 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_mult_1'
% 5.25/5.55 thf(fact_7405_gbinomial__mult__1_H,axiom,
% 5.25/5.55 ! [A: rat,K: nat] :
% 5.25/5.55 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 5.25/5.55 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_mult_1'
% 5.25/5.55 thf(fact_7406_gbinomial__mult__1,axiom,
% 5.25/5.55 ! [A: real,K: nat] :
% 5.25/5.55 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 5.25/5.55 = ( 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 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_mult_1
% 5.25/5.55 thf(fact_7407_gbinomial__mult__1,axiom,
% 5.25/5.55 ! [A: rat,K: nat] :
% 5.25/5.55 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 5.25/5.55 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % gbinomial_mult_1
% 5.25/5.55 thf(fact_7408_prod__int__plus__eq,axiom,
% 5.25/5.55 ! [I2: nat,J2: nat] :
% 5.25/5.55 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J2 ) ) )
% 5.25/5.55 = ( groups1705073143266064639nt_int
% 5.25/5.55 @ ^ [X2: int] : X2
% 5.25/5.55 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J2 ) ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % prod_int_plus_eq
% 5.25/5.55 thf(fact_7409_binomial__ge__n__over__k__pow__k,axiom,
% 5.25/5.55 ! [K: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.55 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) ) ) ).
% 5.25/5.55
% 5.25/5.55 % binomial_ge_n_over_k_pow_k
% 5.25/5.55 thf(fact_7410_binomial__ge__n__over__k__pow__k,axiom,
% 5.25/5.55 ! [K: nat,N: nat] :
% 5.25/5.55 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.55 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_ge_n_over_k_pow_k
% 5.25/5.56 thf(fact_7411_binomial__mono,axiom,
% 5.25/5.56 ! [K: nat,K6: nat,N: nat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ K @ K6 )
% 5.25/5.56 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.25/5.56 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_mono
% 5.25/5.56 thf(fact_7412_binomial__maximum_H,axiom,
% 5.25/5.56 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_maximum'
% 5.25/5.56 thf(fact_7413_binomial__maximum,axiom,
% 5.25/5.56 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_maximum
% 5.25/5.56 thf(fact_7414_binomial__antimono,axiom,
% 5.25/5.56 ! [K: nat,K6: nat,N: nat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ K @ K6 )
% 5.25/5.56 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.25/5.56 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.25/5.56 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_antimono
% 5.25/5.56 thf(fact_7415_ln__2__less__1,axiom,
% 5.25/5.56 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.25/5.56
% 5.25/5.56 % ln_2_less_1
% 5.25/5.56 thf(fact_7416_binomial__le__pow2,axiom,
% 5.25/5.56 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_le_pow2
% 5.25/5.56 thf(fact_7417_choose__reduce__nat,axiom,
% 5.25/5.56 ! [N: nat,K: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.56 => ( ( binomial @ N @ K )
% 5.25/5.56 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_reduce_nat
% 5.25/5.56 thf(fact_7418_times__binomial__minus1__eq,axiom,
% 5.25/5.56 ! [K: nat,N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.56 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 5.25/5.56 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % times_binomial_minus1_eq
% 5.25/5.56 thf(fact_7419_ln__le__minus__one,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.56 => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( minus_minus_real @ X3 @ one_one_real ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % ln_le_minus_one
% 5.25/5.56 thf(fact_7420_ln__diff__le,axiom,
% 5.25/5.56 ! [X3: real,Y: real] :
% 5.25/5.56 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.56 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.56 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X3 @ Y ) @ Y ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % ln_diff_le
% 5.25/5.56 thf(fact_7421_ln__add__one__self__le__self2,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.56 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) ).
% 5.25/5.56
% 5.25/5.56 % ln_add_one_self_le_self2
% 5.25/5.56 thf(fact_7422_ln__realpow,axiom,
% 5.25/5.56 ! [X3: real,N: nat] :
% 5.25/5.56 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.56 => ( ( ln_ln_real @ ( power_power_real @ X3 @ N ) )
% 5.25/5.56 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X3 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % ln_realpow
% 5.25/5.56 thf(fact_7423_Suc__times__gbinomial,axiom,
% 5.25/5.56 ! [K: nat,A: complex] :
% 5.25/5.56 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 5.25/5.56 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % Suc_times_gbinomial
% 5.25/5.56 thf(fact_7424_Suc__times__gbinomial,axiom,
% 5.25/5.56 ! [K: nat,A: real] :
% 5.25/5.56 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 5.25/5.56 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % Suc_times_gbinomial
% 5.25/5.56 thf(fact_7425_Suc__times__gbinomial,axiom,
% 5.25/5.56 ! [K: nat,A: rat] :
% 5.25/5.56 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 5.25/5.56 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % Suc_times_gbinomial
% 5.25/5.56 thf(fact_7426_gbinomial__absorption,axiom,
% 5.25/5.56 ! [K: nat,A: complex] :
% 5.25/5.56 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 5.25/5.56 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_absorption
% 5.25/5.56 thf(fact_7427_gbinomial__absorption,axiom,
% 5.25/5.56 ! [K: nat,A: real] :
% 5.25/5.56 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 5.25/5.56 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_absorption
% 5.25/5.56 thf(fact_7428_gbinomial__absorption,axiom,
% 5.25/5.56 ! [K: nat,A: rat] :
% 5.25/5.56 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 5.25/5.56 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_absorption
% 5.25/5.56 thf(fact_7429_gbinomial__trinomial__revision,axiom,
% 5.25/5.56 ! [K: nat,M: nat,A: real] :
% 5.25/5.56 ( ( ord_less_eq_nat @ K @ M )
% 5.25/5.56 => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.25/5.56 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_trinomial_revision
% 5.25/5.56 thf(fact_7430_gbinomial__trinomial__revision,axiom,
% 5.25/5.56 ! [K: nat,M: nat,A: rat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ K @ M )
% 5.25/5.56 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.25/5.56 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_trinomial_revision
% 5.25/5.56 thf(fact_7431_binomial__less__binomial__Suc,axiom,
% 5.25/5.56 ! [K: nat,N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.56 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_less_binomial_Suc
% 5.25/5.56 thf(fact_7432_binomial__strict__mono,axiom,
% 5.25/5.56 ! [K: nat,K6: nat,N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ K @ K6 )
% 5.25/5.56 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.25/5.56 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_strict_mono
% 5.25/5.56 thf(fact_7433_binomial__strict__antimono,axiom,
% 5.25/5.56 ! [K: nat,K6: nat,N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ K @ K6 )
% 5.25/5.56 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.25/5.56 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.25/5.56 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_strict_antimono
% 5.25/5.56 thf(fact_7434_central__binomial__odd,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.56 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.56 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % central_binomial_odd
% 5.25/5.56 thf(fact_7435_binomial__addition__formula,axiom,
% 5.25/5.56 ! [N: nat,K: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( binomial @ N @ ( suc @ K ) )
% 5.25/5.56 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_addition_formula
% 5.25/5.56 thf(fact_7436_ln__one__minus__pos__upper__bound,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.56 => ( ( ord_less_real @ X3 @ one_one_real )
% 5.25/5.56 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X3 ) ) @ ( uminus_uminus_real @ X3 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % ln_one_minus_pos_upper_bound
% 5.25/5.56 thf(fact_7437_gbinomial__factors,axiom,
% 5.25/5.56 ! [A: complex,K: nat] :
% 5.25/5.56 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.25/5.56 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_factors
% 5.25/5.56 thf(fact_7438_gbinomial__factors,axiom,
% 5.25/5.56 ! [A: real,K: nat] :
% 5.25/5.56 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.25/5.56 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_factors
% 5.25/5.56 thf(fact_7439_gbinomial__factors,axiom,
% 5.25/5.56 ! [A: rat,K: nat] :
% 5.25/5.56 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.25/5.56 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_factors
% 5.25/5.56 thf(fact_7440_gbinomial__rec,axiom,
% 5.25/5.56 ! [A: complex,K: nat] :
% 5.25/5.56 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.25/5.56 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_rec
% 5.25/5.56 thf(fact_7441_gbinomial__rec,axiom,
% 5.25/5.56 ! [A: real,K: nat] :
% 5.25/5.56 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.25/5.56 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_rec
% 5.25/5.56 thf(fact_7442_gbinomial__rec,axiom,
% 5.25/5.56 ! [A: rat,K: nat] :
% 5.25/5.56 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.25/5.56 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_rec
% 5.25/5.56 thf(fact_7443_gbinomial__negated__upper,axiom,
% 5.25/5.56 ( gbinomial_complex
% 5.25/5.56 = ( ^ [A3: complex,K3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A3 ) @ one_one_complex ) @ K3 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_negated_upper
% 5.25/5.56 thf(fact_7444_gbinomial__negated__upper,axiom,
% 5.25/5.56 ( gbinomial_real
% 5.25/5.56 = ( ^ [A3: 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 ) @ A3 ) @ one_one_real ) @ K3 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_negated_upper
% 5.25/5.56 thf(fact_7445_gbinomial__negated__upper,axiom,
% 5.25/5.56 ( gbinomial_rat
% 5.25/5.56 = ( ^ [A3: rat,K3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A3 ) @ one_one_rat ) @ K3 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_negated_upper
% 5.25/5.56 thf(fact_7446_gbinomial__index__swap,axiom,
% 5.25/5.56 ! [K: nat,N: nat] :
% 5.25/5.56 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K ) )
% 5.25/5.56 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_index_swap
% 5.25/5.56 thf(fact_7447_gbinomial__index__swap,axiom,
% 5.25/5.56 ! [K: nat,N: nat] :
% 5.25/5.56 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ K ) )
% 5.25/5.56 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_index_swap
% 5.25/5.56 thf(fact_7448_gbinomial__index__swap,axiom,
% 5.25/5.56 ! [K: nat,N: nat] :
% 5.25/5.56 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ K ) )
% 5.25/5.56 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_index_swap
% 5.25/5.56 thf(fact_7449_set__decode__plus__power__2,axiom,
% 5.25/5.56 ! [N: nat,Z: nat] :
% 5.25/5.56 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 5.25/5.56 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 5.25/5.56 = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % set_decode_plus_power_2
% 5.25/5.56 thf(fact_7450_choose__two,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.56 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_two
% 5.25/5.56 thf(fact_7451_gbinomial__minus,axiom,
% 5.25/5.56 ! [A: complex,K: nat] :
% 5.25/5.56 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 5.25/5.56 = ( 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 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_minus
% 5.25/5.56 thf(fact_7452_gbinomial__minus,axiom,
% 5.25/5.56 ! [A: real,K: nat] :
% 5.25/5.56 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 5.25/5.56 = ( 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 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_minus
% 5.25/5.56 thf(fact_7453_gbinomial__minus,axiom,
% 5.25/5.56 ! [A: rat,K: nat] :
% 5.25/5.56 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 5.25/5.56 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_minus
% 5.25/5.56 thf(fact_7454_gbinomial__reduce__nat,axiom,
% 5.25/5.56 ! [K: nat,A: complex] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.56 => ( ( gbinomial_complex @ A @ K )
% 5.25/5.56 = ( 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 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_reduce_nat
% 5.25/5.56 thf(fact_7455_gbinomial__reduce__nat,axiom,
% 5.25/5.56 ! [K: nat,A: real] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.56 => ( ( gbinomial_real @ A @ K )
% 5.25/5.56 = ( 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 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_reduce_nat
% 5.25/5.56 thf(fact_7456_gbinomial__reduce__nat,axiom,
% 5.25/5.56 ! [K: nat,A: rat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.56 => ( ( gbinomial_rat @ A @ K )
% 5.25/5.56 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_reduce_nat
% 5.25/5.56 thf(fact_7457_sums__if_H,axiom,
% 5.25/5.56 ! [G: nat > real,X3: real] :
% 5.25/5.56 ( ( sums_real @ G @ X3 )
% 5.25/5.56 => ( sums_real
% 5.25/5.56 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.56 @ X3 ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_if'
% 5.25/5.56 thf(fact_7458_sums__if,axiom,
% 5.25/5.56 ! [G: nat > real,X3: real,F: nat > real,Y: real] :
% 5.25/5.56 ( ( sums_real @ G @ X3 )
% 5.25/5.56 => ( ( sums_real @ F @ Y )
% 5.25/5.56 => ( sums_real
% 5.25/5.56 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( F @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.56 @ ( plus_plus_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_if
% 5.25/5.56 thf(fact_7459_and__int_Opinduct,axiom,
% 5.25/5.56 ! [A0: int,A12: int,P: int > int > $o] :
% 5.25/5.56 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.25/5.56 => ( ! [K2: int,L4: int] :
% 5.25/5.56 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 5.25/5.56 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.25/5.56 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.25/5.56 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.25/5.56 => ( P @ K2 @ L4 ) ) )
% 5.25/5.56 => ( P @ A0 @ A12 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % and_int.pinduct
% 5.25/5.56 thf(fact_7460_ln__one__plus__pos__lower__bound,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.56 => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 5.25/5.56 => ( ord_less_eq_real @ ( minus_minus_real @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % ln_one_plus_pos_lower_bound
% 5.25/5.56 thf(fact_7461_gbinomial__sum__up__index,axiom,
% 5.25/5.56 ! [K: nat,N: nat] :
% 5.25/5.56 ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 5.25/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.25/5.56 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_sum_up_index
% 5.25/5.56 thf(fact_7462_gbinomial__sum__up__index,axiom,
% 5.25/5.56 ! [K: nat,N: nat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 5.25/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.25/5.56 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_sum_up_index
% 5.25/5.56 thf(fact_7463_gbinomial__sum__up__index,axiom,
% 5.25/5.56 ! [K: nat,N: nat] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 5.25/5.56 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.25/5.56 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_sum_up_index
% 5.25/5.56 thf(fact_7464_gbinomial__absorption_H,axiom,
% 5.25/5.56 ! [K: nat,A: complex] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.56 => ( ( gbinomial_complex @ A @ K )
% 5.25/5.56 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_absorption'
% 5.25/5.56 thf(fact_7465_gbinomial__absorption_H,axiom,
% 5.25/5.56 ! [K: nat,A: real] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.56 => ( ( gbinomial_real @ A @ K )
% 5.25/5.56 = ( 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 ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_absorption'
% 5.25/5.56 thf(fact_7466_gbinomial__absorption_H,axiom,
% 5.25/5.56 ! [K: nat,A: rat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.56 => ( ( gbinomial_rat @ A @ K )
% 5.25/5.56 = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_absorption'
% 5.25/5.56 thf(fact_7467_artanh__def,axiom,
% 5.25/5.56 ( artanh_real
% 5.25/5.56 = ( ^ [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 ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % artanh_def
% 5.25/5.56 thf(fact_7468_geometric__sums,axiom,
% 5.25/5.56 ! [C: real] :
% 5.25/5.56 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.25/5.56 => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % geometric_sums
% 5.25/5.56 thf(fact_7469_geometric__sums,axiom,
% 5.25/5.56 ! [C: complex] :
% 5.25/5.56 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.25/5.56 => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % geometric_sums
% 5.25/5.56 thf(fact_7470_power__half__series,axiom,
% 5.25/5.56 ( sums_real
% 5.25/5.56 @ ^ [N2: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N2 ) )
% 5.25/5.56 @ one_one_real ) ).
% 5.25/5.56
% 5.25/5.56 % power_half_series
% 5.25/5.56 thf(fact_7471_sums__split__initial__segment,axiom,
% 5.25/5.56 ! [F: nat > real,S: real,N: nat] :
% 5.25/5.56 ( ( sums_real @ F @ S )
% 5.25/5.56 => ( sums_real
% 5.25/5.56 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 5.25/5.56 @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_split_initial_segment
% 5.25/5.56 thf(fact_7472_sums__iff__shift_H,axiom,
% 5.25/5.56 ! [F: nat > real,N: nat,S: real] :
% 5.25/5.56 ( ( sums_real
% 5.25/5.56 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 5.25/5.56 @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.25/5.56 = ( sums_real @ F @ S ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_iff_shift'
% 5.25/5.56 thf(fact_7473_sums__iff__shift,axiom,
% 5.25/5.56 ! [F: nat > real,N: nat,S: real] :
% 5.25/5.56 ( ( sums_real
% 5.25/5.56 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 5.25/5.56 @ S )
% 5.25/5.56 = ( sums_real @ F @ ( plus_plus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_iff_shift
% 5.25/5.56 thf(fact_7474_sums__le,axiom,
% 5.25/5.56 ! [F: nat > real,G: nat > real,S: real,T: real] :
% 5.25/5.56 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.25/5.56 => ( ( sums_real @ F @ S )
% 5.25/5.56 => ( ( sums_real @ G @ T )
% 5.25/5.56 => ( ord_less_eq_real @ S @ T ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_le
% 5.25/5.56 thf(fact_7475_sums__le,axiom,
% 5.25/5.56 ! [F: nat > nat,G: nat > nat,S: nat,T: nat] :
% 5.25/5.56 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.25/5.56 => ( ( sums_nat @ F @ S )
% 5.25/5.56 => ( ( sums_nat @ G @ T )
% 5.25/5.56 => ( ord_less_eq_nat @ S @ T ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_le
% 5.25/5.56 thf(fact_7476_sums__le,axiom,
% 5.25/5.56 ! [F: nat > int,G: nat > int,S: int,T: int] :
% 5.25/5.56 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.25/5.56 => ( ( sums_int @ F @ S )
% 5.25/5.56 => ( ( sums_int @ G @ T )
% 5.25/5.56 => ( ord_less_eq_int @ S @ T ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_le
% 5.25/5.56 thf(fact_7477_sums__mult,axiom,
% 5.25/5.56 ! [F: nat > real,A: real,C: real] :
% 5.25/5.56 ( ( sums_real @ F @ A )
% 5.25/5.56 => ( sums_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.25/5.56 @ ( times_times_real @ C @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_mult
% 5.25/5.56 thf(fact_7478_sums__mult2,axiom,
% 5.25/5.56 ! [F: nat > real,A: real,C: real] :
% 5.25/5.56 ( ( sums_real @ F @ A )
% 5.25/5.56 => ( sums_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 5.25/5.56 @ ( times_times_real @ A @ C ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_mult2
% 5.25/5.56 thf(fact_7479_sums__add,axiom,
% 5.25/5.56 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.25/5.56 ( ( sums_real @ F @ A )
% 5.25/5.56 => ( ( sums_real @ G @ B )
% 5.25/5.56 => ( sums_real
% 5.25/5.56 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.25/5.56 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_add
% 5.25/5.56 thf(fact_7480_sums__add,axiom,
% 5.25/5.56 ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 5.25/5.56 ( ( sums_nat @ F @ A )
% 5.25/5.56 => ( ( sums_nat @ G @ B )
% 5.25/5.56 => ( sums_nat
% 5.25/5.56 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.25/5.56 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_add
% 5.25/5.56 thf(fact_7481_sums__add,axiom,
% 5.25/5.56 ! [F: nat > int,A: int,G: nat > int,B: int] :
% 5.25/5.56 ( ( sums_int @ F @ A )
% 5.25/5.56 => ( ( sums_int @ G @ B )
% 5.25/5.56 => ( sums_int
% 5.25/5.56 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.25/5.56 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_add
% 5.25/5.56 thf(fact_7482_sums__divide,axiom,
% 5.25/5.56 ! [F: nat > complex,A: complex,C: complex] :
% 5.25/5.56 ( ( sums_complex @ F @ A )
% 5.25/5.56 => ( sums_complex
% 5.25/5.56 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C )
% 5.25/5.56 @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_divide
% 5.25/5.56 thf(fact_7483_sums__divide,axiom,
% 5.25/5.56 ! [F: nat > real,A: real,C: real] :
% 5.25/5.56 ( ( sums_real @ F @ A )
% 5.25/5.56 => ( sums_real
% 5.25/5.56 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C )
% 5.25/5.56 @ ( divide_divide_real @ A @ C ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_divide
% 5.25/5.56 thf(fact_7484_sums__mult__iff,axiom,
% 5.25/5.56 ! [C: complex,F: nat > complex,D: complex] :
% 5.25/5.56 ( ( C != zero_zero_complex )
% 5.25/5.56 => ( ( sums_complex
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 5.25/5.56 @ ( times_times_complex @ C @ D ) )
% 5.25/5.56 = ( sums_complex @ F @ D ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_mult_iff
% 5.25/5.56 thf(fact_7485_sums__mult__iff,axiom,
% 5.25/5.56 ! [C: real,F: nat > real,D: real] :
% 5.25/5.56 ( ( C != zero_zero_real )
% 5.25/5.56 => ( ( sums_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.25/5.56 @ ( times_times_real @ C @ D ) )
% 5.25/5.56 = ( sums_real @ F @ D ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_mult_iff
% 5.25/5.56 thf(fact_7486_sums__mult2__iff,axiom,
% 5.25/5.56 ! [C: complex,F: nat > complex,D: complex] :
% 5.25/5.56 ( ( C != zero_zero_complex )
% 5.25/5.56 => ( ( sums_complex
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ C )
% 5.25/5.56 @ ( times_times_complex @ D @ C ) )
% 5.25/5.56 = ( sums_complex @ F @ D ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_mult2_iff
% 5.25/5.56 thf(fact_7487_sums__mult2__iff,axiom,
% 5.25/5.56 ! [C: real,F: nat > real,D: real] :
% 5.25/5.56 ( ( C != zero_zero_real )
% 5.25/5.56 => ( ( sums_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 5.25/5.56 @ ( times_times_real @ D @ C ) )
% 5.25/5.56 = ( sums_real @ F @ D ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_mult2_iff
% 5.25/5.56 thf(fact_7488_sums__mult__D,axiom,
% 5.25/5.56 ! [C: complex,F: nat > complex,A: complex] :
% 5.25/5.56 ( ( sums_complex
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 5.25/5.56 @ A )
% 5.25/5.56 => ( ( C != zero_zero_complex )
% 5.25/5.56 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_mult_D
% 5.25/5.56 thf(fact_7489_sums__mult__D,axiom,
% 5.25/5.56 ! [C: real,F: nat > real,A: real] :
% 5.25/5.56 ( ( sums_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.25/5.56 @ A )
% 5.25/5.56 => ( ( C != zero_zero_real )
% 5.25/5.56 => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_mult_D
% 5.25/5.56 thf(fact_7490_sums__Suc__imp,axiom,
% 5.25/5.56 ! [F: nat > complex,S: complex] :
% 5.25/5.56 ( ( ( F @ zero_zero_nat )
% 5.25/5.56 = zero_zero_complex )
% 5.25/5.56 => ( ( sums_complex
% 5.25/5.56 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.25/5.56 @ S )
% 5.25/5.56 => ( sums_complex @ F @ S ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_Suc_imp
% 5.25/5.56 thf(fact_7491_sums__Suc__imp,axiom,
% 5.25/5.56 ! [F: nat > real,S: real] :
% 5.25/5.56 ( ( ( F @ zero_zero_nat )
% 5.25/5.56 = zero_zero_real )
% 5.25/5.56 => ( ( sums_real
% 5.25/5.56 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.25/5.56 @ S )
% 5.25/5.56 => ( sums_real @ F @ S ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_Suc_imp
% 5.25/5.56 thf(fact_7492_sums__Suc,axiom,
% 5.25/5.56 ! [F: nat > real,L2: real] :
% 5.25/5.56 ( ( sums_real
% 5.25/5.56 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.25/5.56 @ L2 )
% 5.25/5.56 => ( sums_real @ F @ ( plus_plus_real @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_Suc
% 5.25/5.56 thf(fact_7493_sums__Suc,axiom,
% 5.25/5.56 ! [F: nat > nat,L2: nat] :
% 5.25/5.56 ( ( sums_nat
% 5.25/5.56 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.25/5.56 @ L2 )
% 5.25/5.56 => ( sums_nat @ F @ ( plus_plus_nat @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_Suc
% 5.25/5.56 thf(fact_7494_sums__Suc,axiom,
% 5.25/5.56 ! [F: nat > int,L2: int] :
% 5.25/5.56 ( ( sums_int
% 5.25/5.56 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.25/5.56 @ L2 )
% 5.25/5.56 => ( sums_int @ F @ ( plus_plus_int @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_Suc
% 5.25/5.56 thf(fact_7495_sums__Suc__iff,axiom,
% 5.25/5.56 ! [F: nat > real,S: real] :
% 5.25/5.56 ( ( sums_real
% 5.25/5.56 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.25/5.56 @ S )
% 5.25/5.56 = ( sums_real @ F @ ( plus_plus_real @ S @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_Suc_iff
% 5.25/5.56 thf(fact_7496_sums__zero__iff__shift,axiom,
% 5.25/5.56 ! [N: nat,F: nat > complex,S: complex] :
% 5.25/5.56 ( ! [I4: nat] :
% 5.25/5.56 ( ( ord_less_nat @ I4 @ N )
% 5.25/5.56 => ( ( F @ I4 )
% 5.25/5.56 = zero_zero_complex ) )
% 5.25/5.56 => ( ( sums_complex
% 5.25/5.56 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 5.25/5.56 @ S )
% 5.25/5.56 = ( sums_complex @ F @ S ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_zero_iff_shift
% 5.25/5.56 thf(fact_7497_sums__zero__iff__shift,axiom,
% 5.25/5.56 ! [N: nat,F: nat > real,S: real] :
% 5.25/5.56 ( ! [I4: nat] :
% 5.25/5.56 ( ( ord_less_nat @ I4 @ N )
% 5.25/5.56 => ( ( F @ I4 )
% 5.25/5.56 = zero_zero_real ) )
% 5.25/5.56 => ( ( sums_real
% 5.25/5.56 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 5.25/5.56 @ S )
% 5.25/5.56 = ( sums_real @ F @ S ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sums_zero_iff_shift
% 5.25/5.56 thf(fact_7498_powser__sums__if,axiom,
% 5.25/5.56 ! [M: nat,Z: complex] :
% 5.25/5.56 ( sums_complex
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_complex @ ( if_complex @ ( N2 = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N2 ) )
% 5.25/5.56 @ ( power_power_complex @ Z @ M ) ) ).
% 5.25/5.56
% 5.25/5.56 % powser_sums_if
% 5.25/5.56 thf(fact_7499_powser__sums__if,axiom,
% 5.25/5.56 ! [M: nat,Z: real] :
% 5.25/5.56 ( sums_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ ( if_real @ ( N2 = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N2 ) )
% 5.25/5.56 @ ( power_power_real @ Z @ M ) ) ).
% 5.25/5.56
% 5.25/5.56 % powser_sums_if
% 5.25/5.56 thf(fact_7500_powser__sums__if,axiom,
% 5.25/5.56 ! [M: nat,Z: int] :
% 5.25/5.56 ( sums_int
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_int @ ( if_int @ ( N2 = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N2 ) )
% 5.25/5.56 @ ( power_power_int @ Z @ M ) ) ).
% 5.25/5.56
% 5.25/5.56 % powser_sums_if
% 5.25/5.56 thf(fact_7501_ln__series,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.56 => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.25/5.56 => ( ( ln_ln_real @ X3 )
% 5.25/5.56 = ( suminf_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ one_one_real ) @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % ln_series
% 5.25/5.56 thf(fact_7502_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.56 => ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.56 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.25/5.56 thf(fact_7503_upto_Opinduct,axiom,
% 5.25/5.56 ! [A0: int,A12: int,P: int > int > $o] :
% 5.25/5.56 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.25/5.56 => ( ! [I4: int,J: int] :
% 5.25/5.56 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I4 @ J ) )
% 5.25/5.56 => ( ( ( ord_less_eq_int @ I4 @ J )
% 5.25/5.56 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) @ J ) )
% 5.25/5.56 => ( P @ I4 @ J ) ) )
% 5.25/5.56 => ( P @ A0 @ A12 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % upto.pinduct
% 5.25/5.56 thf(fact_7504_tanh__ln__real,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.56 => ( ( tanh_real @ ( ln_ln_real @ X3 ) )
% 5.25/5.56 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % tanh_ln_real
% 5.25/5.56 thf(fact_7505_gbinomial__partial__row__sum,axiom,
% 5.25/5.56 ! [A: complex,M: nat] :
% 5.25/5.56 ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( 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 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_partial_row_sum
% 5.25/5.56 thf(fact_7506_gbinomial__partial__row__sum,axiom,
% 5.25/5.56 ! [A: rat,M: nat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_partial_row_sum
% 5.25/5.56 thf(fact_7507_gbinomial__partial__row__sum,axiom,
% 5.25/5.56 ! [A: real,M: nat] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( 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 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_partial_row_sum
% 5.25/5.56 thf(fact_7508_abs__idempotent,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.25/5.56 = ( abs_abs_real @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_idempotent
% 5.25/5.56 thf(fact_7509_abs__idempotent,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.25/5.56 = ( abs_abs_int @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_idempotent
% 5.25/5.56 thf(fact_7510_abs__idempotent,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.25/5.56 = ( abs_abs_Code_integer @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_idempotent
% 5.25/5.56 thf(fact_7511_abs__abs,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.25/5.56 = ( abs_abs_real @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_abs
% 5.25/5.56 thf(fact_7512_abs__abs,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.25/5.56 = ( abs_abs_int @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_abs
% 5.25/5.56 thf(fact_7513_abs__abs,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.25/5.56 = ( abs_abs_Code_integer @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_abs
% 5.25/5.56 thf(fact_7514_atMost__eq__iff,axiom,
% 5.25/5.56 ! [X3: nat,Y: nat] :
% 5.25/5.56 ( ( ( set_ord_atMost_nat @ X3 )
% 5.25/5.56 = ( set_ord_atMost_nat @ Y ) )
% 5.25/5.56 = ( X3 = Y ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_eq_iff
% 5.25/5.56 thf(fact_7515_atMost__eq__iff,axiom,
% 5.25/5.56 ! [X3: int,Y: int] :
% 5.25/5.56 ( ( ( set_ord_atMost_int @ X3 )
% 5.25/5.56 = ( set_ord_atMost_int @ Y ) )
% 5.25/5.56 = ( X3 = Y ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_eq_iff
% 5.25/5.56 thf(fact_7516_abs__zero,axiom,
% 5.25/5.56 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.25/5.56 = zero_z3403309356797280102nteger ) ).
% 5.25/5.56
% 5.25/5.56 % abs_zero
% 5.25/5.56 thf(fact_7517_abs__zero,axiom,
% 5.25/5.56 ( ( abs_abs_real @ zero_zero_real )
% 5.25/5.56 = zero_zero_real ) ).
% 5.25/5.56
% 5.25/5.56 % abs_zero
% 5.25/5.56 thf(fact_7518_abs__zero,axiom,
% 5.25/5.56 ( ( abs_abs_rat @ zero_zero_rat )
% 5.25/5.56 = zero_zero_rat ) ).
% 5.25/5.56
% 5.25/5.56 % abs_zero
% 5.25/5.56 thf(fact_7519_abs__zero,axiom,
% 5.25/5.56 ( ( abs_abs_int @ zero_zero_int )
% 5.25/5.56 = zero_zero_int ) ).
% 5.25/5.56
% 5.25/5.56 % abs_zero
% 5.25/5.56 thf(fact_7520_abs__eq__0,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( ( abs_abs_Code_integer @ A )
% 5.25/5.56 = zero_z3403309356797280102nteger )
% 5.25/5.56 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_0
% 5.25/5.56 thf(fact_7521_abs__eq__0,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( ( abs_abs_real @ A )
% 5.25/5.56 = zero_zero_real )
% 5.25/5.56 = ( A = zero_zero_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_0
% 5.25/5.56 thf(fact_7522_abs__eq__0,axiom,
% 5.25/5.56 ! [A: rat] :
% 5.25/5.56 ( ( ( abs_abs_rat @ A )
% 5.25/5.56 = zero_zero_rat )
% 5.25/5.56 = ( A = zero_zero_rat ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_0
% 5.25/5.56 thf(fact_7523_abs__eq__0,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( ( abs_abs_int @ A )
% 5.25/5.56 = zero_zero_int )
% 5.25/5.56 = ( A = zero_zero_int ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_0
% 5.25/5.56 thf(fact_7524_abs__0__eq,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( zero_z3403309356797280102nteger
% 5.25/5.56 = ( abs_abs_Code_integer @ A ) )
% 5.25/5.56 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_0_eq
% 5.25/5.56 thf(fact_7525_abs__0__eq,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( zero_zero_real
% 5.25/5.56 = ( abs_abs_real @ A ) )
% 5.25/5.56 = ( A = zero_zero_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_0_eq
% 5.25/5.56 thf(fact_7526_abs__0__eq,axiom,
% 5.25/5.56 ! [A: rat] :
% 5.25/5.56 ( ( zero_zero_rat
% 5.25/5.56 = ( abs_abs_rat @ A ) )
% 5.25/5.56 = ( A = zero_zero_rat ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_0_eq
% 5.25/5.56 thf(fact_7527_abs__0__eq,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( zero_zero_int
% 5.25/5.56 = ( abs_abs_int @ A ) )
% 5.25/5.56 = ( A = zero_zero_int ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_0_eq
% 5.25/5.56 thf(fact_7528_abs__0,axiom,
% 5.25/5.56 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.25/5.56 = zero_z3403309356797280102nteger ) ).
% 5.25/5.56
% 5.25/5.56 % abs_0
% 5.25/5.56 thf(fact_7529_abs__0,axiom,
% 5.25/5.56 ( ( abs_abs_complex @ zero_zero_complex )
% 5.25/5.56 = zero_zero_complex ) ).
% 5.25/5.56
% 5.25/5.56 % abs_0
% 5.25/5.56 thf(fact_7530_abs__0,axiom,
% 5.25/5.56 ( ( abs_abs_real @ zero_zero_real )
% 5.25/5.56 = zero_zero_real ) ).
% 5.25/5.56
% 5.25/5.56 % abs_0
% 5.25/5.56 thf(fact_7531_abs__0,axiom,
% 5.25/5.56 ( ( abs_abs_rat @ zero_zero_rat )
% 5.25/5.56 = zero_zero_rat ) ).
% 5.25/5.56
% 5.25/5.56 % abs_0
% 5.25/5.56 thf(fact_7532_abs__0,axiom,
% 5.25/5.56 ( ( abs_abs_int @ zero_zero_int )
% 5.25/5.56 = zero_zero_int ) ).
% 5.25/5.56
% 5.25/5.56 % abs_0
% 5.25/5.56 thf(fact_7533_abs__numeral,axiom,
% 5.25/5.56 ! [N: num] :
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.25/5.56 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_numeral
% 5.25/5.56 thf(fact_7534_abs__numeral,axiom,
% 5.25/5.56 ! [N: num] :
% 5.25/5.56 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 5.25/5.56 = ( numeral_numeral_real @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_numeral
% 5.25/5.56 thf(fact_7535_abs__numeral,axiom,
% 5.25/5.56 ! [N: num] :
% 5.25/5.56 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 5.25/5.56 = ( numeral_numeral_rat @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_numeral
% 5.25/5.56 thf(fact_7536_abs__numeral,axiom,
% 5.25/5.56 ! [N: num] :
% 5.25/5.56 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 5.25/5.56 = ( numeral_numeral_int @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_numeral
% 5.25/5.56 thf(fact_7537_abs__mult__self__eq,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.25/5.56 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult_self_eq
% 5.25/5.56 thf(fact_7538_abs__mult__self__eq,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.25/5.56 = ( times_times_real @ A @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult_self_eq
% 5.25/5.56 thf(fact_7539_abs__mult__self__eq,axiom,
% 5.25/5.56 ! [A: rat] :
% 5.25/5.56 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.25/5.56 = ( times_times_rat @ A @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult_self_eq
% 5.25/5.56 thf(fact_7540_abs__mult__self__eq,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.25/5.56 = ( times_times_int @ A @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult_self_eq
% 5.25/5.56 thf(fact_7541_abs__1,axiom,
% 5.25/5.56 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.25/5.56 = one_one_Code_integer ) ).
% 5.25/5.56
% 5.25/5.56 % abs_1
% 5.25/5.56 thf(fact_7542_abs__1,axiom,
% 5.25/5.56 ( ( abs_abs_complex @ one_one_complex )
% 5.25/5.56 = one_one_complex ) ).
% 5.25/5.56
% 5.25/5.56 % abs_1
% 5.25/5.56 thf(fact_7543_abs__1,axiom,
% 5.25/5.56 ( ( abs_abs_real @ one_one_real )
% 5.25/5.56 = one_one_real ) ).
% 5.25/5.56
% 5.25/5.56 % abs_1
% 5.25/5.56 thf(fact_7544_abs__1,axiom,
% 5.25/5.56 ( ( abs_abs_rat @ one_one_rat )
% 5.25/5.56 = one_one_rat ) ).
% 5.25/5.56
% 5.25/5.56 % abs_1
% 5.25/5.56 thf(fact_7545_abs__1,axiom,
% 5.25/5.56 ( ( abs_abs_int @ one_one_int )
% 5.25/5.56 = one_one_int ) ).
% 5.25/5.56
% 5.25/5.56 % abs_1
% 5.25/5.56 thf(fact_7546_abs__add__abs,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] :
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.25/5.56 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_add_abs
% 5.25/5.56 thf(fact_7547_abs__add__abs,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.25/5.56 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_add_abs
% 5.25/5.56 thf(fact_7548_abs__add__abs,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.25/5.56 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_add_abs
% 5.25/5.56 thf(fact_7549_abs__add__abs,axiom,
% 5.25/5.56 ! [A: int,B: int] :
% 5.25/5.56 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.25/5.56 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_add_abs
% 5.25/5.56 thf(fact_7550_abs__divide,axiom,
% 5.25/5.56 ! [A: complex,B: complex] :
% 5.25/5.56 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.25/5.56 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_divide
% 5.25/5.56 thf(fact_7551_abs__divide,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.25/5.56 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_divide
% 5.25/5.56 thf(fact_7552_abs__divide,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.25/5.56 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_divide
% 5.25/5.56 thf(fact_7553_abs__minus__cancel,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.25/5.56 = ( abs_abs_int @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus_cancel
% 5.25/5.56 thf(fact_7554_abs__minus__cancel,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.25/5.56 = ( abs_abs_real @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus_cancel
% 5.25/5.56 thf(fact_7555_abs__minus__cancel,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.25/5.56 = ( abs_abs_Code_integer @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus_cancel
% 5.25/5.56 thf(fact_7556_abs__minus__cancel,axiom,
% 5.25/5.56 ! [A: rat] :
% 5.25/5.56 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.25/5.56 = ( abs_abs_rat @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus_cancel
% 5.25/5.56 thf(fact_7557_abs__minus,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.25/5.56 = ( abs_abs_int @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus
% 5.25/5.56 thf(fact_7558_abs__minus,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.25/5.56 = ( abs_abs_real @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus
% 5.25/5.56 thf(fact_7559_abs__minus,axiom,
% 5.25/5.56 ! [A: complex] :
% 5.25/5.56 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.25/5.56 = ( abs_abs_complex @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus
% 5.25/5.56 thf(fact_7560_abs__minus,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.25/5.56 = ( abs_abs_Code_integer @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus
% 5.25/5.56 thf(fact_7561_abs__minus,axiom,
% 5.25/5.56 ! [A: rat] :
% 5.25/5.56 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.25/5.56 = ( abs_abs_rat @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus
% 5.25/5.56 thf(fact_7562_dvd__abs__iff,axiom,
% 5.25/5.56 ! [M: real,K: real] :
% 5.25/5.56 ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 5.25/5.56 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % dvd_abs_iff
% 5.25/5.56 thf(fact_7563_dvd__abs__iff,axiom,
% 5.25/5.56 ! [M: int,K: int] :
% 5.25/5.56 ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 5.25/5.56 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % dvd_abs_iff
% 5.25/5.56 thf(fact_7564_dvd__abs__iff,axiom,
% 5.25/5.56 ! [M: code_integer,K: code_integer] :
% 5.25/5.56 ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 5.25/5.56 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % dvd_abs_iff
% 5.25/5.56 thf(fact_7565_abs__dvd__iff,axiom,
% 5.25/5.56 ! [M: real,K: real] :
% 5.25/5.56 ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 5.25/5.56 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_dvd_iff
% 5.25/5.56 thf(fact_7566_abs__dvd__iff,axiom,
% 5.25/5.56 ! [M: int,K: int] :
% 5.25/5.56 ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 5.25/5.56 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_dvd_iff
% 5.25/5.56 thf(fact_7567_abs__dvd__iff,axiom,
% 5.25/5.56 ! [M: code_integer,K: code_integer] :
% 5.25/5.56 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 5.25/5.56 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_dvd_iff
% 5.25/5.56 thf(fact_7568_atMost__iff,axiom,
% 5.25/5.56 ! [I2: real,K: real] :
% 5.25/5.56 ( ( member_real @ I2 @ ( set_ord_atMost_real @ K ) )
% 5.25/5.56 = ( ord_less_eq_real @ I2 @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_iff
% 5.25/5.56 thf(fact_7569_atMost__iff,axiom,
% 5.25/5.56 ! [I2: set_int,K: set_int] :
% 5.25/5.56 ( ( member_set_int @ I2 @ ( set_or58775011639299419et_int @ K ) )
% 5.25/5.56 = ( ord_less_eq_set_int @ I2 @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_iff
% 5.25/5.56 thf(fact_7570_atMost__iff,axiom,
% 5.25/5.56 ! [I2: rat,K: rat] :
% 5.25/5.56 ( ( member_rat @ I2 @ ( set_ord_atMost_rat @ K ) )
% 5.25/5.56 = ( ord_less_eq_rat @ I2 @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_iff
% 5.25/5.56 thf(fact_7571_atMost__iff,axiom,
% 5.25/5.56 ! [I2: num,K: num] :
% 5.25/5.56 ( ( member_num @ I2 @ ( set_ord_atMost_num @ K ) )
% 5.25/5.56 = ( ord_less_eq_num @ I2 @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_iff
% 5.25/5.56 thf(fact_7572_atMost__iff,axiom,
% 5.25/5.56 ! [I2: nat,K: nat] :
% 5.25/5.56 ( ( member_nat @ I2 @ ( set_ord_atMost_nat @ K ) )
% 5.25/5.56 = ( ord_less_eq_nat @ I2 @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_iff
% 5.25/5.56 thf(fact_7573_atMost__iff,axiom,
% 5.25/5.56 ! [I2: int,K: int] :
% 5.25/5.56 ( ( member_int @ I2 @ ( set_ord_atMost_int @ K ) )
% 5.25/5.56 = ( ord_less_eq_int @ I2 @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_iff
% 5.25/5.56 thf(fact_7574_abs__of__nat,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.25/5.56 = ( semiri4939895301339042750nteger @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_nat
% 5.25/5.56 thf(fact_7575_abs__of__nat,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.25/5.56 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_nat
% 5.25/5.56 thf(fact_7576_abs__of__nat,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.25/5.56 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_nat
% 5.25/5.56 thf(fact_7577_abs__of__nat,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.25/5.56 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_nat
% 5.25/5.56 thf(fact_7578_abs__bool__eq,axiom,
% 5.25/5.56 ! [P: $o] :
% 5.25/5.56 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.25/5.56 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_bool_eq
% 5.25/5.56 thf(fact_7579_abs__bool__eq,axiom,
% 5.25/5.56 ! [P: $o] :
% 5.25/5.56 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.25/5.56 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_bool_eq
% 5.25/5.56 thf(fact_7580_abs__bool__eq,axiom,
% 5.25/5.56 ! [P: $o] :
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 5.25/5.56 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_bool_eq
% 5.25/5.56 thf(fact_7581_tanh__real__le__iff,axiom,
% 5.25/5.56 ! [X3: real,Y: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( tanh_real @ X3 ) @ ( tanh_real @ Y ) )
% 5.25/5.56 = ( ord_less_eq_real @ X3 @ Y ) ) ).
% 5.25/5.56
% 5.25/5.56 % tanh_real_le_iff
% 5.25/5.56 thf(fact_7582_abs__le__zero__iff,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.25/5.56 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_zero_iff
% 5.25/5.56 thf(fact_7583_abs__le__zero__iff,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.25/5.56 = ( A = zero_zero_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_zero_iff
% 5.25/5.56 thf(fact_7584_abs__le__zero__iff,axiom,
% 5.25/5.56 ! [A: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.25/5.56 = ( A = zero_zero_rat ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_zero_iff
% 5.25/5.56 thf(fact_7585_abs__le__zero__iff,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.25/5.56 = ( A = zero_zero_int ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_zero_iff
% 5.25/5.56 thf(fact_7586_abs__le__self__iff,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.25/5.56 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_self_iff
% 5.25/5.56 thf(fact_7587_abs__le__self__iff,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.25/5.56 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_self_iff
% 5.25/5.56 thf(fact_7588_abs__le__self__iff,axiom,
% 5.25/5.56 ! [A: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.25/5.56 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_self_iff
% 5.25/5.56 thf(fact_7589_abs__le__self__iff,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.25/5.56 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_self_iff
% 5.25/5.56 thf(fact_7590_abs__of__nonneg,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.56 => ( ( abs_abs_Code_integer @ A )
% 5.25/5.56 = A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_nonneg
% 5.25/5.56 thf(fact_7591_abs__of__nonneg,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.56 => ( ( abs_abs_real @ A )
% 5.25/5.56 = A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_nonneg
% 5.25/5.56 thf(fact_7592_abs__of__nonneg,axiom,
% 5.25/5.56 ! [A: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.56 => ( ( abs_abs_rat @ A )
% 5.25/5.56 = A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_nonneg
% 5.25/5.56 thf(fact_7593_abs__of__nonneg,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.56 => ( ( abs_abs_int @ A )
% 5.25/5.56 = A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_nonneg
% 5.25/5.56 thf(fact_7594_zero__less__abs__iff,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.25/5.56 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_less_abs_iff
% 5.25/5.56 thf(fact_7595_zero__less__abs__iff,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.25/5.56 = ( A != zero_zero_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_less_abs_iff
% 5.25/5.56 thf(fact_7596_zero__less__abs__iff,axiom,
% 5.25/5.56 ! [A: rat] :
% 5.25/5.56 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.25/5.56 = ( A != zero_zero_rat ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_less_abs_iff
% 5.25/5.56 thf(fact_7597_zero__less__abs__iff,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.25/5.56 = ( A != zero_zero_int ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_less_abs_iff
% 5.25/5.56 thf(fact_7598_abs__neg__numeral,axiom,
% 5.25/5.56 ! [N: num] :
% 5.25/5.56 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.56 = ( numeral_numeral_int @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_neg_numeral
% 5.25/5.56 thf(fact_7599_abs__neg__numeral,axiom,
% 5.25/5.56 ! [N: num] :
% 5.25/5.56 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.25/5.56 = ( numeral_numeral_real @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_neg_numeral
% 5.25/5.56 thf(fact_7600_abs__neg__numeral,axiom,
% 5.25/5.56 ! [N: num] :
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.25/5.56 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_neg_numeral
% 5.25/5.56 thf(fact_7601_abs__neg__numeral,axiom,
% 5.25/5.56 ! [N: num] :
% 5.25/5.56 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.25/5.56 = ( numeral_numeral_rat @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_neg_numeral
% 5.25/5.56 thf(fact_7602_abs__neg__one,axiom,
% 5.25/5.56 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.56 = one_one_int ) ).
% 5.25/5.56
% 5.25/5.56 % abs_neg_one
% 5.25/5.56 thf(fact_7603_abs__neg__one,axiom,
% 5.25/5.56 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.56 = one_one_real ) ).
% 5.25/5.56
% 5.25/5.56 % abs_neg_one
% 5.25/5.56 thf(fact_7604_abs__neg__one,axiom,
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.25/5.56 = one_one_Code_integer ) ).
% 5.25/5.56
% 5.25/5.56 % abs_neg_one
% 5.25/5.56 thf(fact_7605_abs__neg__one,axiom,
% 5.25/5.56 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.56 = one_one_rat ) ).
% 5.25/5.56
% 5.25/5.56 % abs_neg_one
% 5.25/5.56 thf(fact_7606_abs__power__minus,axiom,
% 5.25/5.56 ! [A: int,N: nat] :
% 5.25/5.56 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.25/5.56 = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_power_minus
% 5.25/5.56 thf(fact_7607_abs__power__minus,axiom,
% 5.25/5.56 ! [A: real,N: nat] :
% 5.25/5.56 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.25/5.56 = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_power_minus
% 5.25/5.56 thf(fact_7608_abs__power__minus,axiom,
% 5.25/5.56 ! [A: code_integer,N: nat] :
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.25/5.56 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_power_minus
% 5.25/5.56 thf(fact_7609_abs__power__minus,axiom,
% 5.25/5.56 ! [A: rat,N: nat] :
% 5.25/5.56 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.25/5.56 = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_power_minus
% 5.25/5.56 thf(fact_7610_atMost__subset__iff,axiom,
% 5.25/5.56 ! [X3: set_int,Y: set_int] :
% 5.25/5.56 ( ( ord_le4403425263959731960et_int @ ( set_or58775011639299419et_int @ X3 ) @ ( set_or58775011639299419et_int @ Y ) )
% 5.25/5.56 = ( ord_less_eq_set_int @ X3 @ Y ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_subset_iff
% 5.25/5.56 thf(fact_7611_atMost__subset__iff,axiom,
% 5.25/5.56 ! [X3: rat,Y: rat] :
% 5.25/5.56 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X3 ) @ ( set_ord_atMost_rat @ Y ) )
% 5.25/5.56 = ( ord_less_eq_rat @ X3 @ Y ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_subset_iff
% 5.25/5.56 thf(fact_7612_atMost__subset__iff,axiom,
% 5.25/5.56 ! [X3: num,Y: num] :
% 5.25/5.56 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X3 ) @ ( set_ord_atMost_num @ Y ) )
% 5.25/5.56 = ( ord_less_eq_num @ X3 @ Y ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_subset_iff
% 5.25/5.56 thf(fact_7613_atMost__subset__iff,axiom,
% 5.25/5.56 ! [X3: nat,Y: nat] :
% 5.25/5.56 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X3 ) @ ( set_ord_atMost_nat @ Y ) )
% 5.25/5.56 = ( ord_less_eq_nat @ X3 @ Y ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_subset_iff
% 5.25/5.56 thf(fact_7614_atMost__subset__iff,axiom,
% 5.25/5.56 ! [X3: int,Y: int] :
% 5.25/5.56 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X3 ) @ ( set_ord_atMost_int @ Y ) )
% 5.25/5.56 = ( ord_less_eq_int @ X3 @ Y ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_subset_iff
% 5.25/5.56 thf(fact_7615_tanh__real__nonneg__iff,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X3 ) )
% 5.25/5.56 = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 5.25/5.56
% 5.25/5.56 % tanh_real_nonneg_iff
% 5.25/5.56 thf(fact_7616_tanh__real__nonpos__iff,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( tanh_real @ X3 ) @ zero_zero_real )
% 5.25/5.56 = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % tanh_real_nonpos_iff
% 5.25/5.56 thf(fact_7617_sum__abs,axiom,
% 5.25/5.56 ! [F: int > int,A2: set_int] :
% 5.25/5.56 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.25/5.56 @ ( groups4538972089207619220nt_int
% 5.25/5.56 @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 5.25/5.56 @ A2 ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_abs
% 5.25/5.56 thf(fact_7618_sum__abs,axiom,
% 5.25/5.56 ! [F: nat > real,A2: set_nat] :
% 5.25/5.56 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 5.25/5.56 @ A2 ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_abs
% 5.25/5.56 thf(fact_7619_zero__le__divide__abs__iff,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.25/5.56 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.56 | ( B = zero_zero_real ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_le_divide_abs_iff
% 5.25/5.56 thf(fact_7620_zero__le__divide__abs__iff,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.25/5.56 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.56 | ( B = zero_zero_rat ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_le_divide_abs_iff
% 5.25/5.56 thf(fact_7621_divide__le__0__abs__iff,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.25/5.56 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.56 | ( B = zero_zero_real ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % divide_le_0_abs_iff
% 5.25/5.56 thf(fact_7622_divide__le__0__abs__iff,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.25/5.56 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.56 | ( B = zero_zero_rat ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % divide_le_0_abs_iff
% 5.25/5.56 thf(fact_7623_abs__of__nonpos,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.56 => ( ( abs_abs_real @ A )
% 5.25/5.56 = ( uminus_uminus_real @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_nonpos
% 5.25/5.56 thf(fact_7624_abs__of__nonpos,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.25/5.56 => ( ( abs_abs_Code_integer @ A )
% 5.25/5.56 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_nonpos
% 5.25/5.56 thf(fact_7625_abs__of__nonpos,axiom,
% 5.25/5.56 ! [A: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.56 => ( ( abs_abs_rat @ A )
% 5.25/5.56 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_nonpos
% 5.25/5.56 thf(fact_7626_abs__of__nonpos,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.56 => ( ( abs_abs_int @ A )
% 5.25/5.56 = ( uminus_uminus_int @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_nonpos
% 5.25/5.56 thf(fact_7627_Icc__subset__Iic__iff,axiom,
% 5.25/5.56 ! [L2: set_int,H2: set_int,H3: set_int] :
% 5.25/5.56 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ L2 @ H2 ) @ ( set_or58775011639299419et_int @ H3 ) )
% 5.25/5.56 = ( ~ ( ord_less_eq_set_int @ L2 @ H2 )
% 5.25/5.56 | ( ord_less_eq_set_int @ H2 @ H3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % Icc_subset_Iic_iff
% 5.25/5.56 thf(fact_7628_Icc__subset__Iic__iff,axiom,
% 5.25/5.56 ! [L2: rat,H2: rat,H3: rat] :
% 5.25/5.56 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L2 @ H2 ) @ ( set_ord_atMost_rat @ H3 ) )
% 5.25/5.56 = ( ~ ( ord_less_eq_rat @ L2 @ H2 )
% 5.25/5.56 | ( ord_less_eq_rat @ H2 @ H3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % Icc_subset_Iic_iff
% 5.25/5.56 thf(fact_7629_Icc__subset__Iic__iff,axiom,
% 5.25/5.56 ! [L2: num,H2: num,H3: num] :
% 5.25/5.56 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L2 @ H2 ) @ ( set_ord_atMost_num @ H3 ) )
% 5.25/5.56 = ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 5.25/5.56 | ( ord_less_eq_num @ H2 @ H3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % Icc_subset_Iic_iff
% 5.25/5.56 thf(fact_7630_Icc__subset__Iic__iff,axiom,
% 5.25/5.56 ! [L2: nat,H2: nat,H3: nat] :
% 5.25/5.56 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L2 @ H2 ) @ ( set_ord_atMost_nat @ H3 ) )
% 5.25/5.56 = ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 5.25/5.56 | ( ord_less_eq_nat @ H2 @ H3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % Icc_subset_Iic_iff
% 5.25/5.56 thf(fact_7631_Icc__subset__Iic__iff,axiom,
% 5.25/5.56 ! [L2: int,H2: int,H3: int] :
% 5.25/5.56 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L2 @ H2 ) @ ( set_ord_atMost_int @ H3 ) )
% 5.25/5.56 = ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 5.25/5.56 | ( ord_less_eq_int @ H2 @ H3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % Icc_subset_Iic_iff
% 5.25/5.56 thf(fact_7632_Icc__subset__Iic__iff,axiom,
% 5.25/5.56 ! [L2: real,H2: real,H3: real] :
% 5.25/5.56 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L2 @ H2 ) @ ( set_ord_atMost_real @ H3 ) )
% 5.25/5.56 = ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 5.25/5.56 | ( ord_less_eq_real @ H2 @ H3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % Icc_subset_Iic_iff
% 5.25/5.56 thf(fact_7633_sum_OatMost__Suc,axiom,
% 5.25/5.56 ! [G: nat > rat,N: nat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.atMost_Suc
% 5.25/5.56 thf(fact_7634_sum_OatMost__Suc,axiom,
% 5.25/5.56 ! [G: nat > int,N: nat] :
% 5.25/5.56 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.atMost_Suc
% 5.25/5.56 thf(fact_7635_sum_OatMost__Suc,axiom,
% 5.25/5.56 ! [G: nat > nat,N: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.atMost_Suc
% 5.25/5.56 thf(fact_7636_sum_OatMost__Suc,axiom,
% 5.25/5.56 ! [G: nat > real,N: nat] :
% 5.25/5.56 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.atMost_Suc
% 5.25/5.56 thf(fact_7637_prod_OatMost__Suc,axiom,
% 5.25/5.56 ! [G: nat > real,N: nat] :
% 5.25/5.56 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.atMost_Suc
% 5.25/5.56 thf(fact_7638_prod_OatMost__Suc,axiom,
% 5.25/5.56 ! [G: nat > rat,N: nat] :
% 5.25/5.56 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.atMost_Suc
% 5.25/5.56 thf(fact_7639_prod_OatMost__Suc,axiom,
% 5.25/5.56 ! [G: nat > int,N: nat] :
% 5.25/5.56 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.atMost_Suc
% 5.25/5.56 thf(fact_7640_prod_OatMost__Suc,axiom,
% 5.25/5.56 ! [G: nat > nat,N: nat] :
% 5.25/5.56 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.atMost_Suc
% 5.25/5.56 thf(fact_7641_artanh__minus__real,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.56 => ( ( artanh_real @ ( uminus_uminus_real @ X3 ) )
% 5.25/5.56 = ( uminus_uminus_real @ ( artanh_real @ X3 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % artanh_minus_real
% 5.25/5.56 thf(fact_7642_sum__abs__ge__zero,axiom,
% 5.25/5.56 ! [F: int > int,A2: set_int] :
% 5.25/5.56 ( ord_less_eq_int @ zero_zero_int
% 5.25/5.56 @ ( groups4538972089207619220nt_int
% 5.25/5.56 @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 5.25/5.56 @ A2 ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_abs_ge_zero
% 5.25/5.56 thf(fact_7643_sum__abs__ge__zero,axiom,
% 5.25/5.56 ! [F: nat > real,A2: set_nat] :
% 5.25/5.56 ( ord_less_eq_real @ zero_zero_real
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 5.25/5.56 @ A2 ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_abs_ge_zero
% 5.25/5.56 thf(fact_7644_atMost__0,axiom,
% 5.25/5.56 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 5.25/5.56 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_0
% 5.25/5.56 thf(fact_7645_zero__less__power__abs__iff,axiom,
% 5.25/5.56 ! [A: code_integer,N: nat] :
% 5.25/5.56 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 5.25/5.56 = ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.56 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_less_power_abs_iff
% 5.25/5.56 thf(fact_7646_zero__less__power__abs__iff,axiom,
% 5.25/5.56 ! [A: real,N: nat] :
% 5.25/5.56 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.25/5.56 = ( ( A != zero_zero_real )
% 5.25/5.56 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_less_power_abs_iff
% 5.25/5.56 thf(fact_7647_zero__less__power__abs__iff,axiom,
% 5.25/5.56 ! [A: rat,N: nat] :
% 5.25/5.56 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 5.25/5.56 = ( ( A != zero_zero_rat )
% 5.25/5.56 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_less_power_abs_iff
% 5.25/5.56 thf(fact_7648_zero__less__power__abs__iff,axiom,
% 5.25/5.56 ! [A: int,N: nat] :
% 5.25/5.56 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 5.25/5.56 = ( ( A != zero_zero_int )
% 5.25/5.56 | ( N = zero_zero_nat ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_less_power_abs_iff
% 5.25/5.56 thf(fact_7649_abs__power2,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.56 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_power2
% 5.25/5.56 thf(fact_7650_abs__power2,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.56 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_power2
% 5.25/5.56 thf(fact_7651_abs__power2,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.56 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_power2
% 5.25/5.56 thf(fact_7652_power2__abs,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.56 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power2_abs
% 5.25/5.56 thf(fact_7653_power2__abs,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.56 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power2_abs
% 5.25/5.56 thf(fact_7654_power2__abs,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.56 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power2_abs
% 5.25/5.56 thf(fact_7655_powser__zero,axiom,
% 5.25/5.56 ! [F: nat > complex] :
% 5.25/5.56 ( ( suminf_complex
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) )
% 5.25/5.56 = ( F @ zero_zero_nat ) ) ).
% 5.25/5.56
% 5.25/5.56 % powser_zero
% 5.25/5.56 thf(fact_7656_powser__zero,axiom,
% 5.25/5.56 ! [F: nat > real] :
% 5.25/5.56 ( ( suminf_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) )
% 5.25/5.56 = ( F @ zero_zero_nat ) ) ).
% 5.25/5.56
% 5.25/5.56 % powser_zero
% 5.25/5.56 thf(fact_7657_power__even__abs__numeral,axiom,
% 5.25/5.56 ! [W: num,A: code_integer] :
% 5.25/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.56 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.56 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power_even_abs_numeral
% 5.25/5.56 thf(fact_7658_power__even__abs__numeral,axiom,
% 5.25/5.56 ! [W: num,A: real] :
% 5.25/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.56 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.56 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power_even_abs_numeral
% 5.25/5.56 thf(fact_7659_power__even__abs__numeral,axiom,
% 5.25/5.56 ! [W: num,A: int] :
% 5.25/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.56 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.56 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power_even_abs_numeral
% 5.25/5.56 thf(fact_7660_abs__eq__iff,axiom,
% 5.25/5.56 ! [X3: int,Y: int] :
% 5.25/5.56 ( ( ( abs_abs_int @ X3 )
% 5.25/5.56 = ( abs_abs_int @ Y ) )
% 5.25/5.56 = ( ( X3 = Y )
% 5.25/5.56 | ( X3
% 5.25/5.56 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_iff
% 5.25/5.56 thf(fact_7661_abs__eq__iff,axiom,
% 5.25/5.56 ! [X3: real,Y: real] :
% 5.25/5.56 ( ( ( abs_abs_real @ X3 )
% 5.25/5.56 = ( abs_abs_real @ Y ) )
% 5.25/5.56 = ( ( X3 = Y )
% 5.25/5.56 | ( X3
% 5.25/5.56 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_iff
% 5.25/5.56 thf(fact_7662_abs__eq__iff,axiom,
% 5.25/5.56 ! [X3: code_integer,Y: code_integer] :
% 5.25/5.56 ( ( ( abs_abs_Code_integer @ X3 )
% 5.25/5.56 = ( abs_abs_Code_integer @ Y ) )
% 5.25/5.56 = ( ( X3 = Y )
% 5.25/5.56 | ( X3
% 5.25/5.56 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_iff
% 5.25/5.56 thf(fact_7663_abs__eq__iff,axiom,
% 5.25/5.56 ! [X3: rat,Y: rat] :
% 5.25/5.56 ( ( ( abs_abs_rat @ X3 )
% 5.25/5.56 = ( abs_abs_rat @ Y ) )
% 5.25/5.56 = ( ( X3 = Y )
% 5.25/5.56 | ( X3
% 5.25/5.56 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_iff
% 5.25/5.56 thf(fact_7664_power__abs,axiom,
% 5.25/5.56 ! [A: code_integer,N: nat] :
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.25/5.56 = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % power_abs
% 5.25/5.56 thf(fact_7665_power__abs,axiom,
% 5.25/5.56 ! [A: real,N: nat] :
% 5.25/5.56 ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 5.25/5.56 = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % power_abs
% 5.25/5.56 thf(fact_7666_power__abs,axiom,
% 5.25/5.56 ! [A: int,N: nat] :
% 5.25/5.56 ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 5.25/5.56 = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % power_abs
% 5.25/5.56 thf(fact_7667_dvd__if__abs__eq,axiom,
% 5.25/5.56 ! [L2: real,K: real] :
% 5.25/5.56 ( ( ( abs_abs_real @ L2 )
% 5.25/5.56 = ( abs_abs_real @ K ) )
% 5.25/5.56 => ( dvd_dvd_real @ L2 @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % dvd_if_abs_eq
% 5.25/5.56 thf(fact_7668_dvd__if__abs__eq,axiom,
% 5.25/5.56 ! [L2: int,K: int] :
% 5.25/5.56 ( ( ( abs_abs_int @ L2 )
% 5.25/5.56 = ( abs_abs_int @ K ) )
% 5.25/5.56 => ( dvd_dvd_int @ L2 @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % dvd_if_abs_eq
% 5.25/5.56 thf(fact_7669_dvd__if__abs__eq,axiom,
% 5.25/5.56 ! [L2: code_integer,K: code_integer] :
% 5.25/5.56 ( ( ( abs_abs_Code_integer @ L2 )
% 5.25/5.56 = ( abs_abs_Code_integer @ K ) )
% 5.25/5.56 => ( dvd_dvd_Code_integer @ L2 @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % dvd_if_abs_eq
% 5.25/5.56 thf(fact_7670_abs__ge__self,axiom,
% 5.25/5.56 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ge_self
% 5.25/5.56 thf(fact_7671_abs__ge__self,axiom,
% 5.25/5.56 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ge_self
% 5.25/5.56 thf(fact_7672_abs__ge__self,axiom,
% 5.25/5.56 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ge_self
% 5.25/5.56 thf(fact_7673_abs__ge__self,axiom,
% 5.25/5.56 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ge_self
% 5.25/5.56 thf(fact_7674_abs__le__D1,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.25/5.56 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_D1
% 5.25/5.56 thf(fact_7675_abs__le__D1,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.25/5.56 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_D1
% 5.25/5.56 thf(fact_7676_abs__le__D1,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.25/5.56 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_D1
% 5.25/5.56 thf(fact_7677_abs__le__D1,axiom,
% 5.25/5.56 ! [A: int,B: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.25/5.56 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_D1
% 5.25/5.56 thf(fact_7678_abs__eq__0__iff,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( ( abs_abs_Code_integer @ A )
% 5.25/5.56 = zero_z3403309356797280102nteger )
% 5.25/5.56 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_0_iff
% 5.25/5.56 thf(fact_7679_abs__eq__0__iff,axiom,
% 5.25/5.56 ! [A: complex] :
% 5.25/5.56 ( ( ( abs_abs_complex @ A )
% 5.25/5.56 = zero_zero_complex )
% 5.25/5.56 = ( A = zero_zero_complex ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_0_iff
% 5.25/5.56 thf(fact_7680_abs__eq__0__iff,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( ( abs_abs_real @ A )
% 5.25/5.56 = zero_zero_real )
% 5.25/5.56 = ( A = zero_zero_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_0_iff
% 5.25/5.56 thf(fact_7681_abs__eq__0__iff,axiom,
% 5.25/5.56 ! [A: rat] :
% 5.25/5.56 ( ( ( abs_abs_rat @ A )
% 5.25/5.56 = zero_zero_rat )
% 5.25/5.56 = ( A = zero_zero_rat ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_0_iff
% 5.25/5.56 thf(fact_7682_abs__eq__0__iff,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( ( abs_abs_int @ A )
% 5.25/5.56 = zero_zero_int )
% 5.25/5.56 = ( A = zero_zero_int ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_0_iff
% 5.25/5.56 thf(fact_7683_abs__minus__commute,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] :
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.25/5.56 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus_commute
% 5.25/5.56 thf(fact_7684_abs__minus__commute,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 5.25/5.56 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus_commute
% 5.25/5.56 thf(fact_7685_abs__minus__commute,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 5.25/5.56 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus_commute
% 5.25/5.56 thf(fact_7686_abs__minus__commute,axiom,
% 5.25/5.56 ! [A: int,B: int] :
% 5.25/5.56 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 5.25/5.56 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus_commute
% 5.25/5.56 thf(fact_7687_abs__one,axiom,
% 5.25/5.56 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.25/5.56 = one_one_Code_integer ) ).
% 5.25/5.56
% 5.25/5.56 % abs_one
% 5.25/5.56 thf(fact_7688_abs__one,axiom,
% 5.25/5.56 ( ( abs_abs_real @ one_one_real )
% 5.25/5.56 = one_one_real ) ).
% 5.25/5.56
% 5.25/5.56 % abs_one
% 5.25/5.56 thf(fact_7689_abs__one,axiom,
% 5.25/5.56 ( ( abs_abs_rat @ one_one_rat )
% 5.25/5.56 = one_one_rat ) ).
% 5.25/5.56
% 5.25/5.56 % abs_one
% 5.25/5.56 thf(fact_7690_abs__one,axiom,
% 5.25/5.56 ( ( abs_abs_int @ one_one_int )
% 5.25/5.56 = one_one_int ) ).
% 5.25/5.56
% 5.25/5.56 % abs_one
% 5.25/5.56 thf(fact_7691_abs__mult,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] :
% 5.25/5.56 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.25/5.56 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult
% 5.25/5.56 thf(fact_7692_abs__mult,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.25/5.56 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult
% 5.25/5.56 thf(fact_7693_abs__mult,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.56 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult
% 5.25/5.56 thf(fact_7694_abs__mult,axiom,
% 5.25/5.56 ! [A: int,B: int] :
% 5.25/5.56 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.25/5.56 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult
% 5.25/5.56 thf(fact_7695_not__empty__eq__Iic__eq__empty,axiom,
% 5.25/5.56 ! [H2: real] :
% 5.25/5.56 ( bot_bot_set_real
% 5.25/5.56 != ( set_ord_atMost_real @ H2 ) ) ).
% 5.25/5.56
% 5.25/5.56 % not_empty_eq_Iic_eq_empty
% 5.25/5.56 thf(fact_7696_not__empty__eq__Iic__eq__empty,axiom,
% 5.25/5.56 ! [H2: nat] :
% 5.25/5.56 ( bot_bot_set_nat
% 5.25/5.56 != ( set_ord_atMost_nat @ H2 ) ) ).
% 5.25/5.56
% 5.25/5.56 % not_empty_eq_Iic_eq_empty
% 5.25/5.56 thf(fact_7697_not__empty__eq__Iic__eq__empty,axiom,
% 5.25/5.56 ! [H2: int] :
% 5.25/5.56 ( bot_bot_set_int
% 5.25/5.56 != ( set_ord_atMost_int @ H2 ) ) ).
% 5.25/5.56
% 5.25/5.56 % not_empty_eq_Iic_eq_empty
% 5.25/5.56 thf(fact_7698_not__Iic__eq__Icc,axiom,
% 5.25/5.56 ! [H3: int,L2: int,H2: int] :
% 5.25/5.56 ( ( set_ord_atMost_int @ H3 )
% 5.25/5.56 != ( set_or1266510415728281911st_int @ L2 @ H2 ) ) ).
% 5.25/5.56
% 5.25/5.56 % not_Iic_eq_Icc
% 5.25/5.56 thf(fact_7699_not__Iic__eq__Icc,axiom,
% 5.25/5.56 ! [H3: real,L2: real,H2: real] :
% 5.25/5.56 ( ( set_ord_atMost_real @ H3 )
% 5.25/5.56 != ( set_or1222579329274155063t_real @ L2 @ H2 ) ) ).
% 5.25/5.56
% 5.25/5.56 % not_Iic_eq_Icc
% 5.25/5.56 thf(fact_7700_atMost__def,axiom,
% 5.25/5.56 ( set_ord_atMost_real
% 5.25/5.56 = ( ^ [U2: real] :
% 5.25/5.56 ( collect_real
% 5.25/5.56 @ ^ [X2: real] : ( ord_less_eq_real @ X2 @ U2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_def
% 5.25/5.56 thf(fact_7701_atMost__def,axiom,
% 5.25/5.56 ( set_or58775011639299419et_int
% 5.25/5.56 = ( ^ [U2: set_int] :
% 5.25/5.56 ( collect_set_int
% 5.25/5.56 @ ^ [X2: set_int] : ( ord_less_eq_set_int @ X2 @ U2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_def
% 5.25/5.56 thf(fact_7702_atMost__def,axiom,
% 5.25/5.56 ( set_ord_atMost_rat
% 5.25/5.56 = ( ^ [U2: rat] :
% 5.25/5.56 ( collect_rat
% 5.25/5.56 @ ^ [X2: rat] : ( ord_less_eq_rat @ X2 @ U2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_def
% 5.25/5.56 thf(fact_7703_atMost__def,axiom,
% 5.25/5.56 ( set_ord_atMost_num
% 5.25/5.56 = ( ^ [U2: num] :
% 5.25/5.56 ( collect_num
% 5.25/5.56 @ ^ [X2: num] : ( ord_less_eq_num @ X2 @ U2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_def
% 5.25/5.56 thf(fact_7704_atMost__def,axiom,
% 5.25/5.56 ( set_ord_atMost_nat
% 5.25/5.56 = ( ^ [U2: nat] :
% 5.25/5.56 ( collect_nat
% 5.25/5.56 @ ^ [X2: nat] : ( ord_less_eq_nat @ X2 @ U2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_def
% 5.25/5.56 thf(fact_7705_atMost__def,axiom,
% 5.25/5.56 ( set_ord_atMost_int
% 5.25/5.56 = ( ^ [U2: int] :
% 5.25/5.56 ( collect_int
% 5.25/5.56 @ ^ [X2: int] : ( ord_less_eq_int @ X2 @ U2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_def
% 5.25/5.56 thf(fact_7706_abs__ge__zero,axiom,
% 5.25/5.56 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ge_zero
% 5.25/5.56 thf(fact_7707_abs__ge__zero,axiom,
% 5.25/5.56 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ge_zero
% 5.25/5.56 thf(fact_7708_abs__ge__zero,axiom,
% 5.25/5.56 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ge_zero
% 5.25/5.56 thf(fact_7709_abs__ge__zero,axiom,
% 5.25/5.56 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ge_zero
% 5.25/5.56 thf(fact_7710_abs__not__less__zero,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.25/5.56
% 5.25/5.56 % abs_not_less_zero
% 5.25/5.56 thf(fact_7711_abs__not__less__zero,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.25/5.56
% 5.25/5.56 % abs_not_less_zero
% 5.25/5.56 thf(fact_7712_abs__not__less__zero,axiom,
% 5.25/5.56 ! [A: rat] :
% 5.25/5.56 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.25/5.56
% 5.25/5.56 % abs_not_less_zero
% 5.25/5.56 thf(fact_7713_abs__not__less__zero,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.25/5.56
% 5.25/5.56 % abs_not_less_zero
% 5.25/5.56 thf(fact_7714_abs__of__pos,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.56 => ( ( abs_abs_Code_integer @ A )
% 5.25/5.56 = A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_pos
% 5.25/5.56 thf(fact_7715_abs__of__pos,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.56 => ( ( abs_abs_real @ A )
% 5.25/5.56 = A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_pos
% 5.25/5.56 thf(fact_7716_abs__of__pos,axiom,
% 5.25/5.56 ! [A: rat] :
% 5.25/5.56 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.56 => ( ( abs_abs_rat @ A )
% 5.25/5.56 = A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_pos
% 5.25/5.56 thf(fact_7717_abs__of__pos,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.56 => ( ( abs_abs_int @ A )
% 5.25/5.56 = A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_pos
% 5.25/5.56 thf(fact_7718_abs__triangle__ineq,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq
% 5.25/5.56 thf(fact_7719_abs__triangle__ineq,axiom,
% 5.25/5.56 ! [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 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq
% 5.25/5.56 thf(fact_7720_abs__triangle__ineq,axiom,
% 5.25/5.56 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq
% 5.25/5.56 thf(fact_7721_abs__triangle__ineq,axiom,
% 5.25/5.56 ! [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 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq
% 5.25/5.56 thf(fact_7722_abs__mult__less,axiom,
% 5.25/5.56 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.25/5.56 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.25/5.56 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 5.25/5.56 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult_less
% 5.25/5.56 thf(fact_7723_abs__mult__less,axiom,
% 5.25/5.56 ! [A: real,C: real,B: real,D: real] :
% 5.25/5.56 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.25/5.56 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 5.25/5.56 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult_less
% 5.25/5.56 thf(fact_7724_abs__mult__less,axiom,
% 5.25/5.56 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.25/5.56 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.25/5.56 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 5.25/5.56 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult_less
% 5.25/5.56 thf(fact_7725_abs__mult__less,axiom,
% 5.25/5.56 ! [A: int,C: int,B: int,D: int] :
% 5.25/5.56 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.25/5.56 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 5.25/5.56 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult_less
% 5.25/5.56 thf(fact_7726_abs__triangle__ineq2,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq2
% 5.25/5.56 thf(fact_7727_abs__triangle__ineq2,axiom,
% 5.25/5.56 ! [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 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq2
% 5.25/5.56 thf(fact_7728_abs__triangle__ineq2,axiom,
% 5.25/5.56 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq2
% 5.25/5.56 thf(fact_7729_abs__triangle__ineq2,axiom,
% 5.25/5.56 ! [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 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq2
% 5.25/5.56 thf(fact_7730_abs__triangle__ineq3,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq3
% 5.25/5.56 thf(fact_7731_abs__triangle__ineq3,axiom,
% 5.25/5.56 ! [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 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq3
% 5.25/5.56 thf(fact_7732_abs__triangle__ineq3,axiom,
% 5.25/5.56 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq3
% 5.25/5.56 thf(fact_7733_abs__triangle__ineq3,axiom,
% 5.25/5.56 ! [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 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq3
% 5.25/5.56 thf(fact_7734_abs__triangle__ineq2__sym,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq2_sym
% 5.25/5.56 thf(fact_7735_abs__triangle__ineq2__sym,axiom,
% 5.25/5.56 ! [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 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq2_sym
% 5.25/5.56 thf(fact_7736_abs__triangle__ineq2__sym,axiom,
% 5.25/5.56 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq2_sym
% 5.25/5.56 thf(fact_7737_abs__triangle__ineq2__sym,axiom,
% 5.25/5.56 ! [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 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq2_sym
% 5.25/5.56 thf(fact_7738_nonzero__abs__divide,axiom,
% 5.25/5.56 ! [B: real,A: real] :
% 5.25/5.56 ( ( B != zero_zero_real )
% 5.25/5.56 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.25/5.56 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % nonzero_abs_divide
% 5.25/5.56 thf(fact_7739_nonzero__abs__divide,axiom,
% 5.25/5.56 ! [B: rat,A: rat] :
% 5.25/5.56 ( ( B != zero_zero_rat )
% 5.25/5.56 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.25/5.56 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % nonzero_abs_divide
% 5.25/5.56 thf(fact_7740_abs__ge__minus__self,axiom,
% 5.25/5.56 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ge_minus_self
% 5.25/5.56 thf(fact_7741_abs__ge__minus__self,axiom,
% 5.25/5.56 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ge_minus_self
% 5.25/5.56 thf(fact_7742_abs__ge__minus__self,axiom,
% 5.25/5.56 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ge_minus_self
% 5.25/5.56 thf(fact_7743_abs__ge__minus__self,axiom,
% 5.25/5.56 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ge_minus_self
% 5.25/5.56 thf(fact_7744_abs__le__iff,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.25/5.56 = ( ( ord_less_eq_real @ A @ B )
% 5.25/5.56 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_iff
% 5.25/5.56 thf(fact_7745_abs__le__iff,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.25/5.56 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.25/5.56 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_iff
% 5.25/5.56 thf(fact_7746_abs__le__iff,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.25/5.56 = ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.56 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_iff
% 5.25/5.56 thf(fact_7747_abs__le__iff,axiom,
% 5.25/5.56 ! [A: int,B: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.25/5.56 = ( ( ord_less_eq_int @ A @ B )
% 5.25/5.56 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_iff
% 5.25/5.56 thf(fact_7748_abs__le__D2,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.25/5.56 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_D2
% 5.25/5.56 thf(fact_7749_abs__le__D2,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.25/5.56 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_D2
% 5.25/5.56 thf(fact_7750_abs__le__D2,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.25/5.56 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_D2
% 5.25/5.56 thf(fact_7751_abs__le__D2,axiom,
% 5.25/5.56 ! [A: int,B: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.25/5.56 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_D2
% 5.25/5.56 thf(fact_7752_abs__leI,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.56 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.25/5.56 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_leI
% 5.25/5.56 thf(fact_7753_abs__leI,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.25/5.56 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.25/5.56 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_leI
% 5.25/5.56 thf(fact_7754_abs__leI,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.56 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.25/5.56 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_leI
% 5.25/5.56 thf(fact_7755_abs__leI,axiom,
% 5.25/5.56 ! [A: int,B: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.56 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.25/5.56 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_leI
% 5.25/5.56 thf(fact_7756_abs__less__iff,axiom,
% 5.25/5.56 ! [A: int,B: int] :
% 5.25/5.56 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.25/5.56 = ( ( ord_less_int @ A @ B )
% 5.25/5.56 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_less_iff
% 5.25/5.56 thf(fact_7757_abs__less__iff,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.25/5.56 = ( ( ord_less_real @ A @ B )
% 5.25/5.56 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_less_iff
% 5.25/5.56 thf(fact_7758_abs__less__iff,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] :
% 5.25/5.56 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.25/5.56 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.25/5.56 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_less_iff
% 5.25/5.56 thf(fact_7759_abs__less__iff,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.25/5.56 = ( ( ord_less_rat @ A @ B )
% 5.25/5.56 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_less_iff
% 5.25/5.56 thf(fact_7760_atMost__atLeast0,axiom,
% 5.25/5.56 ( set_ord_atMost_nat
% 5.25/5.56 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_atLeast0
% 5.25/5.56 thf(fact_7761_lessThan__Suc__atMost,axiom,
% 5.25/5.56 ! [K: nat] :
% 5.25/5.56 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.25/5.56 = ( set_ord_atMost_nat @ K ) ) ).
% 5.25/5.56
% 5.25/5.56 % lessThan_Suc_atMost
% 5.25/5.56 thf(fact_7762_atMost__Suc,axiom,
% 5.25/5.56 ! [K: nat] :
% 5.25/5.56 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.25/5.56 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_Suc
% 5.25/5.56 thf(fact_7763_not__Iic__le__Icc,axiom,
% 5.25/5.56 ! [H2: int,L3: int,H3: int] :
% 5.25/5.56 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H2 ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 5.25/5.56
% 5.25/5.56 % not_Iic_le_Icc
% 5.25/5.56 thf(fact_7764_not__Iic__le__Icc,axiom,
% 5.25/5.56 ! [H2: real,L3: real,H3: real] :
% 5.25/5.56 ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H2 ) @ ( set_or1222579329274155063t_real @ L3 @ H3 ) ) ).
% 5.25/5.56
% 5.25/5.56 % not_Iic_le_Icc
% 5.25/5.56 thf(fact_7765_tanh__real__lt__1,axiom,
% 5.25/5.56 ! [X3: real] : ( ord_less_real @ ( tanh_real @ X3 ) @ one_one_real ) ).
% 5.25/5.56
% 5.25/5.56 % tanh_real_lt_1
% 5.25/5.56 thf(fact_7766_dense__eq0__I,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ! [E2: real] :
% 5.25/5.56 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.25/5.56 => ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ E2 ) )
% 5.25/5.56 => ( X3 = zero_zero_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % dense_eq0_I
% 5.25/5.56 thf(fact_7767_dense__eq0__I,axiom,
% 5.25/5.56 ! [X3: rat] :
% 5.25/5.56 ( ! [E2: rat] :
% 5.25/5.56 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.25/5.56 => ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ E2 ) )
% 5.25/5.56 => ( X3 = zero_zero_rat ) ) ).
% 5.25/5.56
% 5.25/5.56 % dense_eq0_I
% 5.25/5.56 thf(fact_7768_abs__mult__pos,axiom,
% 5.25/5.56 ! [X3: code_integer,Y: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 5.25/5.56 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X3 )
% 5.25/5.56 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X3 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult_pos
% 5.25/5.56 thf(fact_7769_abs__mult__pos,axiom,
% 5.25/5.56 ! [X3: real,Y: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.56 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X3 )
% 5.25/5.56 = ( abs_abs_real @ ( times_times_real @ Y @ X3 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult_pos
% 5.25/5.56 thf(fact_7770_abs__mult__pos,axiom,
% 5.25/5.56 ! [X3: rat,Y: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.25/5.56 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X3 )
% 5.25/5.56 = ( abs_abs_rat @ ( times_times_rat @ Y @ X3 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult_pos
% 5.25/5.56 thf(fact_7771_abs__mult__pos,axiom,
% 5.25/5.56 ! [X3: int,Y: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.56 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X3 )
% 5.25/5.56 = ( abs_abs_int @ ( times_times_int @ Y @ X3 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_mult_pos
% 5.25/5.56 thf(fact_7772_abs__eq__mult,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] :
% 5.25/5.56 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.56 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.25/5.56 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.25/5.56 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.25/5.56 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.25/5.56 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_mult
% 5.25/5.56 thf(fact_7773_abs__eq__mult,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.56 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.25/5.56 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.56 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.25/5.56 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.25/5.56 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_mult
% 5.25/5.56 thf(fact_7774_abs__eq__mult,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.56 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.25/5.56 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.56 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.25/5.56 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.56 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_mult
% 5.25/5.56 thf(fact_7775_abs__eq__mult,axiom,
% 5.25/5.56 ! [A: int,B: int] :
% 5.25/5.56 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.56 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.25/5.56 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.56 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.25/5.56 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.25/5.56 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_mult
% 5.25/5.56 thf(fact_7776_abs__minus__le__zero,axiom,
% 5.25/5.56 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus_le_zero
% 5.25/5.56 thf(fact_7777_abs__minus__le__zero,axiom,
% 5.25/5.56 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus_le_zero
% 5.25/5.56 thf(fact_7778_abs__minus__le__zero,axiom,
% 5.25/5.56 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus_le_zero
% 5.25/5.56 thf(fact_7779_abs__minus__le__zero,axiom,
% 5.25/5.56 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.25/5.56
% 5.25/5.56 % abs_minus_le_zero
% 5.25/5.56 thf(fact_7780_eq__abs__iff_H,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( A
% 5.25/5.56 = ( abs_abs_real @ B ) )
% 5.25/5.56 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.56 & ( ( B = A )
% 5.25/5.56 | ( B
% 5.25/5.56 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % eq_abs_iff'
% 5.25/5.56 thf(fact_7781_eq__abs__iff_H,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] :
% 5.25/5.56 ( ( A
% 5.25/5.56 = ( abs_abs_Code_integer @ B ) )
% 5.25/5.56 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.56 & ( ( B = A )
% 5.25/5.56 | ( B
% 5.25/5.56 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % eq_abs_iff'
% 5.25/5.56 thf(fact_7782_eq__abs__iff_H,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( A
% 5.25/5.56 = ( abs_abs_rat @ B ) )
% 5.25/5.56 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.56 & ( ( B = A )
% 5.25/5.56 | ( B
% 5.25/5.56 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % eq_abs_iff'
% 5.25/5.56 thf(fact_7783_eq__abs__iff_H,axiom,
% 5.25/5.56 ! [A: int,B: int] :
% 5.25/5.56 ( ( A
% 5.25/5.56 = ( abs_abs_int @ B ) )
% 5.25/5.56 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.56 & ( ( B = A )
% 5.25/5.56 | ( B
% 5.25/5.56 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % eq_abs_iff'
% 5.25/5.56 thf(fact_7784_abs__eq__iff_H,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( ( abs_abs_real @ A )
% 5.25/5.56 = B )
% 5.25/5.56 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.56 & ( ( A = B )
% 5.25/5.56 | ( A
% 5.25/5.56 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_iff'
% 5.25/5.56 thf(fact_7785_abs__eq__iff_H,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] :
% 5.25/5.56 ( ( ( abs_abs_Code_integer @ A )
% 5.25/5.56 = B )
% 5.25/5.56 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.25/5.56 & ( ( A = B )
% 5.25/5.56 | ( A
% 5.25/5.56 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_iff'
% 5.25/5.56 thf(fact_7786_abs__eq__iff_H,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( ( abs_abs_rat @ A )
% 5.25/5.56 = B )
% 5.25/5.56 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.56 & ( ( A = B )
% 5.25/5.56 | ( A
% 5.25/5.56 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_iff'
% 5.25/5.56 thf(fact_7787_abs__eq__iff_H,axiom,
% 5.25/5.56 ! [A: int,B: int] :
% 5.25/5.56 ( ( ( abs_abs_int @ A )
% 5.25/5.56 = B )
% 5.25/5.56 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.56 & ( ( A = B )
% 5.25/5.56 | ( A
% 5.25/5.56 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_eq_iff'
% 5.25/5.56 thf(fact_7788_abs__div__pos,axiom,
% 5.25/5.56 ! [Y: real,X3: real] :
% 5.25/5.56 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.56 => ( ( divide_divide_real @ ( abs_abs_real @ X3 ) @ Y )
% 5.25/5.56 = ( abs_abs_real @ ( divide_divide_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_div_pos
% 5.25/5.56 thf(fact_7789_abs__div__pos,axiom,
% 5.25/5.56 ! [Y: rat,X3: rat] :
% 5.25/5.56 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.56 => ( ( divide_divide_rat @ ( abs_abs_rat @ X3 ) @ Y )
% 5.25/5.56 = ( abs_abs_rat @ ( divide_divide_rat @ X3 @ Y ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_div_pos
% 5.25/5.56 thf(fact_7790_zero__le__power__abs,axiom,
% 5.25/5.56 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_le_power_abs
% 5.25/5.56 thf(fact_7791_zero__le__power__abs,axiom,
% 5.25/5.56 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_le_power_abs
% 5.25/5.56 thf(fact_7792_zero__le__power__abs,axiom,
% 5.25/5.56 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_le_power_abs
% 5.25/5.56 thf(fact_7793_zero__le__power__abs,axiom,
% 5.25/5.56 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_le_power_abs
% 5.25/5.56 thf(fact_7794_abs__if,axiom,
% 5.25/5.56 ( abs_abs_int
% 5.25/5.56 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_if
% 5.25/5.56 thf(fact_7795_abs__if,axiom,
% 5.25/5.56 ( abs_abs_real
% 5.25/5.56 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_if
% 5.25/5.56 thf(fact_7796_abs__if,axiom,
% 5.25/5.56 ( abs_abs_Code_integer
% 5.25/5.56 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_if
% 5.25/5.56 thf(fact_7797_abs__if,axiom,
% 5.25/5.56 ( abs_abs_rat
% 5.25/5.56 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_if
% 5.25/5.56 thf(fact_7798_abs__of__neg,axiom,
% 5.25/5.56 ! [A: int] :
% 5.25/5.56 ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.56 => ( ( abs_abs_int @ A )
% 5.25/5.56 = ( uminus_uminus_int @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_neg
% 5.25/5.56 thf(fact_7799_abs__of__neg,axiom,
% 5.25/5.56 ! [A: real] :
% 5.25/5.56 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.56 => ( ( abs_abs_real @ A )
% 5.25/5.56 = ( uminus_uminus_real @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_neg
% 5.25/5.56 thf(fact_7800_abs__of__neg,axiom,
% 5.25/5.56 ! [A: code_integer] :
% 5.25/5.56 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.25/5.56 => ( ( abs_abs_Code_integer @ A )
% 5.25/5.56 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_neg
% 5.25/5.56 thf(fact_7801_abs__of__neg,axiom,
% 5.25/5.56 ! [A: rat] :
% 5.25/5.56 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.56 => ( ( abs_abs_rat @ A )
% 5.25/5.56 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_of_neg
% 5.25/5.56 thf(fact_7802_abs__if__raw,axiom,
% 5.25/5.56 ( abs_abs_int
% 5.25/5.56 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_if_raw
% 5.25/5.56 thf(fact_7803_abs__if__raw,axiom,
% 5.25/5.56 ( abs_abs_real
% 5.25/5.56 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_if_raw
% 5.25/5.56 thf(fact_7804_abs__if__raw,axiom,
% 5.25/5.56 ( abs_abs_Code_integer
% 5.25/5.56 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_if_raw
% 5.25/5.56 thf(fact_7805_abs__if__raw,axiom,
% 5.25/5.56 ( abs_abs_rat
% 5.25/5.56 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_if_raw
% 5.25/5.56 thf(fact_7806_abs__diff__triangle__ineq,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_diff_triangle_ineq
% 5.25/5.56 thf(fact_7807_abs__diff__triangle__ineq,axiom,
% 5.25/5.56 ! [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 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_diff_triangle_ineq
% 5.25/5.56 thf(fact_7808_abs__diff__triangle__ineq,axiom,
% 5.25/5.56 ! [A: rat,B: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_diff_triangle_ineq
% 5.25/5.56 thf(fact_7809_abs__diff__triangle__ineq,axiom,
% 5.25/5.56 ! [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 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_diff_triangle_ineq
% 5.25/5.56 thf(fact_7810_abs__triangle__ineq4,axiom,
% 5.25/5.56 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq4
% 5.25/5.56 thf(fact_7811_abs__triangle__ineq4,axiom,
% 5.25/5.56 ! [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 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq4
% 5.25/5.56 thf(fact_7812_abs__triangle__ineq4,axiom,
% 5.25/5.56 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq4
% 5.25/5.56 thf(fact_7813_abs__triangle__ineq4,axiom,
% 5.25/5.56 ! [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 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_triangle_ineq4
% 5.25/5.56 thf(fact_7814_abs__diff__le__iff,axiom,
% 5.25/5.56 ! [X3: code_integer,A: code_integer,R2: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X3 @ A ) ) @ R2 )
% 5.25/5.56 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X3 )
% 5.25/5.56 & ( ord_le3102999989581377725nteger @ X3 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_diff_le_iff
% 5.25/5.56 thf(fact_7815_abs__diff__le__iff,axiom,
% 5.25/5.56 ! [X3: real,A: real,R2: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ A ) ) @ R2 )
% 5.25/5.56 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X3 )
% 5.25/5.56 & ( ord_less_eq_real @ X3 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_diff_le_iff
% 5.25/5.56 thf(fact_7816_abs__diff__le__iff,axiom,
% 5.25/5.56 ! [X3: rat,A: rat,R2: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ A ) ) @ R2 )
% 5.25/5.56 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X3 )
% 5.25/5.56 & ( ord_less_eq_rat @ X3 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_diff_le_iff
% 5.25/5.56 thf(fact_7817_abs__diff__le__iff,axiom,
% 5.25/5.56 ! [X3: int,A: int,R2: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ A ) ) @ R2 )
% 5.25/5.56 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X3 )
% 5.25/5.56 & ( ord_less_eq_int @ X3 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_diff_le_iff
% 5.25/5.56 thf(fact_7818_abs__diff__less__iff,axiom,
% 5.25/5.56 ! [X3: code_integer,A: code_integer,R2: code_integer] :
% 5.25/5.56 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X3 @ A ) ) @ R2 )
% 5.25/5.56 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X3 )
% 5.25/5.56 & ( ord_le6747313008572928689nteger @ X3 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_diff_less_iff
% 5.25/5.56 thf(fact_7819_abs__diff__less__iff,axiom,
% 5.25/5.56 ! [X3: real,A: real,R2: real] :
% 5.25/5.56 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ A ) ) @ R2 )
% 5.25/5.56 = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X3 )
% 5.25/5.56 & ( ord_less_real @ X3 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_diff_less_iff
% 5.25/5.56 thf(fact_7820_abs__diff__less__iff,axiom,
% 5.25/5.56 ! [X3: rat,A: rat,R2: rat] :
% 5.25/5.56 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ A ) ) @ R2 )
% 5.25/5.56 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X3 )
% 5.25/5.56 & ( ord_less_rat @ X3 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_diff_less_iff
% 5.25/5.56 thf(fact_7821_abs__diff__less__iff,axiom,
% 5.25/5.56 ! [X3: int,A: int,R2: int] :
% 5.25/5.56 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ A ) ) @ R2 )
% 5.25/5.56 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X3 )
% 5.25/5.56 & ( ord_less_int @ X3 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_diff_less_iff
% 5.25/5.56 thf(fact_7822_abs__real__def,axiom,
% 5.25/5.56 ( abs_abs_real
% 5.25/5.56 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_real_def
% 5.25/5.56 thf(fact_7823_sin__bound__lemma,axiom,
% 5.25/5.56 ! [X3: real,Y: real,U: real,V: real] :
% 5.25/5.56 ( ( X3 = Y )
% 5.25/5.56 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.25/5.56 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X3 @ U ) @ Y ) ) @ V ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sin_bound_lemma
% 5.25/5.56 thf(fact_7824_atMost__nat__numeral,axiom,
% 5.25/5.56 ! [K: num] :
% 5.25/5.56 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.25/5.56 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % atMost_nat_numeral
% 5.25/5.56 thf(fact_7825_Iic__subset__Iio__iff,axiom,
% 5.25/5.56 ! [A: rat,B: rat] :
% 5.25/5.56 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 5.25/5.56 = ( ord_less_rat @ A @ B ) ) ).
% 5.25/5.56
% 5.25/5.56 % Iic_subset_Iio_iff
% 5.25/5.56 thf(fact_7826_Iic__subset__Iio__iff,axiom,
% 5.25/5.56 ! [A: num,B: num] :
% 5.25/5.56 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 5.25/5.56 = ( ord_less_num @ A @ B ) ) ).
% 5.25/5.56
% 5.25/5.56 % Iic_subset_Iio_iff
% 5.25/5.56 thf(fact_7827_Iic__subset__Iio__iff,axiom,
% 5.25/5.56 ! [A: nat,B: nat] :
% 5.25/5.56 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 5.25/5.56 = ( ord_less_nat @ A @ B ) ) ).
% 5.25/5.56
% 5.25/5.56 % Iic_subset_Iio_iff
% 5.25/5.56 thf(fact_7828_Iic__subset__Iio__iff,axiom,
% 5.25/5.56 ! [A: int,B: int] :
% 5.25/5.56 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 5.25/5.56 = ( ord_less_int @ A @ B ) ) ).
% 5.25/5.56
% 5.25/5.56 % Iic_subset_Iio_iff
% 5.25/5.56 thf(fact_7829_Iic__subset__Iio__iff,axiom,
% 5.25/5.56 ! [A: real,B: real] :
% 5.25/5.56 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 5.25/5.56 = ( ord_less_real @ A @ B ) ) ).
% 5.25/5.56
% 5.25/5.56 % Iic_subset_Iio_iff
% 5.25/5.56 thf(fact_7830_sum__choose__upper,axiom,
% 5.25/5.56 ! [M: nat,N: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_choose_upper
% 5.25/5.56 thf(fact_7831_tanh__real__gt__neg1,axiom,
% 5.25/5.56 ! [X3: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X3 ) ) ).
% 5.25/5.56
% 5.25/5.56 % tanh_real_gt_neg1
% 5.25/5.56 thf(fact_7832_abs__add__one__gt__zero,axiom,
% 5.25/5.56 ! [X3: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_add_one_gt_zero
% 5.25/5.56 thf(fact_7833_abs__add__one__gt__zero,axiom,
% 5.25/5.56 ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_add_one_gt_zero
% 5.25/5.56 thf(fact_7834_abs__add__one__gt__zero,axiom,
% 5.25/5.56 ! [X3: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_add_one_gt_zero
% 5.25/5.56 thf(fact_7835_abs__add__one__gt__zero,axiom,
% 5.25/5.56 ! [X3: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_add_one_gt_zero
% 5.25/5.56 thf(fact_7836_of__int__leD,axiom,
% 5.25/5.56 ! [N: int,X3: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X3 )
% 5.25/5.56 => ( ( N = zero_zero_int )
% 5.25/5.56 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % of_int_leD
% 5.25/5.56 thf(fact_7837_of__int__leD,axiom,
% 5.25/5.56 ! [N: int,X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X3 )
% 5.25/5.56 => ( ( N = zero_zero_int )
% 5.25/5.56 | ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % of_int_leD
% 5.25/5.56 thf(fact_7838_of__int__leD,axiom,
% 5.25/5.56 ! [N: int,X3: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X3 )
% 5.25/5.56 => ( ( N = zero_zero_int )
% 5.25/5.56 | ( ord_less_eq_rat @ one_one_rat @ X3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % of_int_leD
% 5.25/5.56 thf(fact_7839_of__int__leD,axiom,
% 5.25/5.56 ! [N: int,X3: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X3 )
% 5.25/5.56 => ( ( N = zero_zero_int )
% 5.25/5.56 | ( ord_less_eq_int @ one_one_int @ X3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % of_int_leD
% 5.25/5.56 thf(fact_7840_of__int__lessD,axiom,
% 5.25/5.56 ! [N: int,X3: code_integer] :
% 5.25/5.56 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X3 )
% 5.25/5.56 => ( ( N = zero_zero_int )
% 5.25/5.56 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % of_int_lessD
% 5.25/5.56 thf(fact_7841_of__int__lessD,axiom,
% 5.25/5.56 ! [N: int,X3: real] :
% 5.25/5.56 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X3 )
% 5.25/5.56 => ( ( N = zero_zero_int )
% 5.25/5.56 | ( ord_less_real @ one_one_real @ X3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % of_int_lessD
% 5.25/5.56 thf(fact_7842_of__int__lessD,axiom,
% 5.25/5.56 ! [N: int,X3: rat] :
% 5.25/5.56 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X3 )
% 5.25/5.56 => ( ( N = zero_zero_int )
% 5.25/5.56 | ( ord_less_rat @ one_one_rat @ X3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % of_int_lessD
% 5.25/5.56 thf(fact_7843_of__int__lessD,axiom,
% 5.25/5.56 ! [N: int,X3: int] :
% 5.25/5.56 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X3 )
% 5.25/5.56 => ( ( N = zero_zero_int )
% 5.25/5.56 | ( ord_less_int @ one_one_int @ X3 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % of_int_lessD
% 5.25/5.56 thf(fact_7844_lemma__interval,axiom,
% 5.25/5.56 ! [A: real,X3: real,B: real] :
% 5.25/5.56 ( ( ord_less_real @ A @ X3 )
% 5.25/5.56 => ( ( ord_less_real @ X3 @ B )
% 5.25/5.56 => ? [D3: real] :
% 5.25/5.56 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.25/5.56 & ! [Y4: real] :
% 5.25/5.56 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y4 ) ) @ D3 )
% 5.25/5.56 => ( ( ord_less_eq_real @ A @ Y4 )
% 5.25/5.56 & ( ord_less_eq_real @ Y4 @ B ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % lemma_interval
% 5.25/5.56 thf(fact_7845_norm__triangle__ineq3,axiom,
% 5.25/5.56 ! [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 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % norm_triangle_ineq3
% 5.25/5.56 thf(fact_7846_norm__triangle__ineq3,axiom,
% 5.25/5.56 ! [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 ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % norm_triangle_ineq3
% 5.25/5.56 thf(fact_7847_round__diff__minimal,axiom,
% 5.25/5.56 ! [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 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % round_diff_minimal
% 5.25/5.56 thf(fact_7848_round__diff__minimal,axiom,
% 5.25/5.56 ! [Z: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % round_diff_minimal
% 5.25/5.56 thf(fact_7849_sum_OatMost__Suc__shift,axiom,
% 5.25/5.56 ! [G: nat > rat,N: nat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.atMost_Suc_shift
% 5.25/5.56 thf(fact_7850_sum_OatMost__Suc__shift,axiom,
% 5.25/5.56 ! [G: nat > int,N: nat] :
% 5.25/5.56 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.atMost_Suc_shift
% 5.25/5.56 thf(fact_7851_sum_OatMost__Suc__shift,axiom,
% 5.25/5.56 ! [G: nat > nat,N: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.atMost_Suc_shift
% 5.25/5.56 thf(fact_7852_sum_OatMost__Suc__shift,axiom,
% 5.25/5.56 ! [G: nat > real,N: nat] :
% 5.25/5.56 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.atMost_Suc_shift
% 5.25/5.56 thf(fact_7853_sum__telescope,axiom,
% 5.25/5.56 ! [F: nat > rat,I2: nat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ I2 ) )
% 5.25/5.56 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_telescope
% 5.25/5.56 thf(fact_7854_sum__telescope,axiom,
% 5.25/5.56 ! [F: nat > int,I2: nat] :
% 5.25/5.56 ( ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ I2 ) )
% 5.25/5.56 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_telescope
% 5.25/5.56 thf(fact_7855_sum__telescope,axiom,
% 5.25/5.56 ! [F: nat > real,I2: nat] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( minus_minus_real @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ I2 ) )
% 5.25/5.56 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_telescope
% 5.25/5.56 thf(fact_7856_polyfun__eq__coeffs,axiom,
% 5.25/5.56 ! [C: nat > complex,N: nat,D: nat > complex] :
% 5.25/5.56 ( ( ! [X2: complex] :
% 5.25/5.56 ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X2 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( D @ I3 ) @ ( power_power_complex @ X2 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) )
% 5.25/5.56 = ( ! [I3: nat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ I3 @ N )
% 5.25/5.56 => ( ( C @ I3 )
% 5.25/5.56 = ( D @ I3 ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_eq_coeffs
% 5.25/5.56 thf(fact_7857_polyfun__eq__coeffs,axiom,
% 5.25/5.56 ! [C: nat > real,N: nat,D: nat > real] :
% 5.25/5.56 ( ( ! [X2: real] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X2 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( D @ I3 ) @ ( power_power_real @ X2 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) )
% 5.25/5.56 = ( ! [I3: nat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ I3 @ N )
% 5.25/5.56 => ( ( C @ I3 )
% 5.25/5.56 = ( D @ I3 ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_eq_coeffs
% 5.25/5.56 thf(fact_7858_prod_OatMost__Suc__shift,axiom,
% 5.25/5.56 ! [G: nat > real,N: nat] :
% 5.25/5.56 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups129246275422532515t_real
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.atMost_Suc_shift
% 5.25/5.56 thf(fact_7859_prod_OatMost__Suc__shift,axiom,
% 5.25/5.56 ! [G: nat > rat,N: nat] :
% 5.25/5.56 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups73079841787564623at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.atMost_Suc_shift
% 5.25/5.56 thf(fact_7860_prod_OatMost__Suc__shift,axiom,
% 5.25/5.56 ! [G: nat > int,N: nat] :
% 5.25/5.56 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups705719431365010083at_int
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.atMost_Suc_shift
% 5.25/5.56 thf(fact_7861_prod_OatMost__Suc__shift,axiom,
% 5.25/5.56 ! [G: nat > nat,N: nat] :
% 5.25/5.56 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.25/5.56 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups708209901874060359at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.atMost_Suc_shift
% 5.25/5.56 thf(fact_7862_sum_Onested__swap_H,axiom,
% 5.25/5.56 ! [A: nat > nat > nat,N: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [J3: nat] :
% 5.25/5.56 ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 5.25/5.56 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.nested_swap'
% 5.25/5.56 thf(fact_7863_sum_Onested__swap_H,axiom,
% 5.25/5.56 ! [A: nat > nat > real,N: nat] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( groups6591440286371151544t_real @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [J3: nat] :
% 5.25/5.56 ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 5.25/5.56 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.nested_swap'
% 5.25/5.56 thf(fact_7864_prod_Onested__swap_H,axiom,
% 5.25/5.56 ! [A: nat > nat > int,N: nat] :
% 5.25/5.56 ( ( groups705719431365010083at_int
% 5.25/5.56 @ ^ [I3: nat] : ( groups705719431365010083at_int @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( groups705719431365010083at_int
% 5.25/5.56 @ ^ [J3: nat] :
% 5.25/5.56 ( groups705719431365010083at_int
% 5.25/5.56 @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 5.25/5.56 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.nested_swap'
% 5.25/5.56 thf(fact_7865_prod_Onested__swap_H,axiom,
% 5.25/5.56 ! [A: nat > nat > nat,N: nat] :
% 5.25/5.56 ( ( groups708209901874060359at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( groups708209901874060359at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( groups708209901874060359at_nat
% 5.25/5.56 @ ^ [J3: nat] :
% 5.25/5.56 ( groups708209901874060359at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 5.25/5.56 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.nested_swap'
% 5.25/5.56 thf(fact_7866_sum__choose__lower,axiom,
% 5.25/5.56 ! [R2: nat,N: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K3 ) @ K3 )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N ) ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_choose_lower
% 5.25/5.56 thf(fact_7867_choose__rising__sum_I1_J,axiom,
% 5.25/5.56 ! [N: nat,M: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_rising_sum(1)
% 5.25/5.56 thf(fact_7868_choose__rising__sum_I2_J,axiom,
% 5.25/5.56 ! [N: nat,M: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_rising_sum(2)
% 5.25/5.56 thf(fact_7869_abs__le__square__iff,axiom,
% 5.25/5.56 ! [X3: code_integer,Y: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ ( abs_abs_Code_integer @ Y ) )
% 5.25/5.56 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_square_iff
% 5.25/5.56 thf(fact_7870_abs__le__square__iff,axiom,
% 5.25/5.56 ! [X3: real,Y: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( abs_abs_real @ Y ) )
% 5.25/5.56 = ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_square_iff
% 5.25/5.56 thf(fact_7871_abs__le__square__iff,axiom,
% 5.25/5.56 ! [X3: rat,Y: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ ( abs_abs_rat @ Y ) )
% 5.25/5.56 = ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_square_iff
% 5.25/5.56 thf(fact_7872_abs__le__square__iff,axiom,
% 5.25/5.56 ! [X3: int,Y: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ ( abs_abs_int @ Y ) )
% 5.25/5.56 = ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_le_square_iff
% 5.25/5.56 thf(fact_7873_abs__square__eq__1,axiom,
% 5.25/5.56 ! [X3: code_integer] :
% 5.25/5.56 ( ( ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.56 = one_one_Code_integer )
% 5.25/5.56 = ( ( abs_abs_Code_integer @ X3 )
% 5.25/5.56 = one_one_Code_integer ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_square_eq_1
% 5.25/5.56 thf(fact_7874_abs__square__eq__1,axiom,
% 5.25/5.56 ! [X3: rat] :
% 5.25/5.56 ( ( ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.56 = one_one_rat )
% 5.25/5.56 = ( ( abs_abs_rat @ X3 )
% 5.25/5.56 = one_one_rat ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_square_eq_1
% 5.25/5.56 thf(fact_7875_abs__square__eq__1,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.56 = one_one_real )
% 5.25/5.56 = ( ( abs_abs_real @ X3 )
% 5.25/5.56 = one_one_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_square_eq_1
% 5.25/5.56 thf(fact_7876_abs__square__eq__1,axiom,
% 5.25/5.56 ! [X3: int] :
% 5.25/5.56 ( ( ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.56 = one_one_int )
% 5.25/5.56 = ( ( abs_abs_int @ X3 )
% 5.25/5.56 = one_one_int ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_square_eq_1
% 5.25/5.56 thf(fact_7877_power__even__abs,axiom,
% 5.25/5.56 ! [N: nat,A: code_integer] :
% 5.25/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.56 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 5.25/5.56 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power_even_abs
% 5.25/5.56 thf(fact_7878_power__even__abs,axiom,
% 5.25/5.56 ! [N: nat,A: real] :
% 5.25/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.56 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 5.25/5.56 = ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power_even_abs
% 5.25/5.56 thf(fact_7879_power__even__abs,axiom,
% 5.25/5.56 ! [N: nat,A: int] :
% 5.25/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.56 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 5.25/5.56 = ( power_power_int @ A @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power_even_abs
% 5.25/5.56 thf(fact_7880_zero__polynom__imp__zero__coeffs,axiom,
% 5.25/5.56 ! [C: nat > complex,N: nat,K: nat] :
% 5.25/5.56 ( ! [W2: complex] :
% 5.25/5.56 ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ W2 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_complex )
% 5.25/5.56 => ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.56 => ( ( C @ K )
% 5.25/5.56 = zero_zero_complex ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_polynom_imp_zero_coeffs
% 5.25/5.56 thf(fact_7881_zero__polynom__imp__zero__coeffs,axiom,
% 5.25/5.56 ! [C: nat > real,N: nat,K: nat] :
% 5.25/5.56 ( ! [W2: real] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ W2 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_real )
% 5.25/5.56 => ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.56 => ( ( C @ K )
% 5.25/5.56 = zero_zero_real ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_polynom_imp_zero_coeffs
% 5.25/5.56 thf(fact_7882_polyfun__eq__0,axiom,
% 5.25/5.56 ! [C: nat > complex,N: nat] :
% 5.25/5.56 ( ( ! [X2: complex] :
% 5.25/5.56 ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X2 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_complex ) )
% 5.25/5.56 = ( ! [I3: nat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ I3 @ N )
% 5.25/5.56 => ( ( C @ I3 )
% 5.25/5.56 = zero_zero_complex ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_eq_0
% 5.25/5.56 thf(fact_7883_polyfun__eq__0,axiom,
% 5.25/5.56 ! [C: nat > real,N: nat] :
% 5.25/5.56 ( ( ! [X2: real] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X2 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_real ) )
% 5.25/5.56 = ( ! [I3: nat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ I3 @ N )
% 5.25/5.56 => ( ( C @ I3 )
% 5.25/5.56 = zero_zero_real ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_eq_0
% 5.25/5.56 thf(fact_7884_sum_OatMost__shift,axiom,
% 5.25/5.56 ! [G: nat > rat,N: nat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.atMost_shift
% 5.25/5.56 thf(fact_7885_sum_OatMost__shift,axiom,
% 5.25/5.56 ! [G: nat > int,N: nat] :
% 5.25/5.56 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.atMost_shift
% 5.25/5.56 thf(fact_7886_sum_OatMost__shift,axiom,
% 5.25/5.56 ! [G: nat > nat,N: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.atMost_shift
% 5.25/5.56 thf(fact_7887_sum_OatMost__shift,axiom,
% 5.25/5.56 ! [G: nat > real,N: nat] :
% 5.25/5.56 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.atMost_shift
% 5.25/5.56 thf(fact_7888_sum__up__index__split,axiom,
% 5.25/5.56 ! [F: nat > rat,M: nat,N: nat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.25/5.56 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_up_index_split
% 5.25/5.56 thf(fact_7889_sum__up__index__split,axiom,
% 5.25/5.56 ! [F: nat > int,M: nat,N: nat] :
% 5.25/5.56 ( ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.25/5.56 = ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_up_index_split
% 5.25/5.56 thf(fact_7890_sum__up__index__split,axiom,
% 5.25/5.56 ! [F: nat > nat,M: nat,N: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.25/5.56 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_up_index_split
% 5.25/5.56 thf(fact_7891_sum__up__index__split,axiom,
% 5.25/5.56 ! [F: nat > real,M: nat,N: nat] :
% 5.25/5.56 ( ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.25/5.56 = ( plus_plus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_up_index_split
% 5.25/5.56 thf(fact_7892_prod_OatMost__shift,axiom,
% 5.25/5.56 ! [G: nat > real,N: nat] :
% 5.25/5.56 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups129246275422532515t_real
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.atMost_shift
% 5.25/5.56 thf(fact_7893_prod_OatMost__shift,axiom,
% 5.25/5.56 ! [G: nat > rat,N: nat] :
% 5.25/5.56 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups73079841787564623at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.atMost_shift
% 5.25/5.56 thf(fact_7894_prod_OatMost__shift,axiom,
% 5.25/5.56 ! [G: nat > int,N: nat] :
% 5.25/5.56 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups705719431365010083at_int
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.atMost_shift
% 5.25/5.56 thf(fact_7895_prod_OatMost__shift,axiom,
% 5.25/5.56 ! [G: nat > nat,N: nat] :
% 5.25/5.56 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.25/5.56 @ ( groups708209901874060359at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.atMost_shift
% 5.25/5.56 thf(fact_7896_atLeast1__atMost__eq__remove0,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.25/5.56 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % atLeast1_atMost_eq_remove0
% 5.25/5.56 thf(fact_7897_gbinomial__parallel__sum,axiom,
% 5.25/5.56 ! [A: complex,N: nat] :
% 5.25/5.56 ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [K3: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K3 ) ) @ K3 )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_parallel_sum
% 5.25/5.56 thf(fact_7898_gbinomial__parallel__sum,axiom,
% 5.25/5.56 ! [A: rat,N: nat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [K3: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K3 ) ) @ K3 )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_parallel_sum
% 5.25/5.56 thf(fact_7899_gbinomial__parallel__sum,axiom,
% 5.25/5.56 ! [A: real,N: nat] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [K3: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K3 ) ) @ K3 )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_parallel_sum
% 5.25/5.56 thf(fact_7900_sum_Otriangle__reindex__eq,axiom,
% 5.25/5.56 ! [G: nat > nat > nat,N: nat] :
% 5.25/5.56 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.25/5.56 @ ( collec3392354462482085612at_nat
% 5.25/5.56 @ ( produc6081775807080527818_nat_o
% 5.25/5.56 @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 5.25/5.56 = ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [K3: nat] :
% 5.25/5.56 ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ K3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.triangle_reindex_eq
% 5.25/5.56 thf(fact_7901_sum_Otriangle__reindex__eq,axiom,
% 5.25/5.56 ! [G: nat > nat > real,N: nat] :
% 5.25/5.56 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 5.25/5.56 @ ( collec3392354462482085612at_nat
% 5.25/5.56 @ ( produc6081775807080527818_nat_o
% 5.25/5.56 @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 5.25/5.56 = ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [K3: nat] :
% 5.25/5.56 ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ K3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.triangle_reindex_eq
% 5.25/5.56 thf(fact_7902_prod_Otriangle__reindex__eq,axiom,
% 5.25/5.56 ! [G: nat > nat > int,N: nat] :
% 5.25/5.56 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 5.25/5.56 @ ( collec3392354462482085612at_nat
% 5.25/5.56 @ ( produc6081775807080527818_nat_o
% 5.25/5.56 @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 5.25/5.56 = ( groups705719431365010083at_int
% 5.25/5.56 @ ^ [K3: nat] :
% 5.25/5.56 ( groups705719431365010083at_int
% 5.25/5.56 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ K3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.triangle_reindex_eq
% 5.25/5.56 thf(fact_7903_prod_Otriangle__reindex__eq,axiom,
% 5.25/5.56 ! [G: nat > nat > nat,N: nat] :
% 5.25/5.56 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.25/5.56 @ ( collec3392354462482085612at_nat
% 5.25/5.56 @ ( produc6081775807080527818_nat_o
% 5.25/5.56 @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 5.25/5.56 = ( groups708209901874060359at_nat
% 5.25/5.56 @ ^ [K3: nat] :
% 5.25/5.56 ( groups708209901874060359at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ K3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.triangle_reindex_eq
% 5.25/5.56 thf(fact_7904_sum__choose__diagonal,axiom,
% 5.25/5.56 ! [M: nat,N: nat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.56 => ( ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_choose_diagonal
% 5.25/5.56 thf(fact_7905_vandermonde,axiom,
% 5.25/5.56 ! [M: nat,N: nat,R2: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N @ ( minus_minus_nat @ R2 @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ R2 ) )
% 5.25/5.56 = ( binomial @ ( plus_plus_nat @ M @ N ) @ R2 ) ) ).
% 5.25/5.56
% 5.25/5.56 % vandermonde
% 5.25/5.56 thf(fact_7906_power2__le__iff__abs__le,axiom,
% 5.25/5.56 ! [Y: code_integer,X3: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.25/5.56 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.56 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ Y ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power2_le_iff_abs_le
% 5.25/5.56 thf(fact_7907_power2__le__iff__abs__le,axiom,
% 5.25/5.56 ! [Y: real,X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.56 => ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.56 = ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ Y ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power2_le_iff_abs_le
% 5.25/5.56 thf(fact_7908_power2__le__iff__abs__le,axiom,
% 5.25/5.56 ! [Y: rat,X3: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.56 => ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.56 = ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ Y ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power2_le_iff_abs_le
% 5.25/5.56 thf(fact_7909_power2__le__iff__abs__le,axiom,
% 5.25/5.56 ! [Y: int,X3: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.56 => ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.56 = ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ Y ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power2_le_iff_abs_le
% 5.25/5.56 thf(fact_7910_abs__square__le__1,axiom,
% 5.25/5.56 ! [X3: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.25/5.56 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X3 ) @ one_one_Code_integer ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_square_le_1
% 5.25/5.56 thf(fact_7911_abs__square__le__1,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.25/5.56 = ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_square_le_1
% 5.25/5.56 thf(fact_7912_abs__square__le__1,axiom,
% 5.25/5.56 ! [X3: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.25/5.56 = ( ord_less_eq_rat @ ( abs_abs_rat @ X3 ) @ one_one_rat ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_square_le_1
% 5.25/5.56 thf(fact_7913_abs__square__le__1,axiom,
% 5.25/5.56 ! [X3: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.25/5.56 = ( ord_less_eq_int @ ( abs_abs_int @ X3 ) @ one_one_int ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_square_le_1
% 5.25/5.56 thf(fact_7914_abs__square__less__1,axiom,
% 5.25/5.56 ! [X3: code_integer] :
% 5.25/5.56 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.25/5.56 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X3 ) @ one_one_Code_integer ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_square_less_1
% 5.25/5.56 thf(fact_7915_abs__square__less__1,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.25/5.56 = ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_square_less_1
% 5.25/5.56 thf(fact_7916_abs__square__less__1,axiom,
% 5.25/5.56 ! [X3: rat] :
% 5.25/5.56 ( ( ord_less_rat @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.25/5.56 = ( ord_less_rat @ ( abs_abs_rat @ X3 ) @ one_one_rat ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_square_less_1
% 5.25/5.56 thf(fact_7917_abs__square__less__1,axiom,
% 5.25/5.56 ! [X3: int] :
% 5.25/5.56 ( ( ord_less_int @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.25/5.56 = ( ord_less_int @ ( abs_abs_int @ X3 ) @ one_one_int ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_square_less_1
% 5.25/5.56 thf(fact_7918_power__mono__even,axiom,
% 5.25/5.56 ! [N: nat,A: code_integer,B: code_integer] :
% 5.25/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.56 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.25/5.56 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power_mono_even
% 5.25/5.56 thf(fact_7919_power__mono__even,axiom,
% 5.25/5.56 ! [N: nat,A: real,B: real] :
% 5.25/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.56 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.25/5.56 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power_mono_even
% 5.25/5.56 thf(fact_7920_power__mono__even,axiom,
% 5.25/5.56 ! [N: nat,A: rat,B: rat] :
% 5.25/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.56 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.25/5.56 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power_mono_even
% 5.25/5.56 thf(fact_7921_power__mono__even,axiom,
% 5.25/5.56 ! [N: nat,A: int,B: int] :
% 5.25/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.56 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.25/5.56 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % power_mono_even
% 5.25/5.56 thf(fact_7922_convex__sum__bound__le,axiom,
% 5.25/5.56 ! [I6: set_nat,X3: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.25/5.56 ( ! [I4: nat] :
% 5.25/5.56 ( ( member_nat @ I4 @ I6 )
% 5.25/5.56 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I4 ) ) )
% 5.25/5.56 => ( ( ( groups7501900531339628137nteger @ X3 @ I6 )
% 5.25/5.56 = one_one_Code_integer )
% 5.25/5.56 => ( ! [I4: nat] :
% 5.25/5.56 ( ( member_nat @ I4 @ I6 )
% 5.25/5.56 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.25/5.56 => ( ord_le3102999989581377725nteger
% 5.25/5.56 @ ( abs_abs_Code_integer
% 5.25/5.56 @ ( minus_8373710615458151222nteger
% 5.25/5.56 @ ( groups7501900531339628137nteger
% 5.25/5.56 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X3 @ I3 ) )
% 5.25/5.56 @ I6 )
% 5.25/5.56 @ B ) )
% 5.25/5.56 @ Delta ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % convex_sum_bound_le
% 5.25/5.56 thf(fact_7923_convex__sum__bound__le,axiom,
% 5.25/5.56 ! [I6: set_real,X3: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 5.25/5.56 ( ! [I4: real] :
% 5.25/5.56 ( ( member_real @ I4 @ I6 )
% 5.25/5.56 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I4 ) ) )
% 5.25/5.56 => ( ( ( groups7713935264441627589nteger @ X3 @ I6 )
% 5.25/5.56 = one_one_Code_integer )
% 5.25/5.56 => ( ! [I4: real] :
% 5.25/5.56 ( ( member_real @ I4 @ I6 )
% 5.25/5.56 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.25/5.56 => ( ord_le3102999989581377725nteger
% 5.25/5.56 @ ( abs_abs_Code_integer
% 5.25/5.56 @ ( minus_8373710615458151222nteger
% 5.25/5.56 @ ( groups7713935264441627589nteger
% 5.25/5.56 @ ^ [I3: real] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X3 @ I3 ) )
% 5.25/5.56 @ I6 )
% 5.25/5.56 @ B ) )
% 5.25/5.56 @ Delta ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % convex_sum_bound_le
% 5.25/5.56 thf(fact_7924_convex__sum__bound__le,axiom,
% 5.25/5.56 ! [I6: set_int,X3: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 5.25/5.56 ( ! [I4: int] :
% 5.25/5.56 ( ( member_int @ I4 @ I6 )
% 5.25/5.56 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I4 ) ) )
% 5.25/5.56 => ( ( ( groups7873554091576472773nteger @ X3 @ I6 )
% 5.25/5.56 = one_one_Code_integer )
% 5.25/5.56 => ( ! [I4: int] :
% 5.25/5.56 ( ( member_int @ I4 @ I6 )
% 5.25/5.56 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.25/5.56 => ( ord_le3102999989581377725nteger
% 5.25/5.56 @ ( abs_abs_Code_integer
% 5.25/5.56 @ ( minus_8373710615458151222nteger
% 5.25/5.56 @ ( groups7873554091576472773nteger
% 5.25/5.56 @ ^ [I3: int] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X3 @ I3 ) )
% 5.25/5.56 @ I6 )
% 5.25/5.56 @ B ) )
% 5.25/5.56 @ Delta ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % convex_sum_bound_le
% 5.25/5.56 thf(fact_7925_convex__sum__bound__le,axiom,
% 5.25/5.56 ! [I6: set_complex,X3: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 5.25/5.56 ( ! [I4: complex] :
% 5.25/5.56 ( ( member_complex @ I4 @ I6 )
% 5.25/5.56 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X3 @ I4 ) ) )
% 5.25/5.56 => ( ( ( groups6621422865394947399nteger @ X3 @ I6 )
% 5.25/5.56 = one_one_Code_integer )
% 5.25/5.56 => ( ! [I4: complex] :
% 5.25/5.56 ( ( member_complex @ I4 @ I6 )
% 5.25/5.56 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.25/5.56 => ( ord_le3102999989581377725nteger
% 5.25/5.56 @ ( abs_abs_Code_integer
% 5.25/5.56 @ ( minus_8373710615458151222nteger
% 5.25/5.56 @ ( groups6621422865394947399nteger
% 5.25/5.56 @ ^ [I3: complex] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X3 @ I3 ) )
% 5.25/5.56 @ I6 )
% 5.25/5.56 @ B ) )
% 5.25/5.56 @ Delta ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % convex_sum_bound_le
% 5.25/5.56 thf(fact_7926_convex__sum__bound__le,axiom,
% 5.25/5.56 ! [I6: set_real,X3: real > real,A: real > real,B: real,Delta: real] :
% 5.25/5.56 ( ! [I4: real] :
% 5.25/5.56 ( ( member_real @ I4 @ I6 )
% 5.25/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( X3 @ I4 ) ) )
% 5.25/5.56 => ( ( ( groups8097168146408367636l_real @ X3 @ I6 )
% 5.25/5.56 = one_one_real )
% 5.25/5.56 => ( ! [I4: real] :
% 5.25/5.56 ( ( member_real @ I4 @ I6 )
% 5.25/5.56 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.25/5.56 => ( ord_less_eq_real
% 5.25/5.56 @ ( abs_abs_real
% 5.25/5.56 @ ( minus_minus_real
% 5.25/5.56 @ ( groups8097168146408367636l_real
% 5.25/5.56 @ ^ [I3: real] : ( times_times_real @ ( A @ I3 ) @ ( X3 @ I3 ) )
% 5.25/5.56 @ I6 )
% 5.25/5.56 @ B ) )
% 5.25/5.56 @ Delta ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % convex_sum_bound_le
% 5.25/5.56 thf(fact_7927_convex__sum__bound__le,axiom,
% 5.25/5.56 ! [I6: set_int,X3: int > real,A: int > real,B: real,Delta: real] :
% 5.25/5.56 ( ! [I4: int] :
% 5.25/5.56 ( ( member_int @ I4 @ I6 )
% 5.25/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( X3 @ I4 ) ) )
% 5.25/5.56 => ( ( ( groups8778361861064173332t_real @ X3 @ I6 )
% 5.25/5.56 = one_one_real )
% 5.25/5.56 => ( ! [I4: int] :
% 5.25/5.56 ( ( member_int @ I4 @ I6 )
% 5.25/5.56 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.25/5.56 => ( ord_less_eq_real
% 5.25/5.56 @ ( abs_abs_real
% 5.25/5.56 @ ( minus_minus_real
% 5.25/5.56 @ ( groups8778361861064173332t_real
% 5.25/5.56 @ ^ [I3: int] : ( times_times_real @ ( A @ I3 ) @ ( X3 @ I3 ) )
% 5.25/5.56 @ I6 )
% 5.25/5.56 @ B ) )
% 5.25/5.56 @ Delta ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % convex_sum_bound_le
% 5.25/5.56 thf(fact_7928_convex__sum__bound__le,axiom,
% 5.25/5.56 ! [I6: set_complex,X3: complex > real,A: complex > real,B: real,Delta: real] :
% 5.25/5.56 ( ! [I4: complex] :
% 5.25/5.56 ( ( member_complex @ I4 @ I6 )
% 5.25/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( X3 @ I4 ) ) )
% 5.25/5.56 => ( ( ( groups5808333547571424918x_real @ X3 @ I6 )
% 5.25/5.56 = one_one_real )
% 5.25/5.56 => ( ! [I4: complex] :
% 5.25/5.56 ( ( member_complex @ I4 @ I6 )
% 5.25/5.56 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.25/5.56 => ( ord_less_eq_real
% 5.25/5.56 @ ( abs_abs_real
% 5.25/5.56 @ ( minus_minus_real
% 5.25/5.56 @ ( groups5808333547571424918x_real
% 5.25/5.56 @ ^ [I3: complex] : ( times_times_real @ ( A @ I3 ) @ ( X3 @ I3 ) )
% 5.25/5.56 @ I6 )
% 5.25/5.56 @ B ) )
% 5.25/5.56 @ Delta ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % convex_sum_bound_le
% 5.25/5.56 thf(fact_7929_convex__sum__bound__le,axiom,
% 5.25/5.56 ! [I6: set_nat,X3: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 5.25/5.56 ( ! [I4: nat] :
% 5.25/5.56 ( ( member_nat @ I4 @ I6 )
% 5.25/5.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I4 ) ) )
% 5.25/5.56 => ( ( ( groups2906978787729119204at_rat @ X3 @ I6 )
% 5.25/5.56 = one_one_rat )
% 5.25/5.56 => ( ! [I4: nat] :
% 5.25/5.56 ( ( member_nat @ I4 @ I6 )
% 5.25/5.56 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.25/5.56 => ( ord_less_eq_rat
% 5.25/5.56 @ ( abs_abs_rat
% 5.25/5.56 @ ( minus_minus_rat
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( X3 @ I3 ) )
% 5.25/5.56 @ I6 )
% 5.25/5.56 @ B ) )
% 5.25/5.56 @ Delta ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % convex_sum_bound_le
% 5.25/5.56 thf(fact_7930_convex__sum__bound__le,axiom,
% 5.25/5.56 ! [I6: set_real,X3: real > rat,A: real > rat,B: rat,Delta: rat] :
% 5.25/5.56 ( ! [I4: real] :
% 5.25/5.56 ( ( member_real @ I4 @ I6 )
% 5.25/5.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I4 ) ) )
% 5.25/5.56 => ( ( ( groups1300246762558778688al_rat @ X3 @ I6 )
% 5.25/5.56 = one_one_rat )
% 5.25/5.56 => ( ! [I4: real] :
% 5.25/5.56 ( ( member_real @ I4 @ I6 )
% 5.25/5.56 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.25/5.56 => ( ord_less_eq_rat
% 5.25/5.56 @ ( abs_abs_rat
% 5.25/5.56 @ ( minus_minus_rat
% 5.25/5.56 @ ( groups1300246762558778688al_rat
% 5.25/5.56 @ ^ [I3: real] : ( times_times_rat @ ( A @ I3 ) @ ( X3 @ I3 ) )
% 5.25/5.56 @ I6 )
% 5.25/5.56 @ B ) )
% 5.25/5.56 @ Delta ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % convex_sum_bound_le
% 5.25/5.56 thf(fact_7931_convex__sum__bound__le,axiom,
% 5.25/5.56 ! [I6: set_int,X3: int > rat,A: int > rat,B: rat,Delta: rat] :
% 5.25/5.56 ( ! [I4: int] :
% 5.25/5.56 ( ( member_int @ I4 @ I6 )
% 5.25/5.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( X3 @ I4 ) ) )
% 5.25/5.56 => ( ( ( groups3906332499630173760nt_rat @ X3 @ I6 )
% 5.25/5.56 = one_one_rat )
% 5.25/5.56 => ( ! [I4: int] :
% 5.25/5.56 ( ( member_int @ I4 @ I6 )
% 5.25/5.56 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.25/5.56 => ( ord_less_eq_rat
% 5.25/5.56 @ ( abs_abs_rat
% 5.25/5.56 @ ( minus_minus_rat
% 5.25/5.56 @ ( groups3906332499630173760nt_rat
% 5.25/5.56 @ ^ [I3: int] : ( times_times_rat @ ( A @ I3 ) @ ( X3 @ I3 ) )
% 5.25/5.56 @ I6 )
% 5.25/5.56 @ B ) )
% 5.25/5.56 @ Delta ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % convex_sum_bound_le
% 5.25/5.56 thf(fact_7932_sum__gp__basic,axiom,
% 5.25/5.56 ! [X3: complex,N: nat] :
% 5.25/5.56 ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X3 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_gp_basic
% 5.25/5.56 thf(fact_7933_sum__gp__basic,axiom,
% 5.25/5.56 ! [X3: rat,N: nat] :
% 5.25/5.56 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X3 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_gp_basic
% 5.25/5.56 thf(fact_7934_sum__gp__basic,axiom,
% 5.25/5.56 ! [X3: int,N: nat] :
% 5.25/5.56 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X3 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X3 @ ( suc @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_gp_basic
% 5.25/5.56 thf(fact_7935_sum__gp__basic,axiom,
% 5.25/5.56 ! [X3: real,N: nat] :
% 5.25/5.56 ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X3 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_gp_basic
% 5.25/5.56 thf(fact_7936_polyfun__linear__factor__root,axiom,
% 5.25/5.56 ! [C: nat > complex,A: complex,N: nat] :
% 5.25/5.56 ( ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ A @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_complex )
% 5.25/5.56 => ~ ! [B5: nat > complex] :
% 5.25/5.56 ~ ! [Z4: complex] :
% 5.25/5.56 ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( B5 @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_linear_factor_root
% 5.25/5.56 thf(fact_7937_polyfun__linear__factor__root,axiom,
% 5.25/5.56 ! [C: nat > rat,A: rat,N: nat] :
% 5.25/5.56 ( ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ A @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_rat )
% 5.25/5.56 => ~ ! [B5: nat > rat] :
% 5.25/5.56 ~ ! [Z4: rat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( times_times_rat @ ( minus_minus_rat @ Z4 @ A )
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( B5 @ I3 ) @ ( power_power_rat @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_linear_factor_root
% 5.25/5.56 thf(fact_7938_polyfun__linear__factor__root,axiom,
% 5.25/5.56 ! [C: nat > int,A: int,N: nat] :
% 5.25/5.56 ( ( ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ A @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_int )
% 5.25/5.56 => ~ ! [B5: nat > int] :
% 5.25/5.56 ~ ! [Z4: int] :
% 5.25/5.56 ( ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( B5 @ I3 ) @ ( power_power_int @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_linear_factor_root
% 5.25/5.56 thf(fact_7939_polyfun__linear__factor__root,axiom,
% 5.25/5.56 ! [C: nat > real,A: real,N: nat] :
% 5.25/5.56 ( ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ A @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_real )
% 5.25/5.56 => ~ ! [B5: nat > real] :
% 5.25/5.56 ~ ! [Z4: real] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( B5 @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_linear_factor_root
% 5.25/5.56 thf(fact_7940_polyfun__linear__factor,axiom,
% 5.25/5.56 ! [C: nat > complex,N: nat,A: complex] :
% 5.25/5.56 ? [B5: nat > complex] :
% 5.25/5.56 ! [Z4: complex] :
% 5.25/5.56 ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( plus_plus_complex
% 5.25/5.56 @ ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( B5 @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ A @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_linear_factor
% 5.25/5.56 thf(fact_7941_polyfun__linear__factor,axiom,
% 5.25/5.56 ! [C: nat > rat,N: nat,A: rat] :
% 5.25/5.56 ? [B5: nat > rat] :
% 5.25/5.56 ! [Z4: rat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( plus_plus_rat
% 5.25/5.56 @ ( times_times_rat @ ( minus_minus_rat @ Z4 @ A )
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( B5 @ I3 ) @ ( power_power_rat @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ A @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_linear_factor
% 5.25/5.56 thf(fact_7942_polyfun__linear__factor,axiom,
% 5.25/5.56 ! [C: nat > int,N: nat,A: int] :
% 5.25/5.56 ? [B5: nat > int] :
% 5.25/5.56 ! [Z4: int] :
% 5.25/5.56 ( ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( plus_plus_int
% 5.25/5.56 @ ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( B5 @ I3 ) @ ( power_power_int @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ A @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_linear_factor
% 5.25/5.56 thf(fact_7943_polyfun__linear__factor,axiom,
% 5.25/5.56 ! [C: nat > real,N: nat,A: real] :
% 5.25/5.56 ? [B5: nat > real] :
% 5.25/5.56 ! [Z4: real] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( plus_plus_real
% 5.25/5.56 @ ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( B5 @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ A @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_linear_factor
% 5.25/5.56 thf(fact_7944_sum__power__shift,axiom,
% 5.25/5.56 ! [M: nat,N: nat,X3: complex] :
% 5.25/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.56 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.56 = ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_power_shift
% 5.25/5.56 thf(fact_7945_sum__power__shift,axiom,
% 5.25/5.56 ! [M: nat,N: nat,X3: rat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.56 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.56 = ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_power_shift
% 5.25/5.56 thf(fact_7946_sum__power__shift,axiom,
% 5.25/5.56 ! [M: nat,N: nat,X3: int] :
% 5.25/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.56 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.56 = ( times_times_int @ ( power_power_int @ X3 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_power_shift
% 5.25/5.56 thf(fact_7947_sum__power__shift,axiom,
% 5.25/5.56 ! [M: nat,N: nat,X3: real] :
% 5.25/5.56 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.56 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.25/5.56 = ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_power_shift
% 5.25/5.56 thf(fact_7948_sum_Otriangle__reindex,axiom,
% 5.25/5.56 ! [G: nat > nat > nat,N: nat] :
% 5.25/5.56 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.25/5.56 @ ( collec3392354462482085612at_nat
% 5.25/5.56 @ ( produc6081775807080527818_nat_o
% 5.25/5.56 @ ^ [I3: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 5.25/5.56 = ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [K3: nat] :
% 5.25/5.56 ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ K3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.triangle_reindex
% 5.25/5.56 thf(fact_7949_sum_Otriangle__reindex,axiom,
% 5.25/5.56 ! [G: nat > nat > real,N: nat] :
% 5.25/5.56 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 5.25/5.56 @ ( collec3392354462482085612at_nat
% 5.25/5.56 @ ( produc6081775807080527818_nat_o
% 5.25/5.56 @ ^ [I3: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 5.25/5.56 = ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [K3: nat] :
% 5.25/5.56 ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ K3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.triangle_reindex
% 5.25/5.56 thf(fact_7950_prod_Otriangle__reindex,axiom,
% 5.25/5.56 ! [G: nat > nat > int,N: nat] :
% 5.25/5.56 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 5.25/5.56 @ ( collec3392354462482085612at_nat
% 5.25/5.56 @ ( produc6081775807080527818_nat_o
% 5.25/5.56 @ ^ [I3: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 5.25/5.56 = ( groups705719431365010083at_int
% 5.25/5.56 @ ^ [K3: nat] :
% 5.25/5.56 ( groups705719431365010083at_int
% 5.25/5.56 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ K3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.triangle_reindex
% 5.25/5.56 thf(fact_7951_prod_Otriangle__reindex,axiom,
% 5.25/5.56 ! [G: nat > nat > nat,N: nat] :
% 5.25/5.56 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.25/5.56 @ ( collec3392354462482085612at_nat
% 5.25/5.56 @ ( produc6081775807080527818_nat_o
% 5.25/5.56 @ ^ [I3: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 5.25/5.56 = ( groups708209901874060359at_nat
% 5.25/5.56 @ ^ [K3: nat] :
% 5.25/5.56 ( groups708209901874060359at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ K3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.triangle_reindex
% 5.25/5.56 thf(fact_7952_choose__row__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_row_sum
% 5.25/5.56 thf(fact_7953_binomial,axiom,
% 5.25/5.56 ! [A: nat,B: nat,N: nat] :
% 5.25/5.56 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.25/5.56 = ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial
% 5.25/5.56 thf(fact_7954_suminf__geometric,axiom,
% 5.25/5.56 ! [C: real] :
% 5.25/5.56 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.25/5.56 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.25/5.56 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % suminf_geometric
% 5.25/5.56 thf(fact_7955_suminf__geometric,axiom,
% 5.25/5.56 ! [C: complex] :
% 5.25/5.56 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.25/5.56 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.25/5.56 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % suminf_geometric
% 5.25/5.56 thf(fact_7956_sum_Oin__pairs__0,axiom,
% 5.25/5.56 ! [G: nat > rat,N: nat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.56 = ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.in_pairs_0
% 5.25/5.56 thf(fact_7957_sum_Oin__pairs__0,axiom,
% 5.25/5.56 ! [G: nat > int,N: nat] :
% 5.25/5.56 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.56 = ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.in_pairs_0
% 5.25/5.56 thf(fact_7958_sum_Oin__pairs__0,axiom,
% 5.25/5.56 ! [G: nat > nat,N: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.56 = ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.in_pairs_0
% 5.25/5.56 thf(fact_7959_sum_Oin__pairs__0,axiom,
% 5.25/5.56 ! [G: nat > real,N: nat] :
% 5.25/5.56 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.56 = ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.in_pairs_0
% 5.25/5.56 thf(fact_7960_polynomial__product,axiom,
% 5.25/5.56 ! [M: nat,A: nat > complex,N: nat,B: nat > complex,X3: complex] :
% 5.25/5.56 ( ! [I4: nat] :
% 5.25/5.56 ( ( ord_less_nat @ M @ I4 )
% 5.25/5.56 => ( ( A @ I4 )
% 5.25/5.56 = zero_zero_complex ) )
% 5.25/5.56 => ( ! [J: nat] :
% 5.25/5.56 ( ( ord_less_nat @ N @ J )
% 5.25/5.56 => ( ( B @ J )
% 5.25/5.56 = zero_zero_complex ) )
% 5.25/5.56 => ( ( times_times_complex
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [J3: nat] : ( times_times_complex @ ( B @ J3 ) @ ( power_power_complex @ X3 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [R5: nat] :
% 5.25/5.56 ( times_times_complex
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_complex @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ R5 ) )
% 5.25/5.56 @ ( power_power_complex @ X3 @ R5 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polynomial_product
% 5.25/5.56 thf(fact_7961_polynomial__product,axiom,
% 5.25/5.56 ! [M: nat,A: nat > rat,N: nat,B: nat > rat,X3: rat] :
% 5.25/5.56 ( ! [I4: nat] :
% 5.25/5.56 ( ( ord_less_nat @ M @ I4 )
% 5.25/5.56 => ( ( A @ I4 )
% 5.25/5.56 = zero_zero_rat ) )
% 5.25/5.56 => ( ! [J: nat] :
% 5.25/5.56 ( ( ord_less_nat @ N @ J )
% 5.25/5.56 => ( ( B @ J )
% 5.25/5.56 = zero_zero_rat ) )
% 5.25/5.56 => ( ( times_times_rat
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [J3: nat] : ( times_times_rat @ ( B @ J3 ) @ ( power_power_rat @ X3 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [R5: nat] :
% 5.25/5.56 ( times_times_rat
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_rat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ R5 ) )
% 5.25/5.56 @ ( power_power_rat @ X3 @ R5 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polynomial_product
% 5.25/5.56 thf(fact_7962_polynomial__product,axiom,
% 5.25/5.56 ! [M: nat,A: nat > int,N: nat,B: nat > int,X3: int] :
% 5.25/5.56 ( ! [I4: nat] :
% 5.25/5.56 ( ( ord_less_nat @ M @ I4 )
% 5.25/5.56 => ( ( A @ I4 )
% 5.25/5.56 = zero_zero_int ) )
% 5.25/5.56 => ( ! [J: nat] :
% 5.25/5.56 ( ( ord_less_nat @ N @ J )
% 5.25/5.56 => ( ( B @ J )
% 5.25/5.56 = zero_zero_int ) )
% 5.25/5.56 => ( ( times_times_int
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [J3: nat] : ( times_times_int @ ( B @ J3 ) @ ( power_power_int @ X3 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [R5: nat] :
% 5.25/5.56 ( times_times_int
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_int @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ R5 ) )
% 5.25/5.56 @ ( power_power_int @ X3 @ R5 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polynomial_product
% 5.25/5.56 thf(fact_7963_polynomial__product,axiom,
% 5.25/5.56 ! [M: nat,A: nat > real,N: nat,B: nat > real,X3: real] :
% 5.25/5.56 ( ! [I4: nat] :
% 5.25/5.56 ( ( ord_less_nat @ M @ I4 )
% 5.25/5.56 => ( ( A @ I4 )
% 5.25/5.56 = zero_zero_real ) )
% 5.25/5.56 => ( ! [J: nat] :
% 5.25/5.56 ( ( ord_less_nat @ N @ J )
% 5.25/5.56 => ( ( B @ J )
% 5.25/5.56 = zero_zero_real ) )
% 5.25/5.56 => ( ( times_times_real
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [J3: nat] : ( times_times_real @ ( B @ J3 ) @ ( power_power_real @ X3 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [R5: nat] :
% 5.25/5.56 ( times_times_real
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_real @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ R5 ) )
% 5.25/5.56 @ ( power_power_real @ X3 @ R5 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polynomial_product
% 5.25/5.56 thf(fact_7964_prod_Oin__pairs__0,axiom,
% 5.25/5.56 ! [G: nat > real,N: nat] :
% 5.25/5.56 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.56 = ( groups129246275422532515t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.in_pairs_0
% 5.25/5.56 thf(fact_7965_prod_Oin__pairs__0,axiom,
% 5.25/5.56 ! [G: nat > rat,N: nat] :
% 5.25/5.56 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.56 = ( groups73079841787564623at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.in_pairs_0
% 5.25/5.56 thf(fact_7966_prod_Oin__pairs__0,axiom,
% 5.25/5.56 ! [G: nat > int,N: nat] :
% 5.25/5.56 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.56 = ( groups705719431365010083at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.in_pairs_0
% 5.25/5.56 thf(fact_7967_prod_Oin__pairs__0,axiom,
% 5.25/5.56 ! [G: nat > nat,N: nat] :
% 5.25/5.56 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.25/5.56 = ( groups708209901874060359at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.in_pairs_0
% 5.25/5.56 thf(fact_7968_polyfun__eq__const,axiom,
% 5.25/5.56 ! [C: nat > complex,N: nat,K: complex] :
% 5.25/5.56 ( ( ! [X2: complex] :
% 5.25/5.56 ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X2 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = K ) )
% 5.25/5.56 = ( ( ( C @ zero_zero_nat )
% 5.25/5.56 = K )
% 5.25/5.56 & ! [X2: nat] :
% 5.25/5.56 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 5.25/5.56 => ( ( C @ X2 )
% 5.25/5.56 = zero_zero_complex ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_eq_const
% 5.25/5.56 thf(fact_7969_polyfun__eq__const,axiom,
% 5.25/5.56 ! [C: nat > real,N: nat,K: real] :
% 5.25/5.56 ( ( ! [X2: real] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X2 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = K ) )
% 5.25/5.56 = ( ( ( C @ zero_zero_nat )
% 5.25/5.56 = K )
% 5.25/5.56 & ! [X2: nat] :
% 5.25/5.56 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 5.25/5.56 => ( ( C @ X2 )
% 5.25/5.56 = zero_zero_real ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_eq_const
% 5.25/5.56 thf(fact_7970_gbinomial__sum__lower__neg,axiom,
% 5.25/5.56 ! [A: complex,M: nat] :
% 5.25/5.56 ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ M ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_sum_lower_neg
% 5.25/5.56 thf(fact_7971_gbinomial__sum__lower__neg,axiom,
% 5.25/5.56 ! [A: rat,M: nat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_sum_lower_neg
% 5.25/5.56 thf(fact_7972_gbinomial__sum__lower__neg,axiom,
% 5.25/5.56 ! [A: real,M: nat] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ M ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_sum_lower_neg
% 5.25/5.56 thf(fact_7973_binomial__ring,axiom,
% 5.25/5.56 ! [A: complex,B: complex,N: nat] :
% 5.25/5.56 ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N )
% 5.25/5.56 = ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K3 ) ) @ ( power_power_complex @ A @ K3 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_ring
% 5.25/5.56 thf(fact_7974_binomial__ring,axiom,
% 5.25/5.56 ! [A: int,B: int,N: nat] :
% 5.25/5.56 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N )
% 5.25/5.56 = ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( power_power_int @ A @ K3 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_ring
% 5.25/5.56 thf(fact_7975_binomial__ring,axiom,
% 5.25/5.56 ! [A: rat,B: rat,N: nat] :
% 5.25/5.56 ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 5.25/5.56 = ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( power_power_rat @ A @ K3 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_ring
% 5.25/5.56 thf(fact_7976_binomial__ring,axiom,
% 5.25/5.56 ! [A: nat,B: nat,N: nat] :
% 5.25/5.56 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.25/5.56 = ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_ring
% 5.25/5.56 thf(fact_7977_binomial__ring,axiom,
% 5.25/5.56 ! [A: real,B: real,N: nat] :
% 5.25/5.56 ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N )
% 5.25/5.56 = ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( power_power_real @ A @ K3 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_ring
% 5.25/5.56 thf(fact_7978_pochhammer__binomial__sum,axiom,
% 5.25/5.56 ! [A: int,B: int,N: nat] :
% 5.25/5.56 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N )
% 5.25/5.56 = ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( comm_s4660882817536571857er_int @ A @ K3 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % pochhammer_binomial_sum
% 5.25/5.56 thf(fact_7979_pochhammer__binomial__sum,axiom,
% 5.25/5.56 ! [A: rat,B: rat,N: nat] :
% 5.25/5.56 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 5.25/5.56 = ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % pochhammer_binomial_sum
% 5.25/5.56 thf(fact_7980_pochhammer__binomial__sum,axiom,
% 5.25/5.56 ! [A: real,B: real,N: nat] :
% 5.25/5.56 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N )
% 5.25/5.56 = ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( comm_s7457072308508201937r_real @ A @ K3 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % pochhammer_binomial_sum
% 5.25/5.56 thf(fact_7981_polynomial__product__nat,axiom,
% 5.25/5.56 ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X3: nat] :
% 5.25/5.56 ( ! [I4: nat] :
% 5.25/5.56 ( ( ord_less_nat @ M @ I4 )
% 5.25/5.56 => ( ( A @ I4 )
% 5.25/5.56 = zero_zero_nat ) )
% 5.25/5.56 => ( ! [J: nat] :
% 5.25/5.56 ( ( ord_less_nat @ N @ J )
% 5.25/5.56 => ( ( B @ J )
% 5.25/5.56 = zero_zero_nat ) )
% 5.25/5.56 => ( ( times_times_nat
% 5.25/5.56 @ ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( power_power_nat @ X3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 @ ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X3 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [R5: nat] :
% 5.25/5.56 ( times_times_nat
% 5.25/5.56 @ ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ R5 ) )
% 5.25/5.56 @ ( power_power_nat @ X3 @ R5 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polynomial_product_nat
% 5.25/5.56 thf(fact_7982_choose__square__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_square_sum
% 5.25/5.56 thf(fact_7983_sum_Ozero__middle,axiom,
% 5.25/5.56 ! [P2: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.25/5.56 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.25/5.56 => ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [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 ) ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ P2 ) )
% 5.25/5.56 = ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.zero_middle
% 5.25/5.56 thf(fact_7984_sum_Ozero__middle,axiom,
% 5.25/5.56 ! [P2: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.25/5.56 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.25/5.56 => ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ zero_zero_rat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ P2 ) )
% 5.25/5.56 = ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.zero_middle
% 5.25/5.56 thf(fact_7985_sum_Ozero__middle,axiom,
% 5.25/5.56 ! [P2: nat,K: nat,G: nat > int,H2: nat > int] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.25/5.56 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.25/5.56 => ( ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [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 ) ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ P2 ) )
% 5.25/5.56 = ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.zero_middle
% 5.25/5.56 thf(fact_7986_sum_Ozero__middle,axiom,
% 5.25/5.56 ! [P2: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.25/5.56 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.25/5.56 => ( ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [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 ) ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ P2 ) )
% 5.25/5.56 = ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.zero_middle
% 5.25/5.56 thf(fact_7987_sum_Ozero__middle,axiom,
% 5.25/5.56 ! [P2: nat,K: nat,G: nat > real,H2: nat > real] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.25/5.56 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.25/5.56 => ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [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 ) ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ P2 ) )
% 5.25/5.56 = ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum.zero_middle
% 5.25/5.56 thf(fact_7988_prod_Ozero__middle,axiom,
% 5.25/5.56 ! [P2: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.25/5.56 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.25/5.56 => ( ( groups6464643781859351333omplex
% 5.25/5.56 @ ^ [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 ) ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ P2 ) )
% 5.25/5.56 = ( groups6464643781859351333omplex
% 5.25/5.56 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.zero_middle
% 5.25/5.56 thf(fact_7989_prod_Ozero__middle,axiom,
% 5.25/5.56 ! [P2: nat,K: nat,G: nat > real,H2: nat > real] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.25/5.56 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.25/5.56 => ( ( groups129246275422532515t_real
% 5.25/5.56 @ ^ [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 ) ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ P2 ) )
% 5.25/5.56 = ( groups129246275422532515t_real
% 5.25/5.56 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.zero_middle
% 5.25/5.56 thf(fact_7990_prod_Ozero__middle,axiom,
% 5.25/5.56 ! [P2: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.25/5.56 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.25/5.56 => ( ( groups73079841787564623at_rat
% 5.25/5.56 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ one_one_rat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ P2 ) )
% 5.25/5.56 = ( groups73079841787564623at_rat
% 5.25/5.56 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.zero_middle
% 5.25/5.56 thf(fact_7991_prod_Ozero__middle,axiom,
% 5.25/5.56 ! [P2: nat,K: nat,G: nat > int,H2: nat > int] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.25/5.56 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.25/5.56 => ( ( groups705719431365010083at_int
% 5.25/5.56 @ ^ [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 ) ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ P2 ) )
% 5.25/5.56 = ( groups705719431365010083at_int
% 5.25/5.56 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.zero_middle
% 5.25/5.56 thf(fact_7992_prod_Ozero__middle,axiom,
% 5.25/5.56 ! [P2: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.25/5.56 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.25/5.56 => ( ( groups708209901874060359at_nat
% 5.25/5.56 @ ^ [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 ) ) ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ P2 ) )
% 5.25/5.56 = ( groups708209901874060359at_nat
% 5.25/5.56 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % prod.zero_middle
% 5.25/5.56 thf(fact_7993_gbinomial__partial__sum__poly,axiom,
% 5.25/5.56 ! [M: nat,A: complex,X3: complex,Y: complex] :
% 5.25/5.56 ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K3 ) @ ( power_power_complex @ X3 @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X3 ) @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X3 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_partial_sum_poly
% 5.25/5.56 thf(fact_7994_gbinomial__partial__sum__poly,axiom,
% 5.25/5.56 ! [M: nat,A: rat,X3: rat,Y: rat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K3 ) @ ( power_power_rat @ X3 @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X3 ) @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_partial_sum_poly
% 5.25/5.56 thf(fact_7995_gbinomial__partial__sum__poly,axiom,
% 5.25/5.56 ! [M: nat,A: real,X3: real,Y: real] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K3 ) @ ( power_power_real @ X3 @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ X3 ) @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X3 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_partial_sum_poly
% 5.25/5.56 thf(fact_7996_of__int__round__abs__le,axiom,
% 5.25/5.56 ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X3 ) ) @ X3 ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % of_int_round_abs_le
% 5.25/5.56 thf(fact_7997_of__int__round__abs__le,axiom,
% 5.25/5.56 ! [X3: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X3 ) ) @ X3 ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % of_int_round_abs_le
% 5.25/5.56 thf(fact_7998_round__unique_H,axiom,
% 5.25/5.56 ! [X3: real,N: int] :
% 5.25/5.56 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.56 => ( ( archim8280529875227126926d_real @ X3 )
% 5.25/5.56 = N ) ) ).
% 5.25/5.56
% 5.25/5.56 % round_unique'
% 5.25/5.56 thf(fact_7999_round__unique_H,axiom,
% 5.25/5.56 ! [X3: rat,N: int] :
% 5.25/5.56 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X3 @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.25/5.56 => ( ( archim7778729529865785530nd_rat @ X3 )
% 5.25/5.56 = N ) ) ).
% 5.25/5.56
% 5.25/5.56 % round_unique'
% 5.25/5.56 thf(fact_8000_root__polyfun,axiom,
% 5.25/5.56 ! [N: nat,Z: int,A: int] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.25/5.56 => ( ( ( power_power_int @ Z @ N )
% 5.25/5.56 = A )
% 5.25/5.56 = ( ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( if_int @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I3 = N ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_int ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % root_polyfun
% 5.25/5.56 thf(fact_8001_root__polyfun,axiom,
% 5.25/5.56 ! [N: nat,Z: complex,A: complex] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.25/5.56 => ( ( ( power_power_complex @ Z @ N )
% 5.25/5.56 = A )
% 5.25/5.56 = ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( if_complex @ ( I3 = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I3 = N ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_complex ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % root_polyfun
% 5.25/5.56 thf(fact_8002_root__polyfun,axiom,
% 5.25/5.56 ! [N: nat,Z: code_integer,A: code_integer] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.25/5.56 => ( ( ( power_8256067586552552935nteger @ Z @ N )
% 5.25/5.56 = A )
% 5.25/5.56 = ( ( groups7501900531339628137nteger
% 5.25/5.56 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I3 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I3 = N ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_z3403309356797280102nteger ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % root_polyfun
% 5.25/5.56 thf(fact_8003_root__polyfun,axiom,
% 5.25/5.56 ! [N: nat,Z: rat,A: rat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.25/5.56 => ( ( ( power_power_rat @ Z @ N )
% 5.25/5.56 = A )
% 5.25/5.56 = ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( if_rat @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_rat @ A ) @ ( if_rat @ ( I3 = N ) @ one_one_rat @ zero_zero_rat ) ) @ ( power_power_rat @ Z @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_rat ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % root_polyfun
% 5.25/5.56 thf(fact_8004_root__polyfun,axiom,
% 5.25/5.56 ! [N: nat,Z: real,A: real] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.25/5.56 => ( ( ( power_power_real @ Z @ N )
% 5.25/5.56 = A )
% 5.25/5.56 = ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( if_real @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I3 = N ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_real ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % root_polyfun
% 5.25/5.56 thf(fact_8005_sum__gp0,axiom,
% 5.25/5.56 ! [X3: complex,N: nat] :
% 5.25/5.56 ( ( ( X3 = one_one_complex )
% 5.25/5.56 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.25/5.56 & ( ( X3 != one_one_complex )
% 5.25/5.56 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X3 ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_gp0
% 5.25/5.56 thf(fact_8006_sum__gp0,axiom,
% 5.25/5.56 ! [X3: rat,N: nat] :
% 5.25/5.56 ( ( ( X3 = one_one_rat )
% 5.25/5.56 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.25/5.56 & ( ( X3 != one_one_rat )
% 5.25/5.56 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X3 ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_gp0
% 5.25/5.56 thf(fact_8007_sum__gp0,axiom,
% 5.25/5.56 ! [X3: real,N: nat] :
% 5.25/5.56 ( ( ( X3 = one_one_real )
% 5.25/5.56 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.25/5.56 & ( ( X3 != one_one_real )
% 5.25/5.56 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X3 ) @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % sum_gp0
% 5.25/5.56 thf(fact_8008_choose__alternating__linear__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( N != one_one_nat )
% 5.25/5.56 => ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I3 ) @ ( semiri8010041392384452111omplex @ I3 ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_complex ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_alternating_linear_sum
% 5.25/5.56 thf(fact_8009_choose__alternating__linear__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( N != one_one_nat )
% 5.25/5.56 => ( ( groups7501900531339628137nteger
% 5.25/5.56 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ I3 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_alternating_linear_sum
% 5.25/5.56 thf(fact_8010_choose__alternating__linear__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( N != one_one_nat )
% 5.25/5.56 => ( ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ I3 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_int ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_alternating_linear_sum
% 5.25/5.56 thf(fact_8011_choose__alternating__linear__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( N != one_one_nat )
% 5.25/5.56 => ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ I3 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_rat ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_alternating_linear_sum
% 5.25/5.56 thf(fact_8012_choose__alternating__linear__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( N != one_one_nat )
% 5.25/5.56 => ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( semiri5074537144036343181t_real @ I3 ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_alternating_linear_sum
% 5.25/5.56 thf(fact_8013_gbinomial__sum__nat__pow2,axiom,
% 5.25/5.56 ! [M: nat] :
% 5.25/5.56 ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [K3: nat] : ( divide1717551699836669952omplex @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ K3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ M ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_sum_nat_pow2
% 5.25/5.56 thf(fact_8014_gbinomial__sum__nat__pow2,axiom,
% 5.25/5.56 ! [M: nat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [K3: nat] : ( divide_divide_rat @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ K3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ M ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_sum_nat_pow2
% 5.25/5.56 thf(fact_8015_gbinomial__sum__nat__pow2,axiom,
% 5.25/5.56 ! [M: nat] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [K3: nat] : ( divide_divide_real @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ K3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ M ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_sum_nat_pow2
% 5.25/5.56 thf(fact_8016_gbinomial__partial__sum__poly__xpos,axiom,
% 5.25/5.56 ! [M: nat,A: complex,X3: complex,Y: complex] :
% 5.25/5.56 ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K3 ) @ ( power_power_complex @ X3 @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [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 @ X3 @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X3 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_partial_sum_poly_xpos
% 5.25/5.56 thf(fact_8017_gbinomial__partial__sum__poly__xpos,axiom,
% 5.25/5.56 ! [M: nat,A: rat,X3: rat,Y: rat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K3 ) @ ( power_power_rat @ X3 @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A ) @ one_one_rat ) @ K3 ) @ ( power_power_rat @ X3 @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X3 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_partial_sum_poly_xpos
% 5.25/5.56 thf(fact_8018_gbinomial__partial__sum__poly__xpos,axiom,
% 5.25/5.56 ! [M: nat,A: real,X3: real,Y: real] :
% 5.25/5.56 ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K3 ) @ ( power_power_real @ X3 @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [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 @ X3 @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X3 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_partial_sum_poly_xpos
% 5.25/5.56 thf(fact_8019_polyfun__diff__alt,axiom,
% 5.25/5.56 ! [N: nat,A: nat > complex,X3: complex,Y: complex] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.25/5.56 => ( ( minus_minus_complex
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y )
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [J3: nat] :
% 5.25/5.56 ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [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 @ X3 @ J3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_diff_alt
% 5.25/5.56 thf(fact_8020_polyfun__diff__alt,axiom,
% 5.25/5.56 ! [N: nat,A: nat > rat,X3: rat,Y: rat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.25/5.56 => ( ( minus_minus_rat
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y )
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [J3: nat] :
% 5.25/5.56 ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_rat @ Y @ K3 ) ) @ ( power_power_rat @ X3 @ J3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_diff_alt
% 5.25/5.56 thf(fact_8021_polyfun__diff__alt,axiom,
% 5.25/5.56 ! [N: nat,A: nat > int,X3: int,Y: int] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.25/5.56 => ( ( minus_minus_int
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( times_times_int @ ( minus_minus_int @ X3 @ Y )
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [J3: nat] :
% 5.25/5.56 ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [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 @ X3 @ J3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_diff_alt
% 5.25/5.56 thf(fact_8022_polyfun__diff__alt,axiom,
% 5.25/5.56 ! [N: nat,A: nat > real,X3: real,Y: real] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.25/5.56 => ( ( minus_minus_real
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( times_times_real @ ( minus_minus_real @ X3 @ Y )
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [J3: nat] :
% 5.25/5.56 ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [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 @ X3 @ J3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_diff_alt
% 5.25/5.56 thf(fact_8023_binomial__r__part__sum,axiom,
% 5.25/5.56 ! [M: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % binomial_r_part_sum
% 5.25/5.56 thf(fact_8024_choose__linear__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( groups3542108847815614940at_nat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_nat @ I3 @ ( binomial @ N @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_linear_sum
% 5.25/5.56 thf(fact_8025_choose__alternating__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I3 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_complex ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_alternating_sum
% 5.25/5.56 thf(fact_8026_choose__alternating__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( groups7501900531339628137nteger
% 5.25/5.56 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_alternating_sum
% 5.25/5.56 thf(fact_8027_choose__alternating__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_int ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_alternating_sum
% 5.25/5.56 thf(fact_8028_choose__alternating__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_rat ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_alternating_sum
% 5.25/5.56 thf(fact_8029_choose__alternating__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 = zero_zero_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_alternating_sum
% 5.25/5.56 thf(fact_8030_polyfun__extremal__lemma,axiom,
% 5.25/5.56 ! [E: real,C: nat > complex,N: nat] :
% 5.25/5.56 ( ( ord_less_real @ zero_zero_real @ E )
% 5.25/5.56 => ? [M8: real] :
% 5.25/5.56 ! [Z4: complex] :
% 5.25/5.56 ( ( ord_less_eq_real @ M8 @ ( real_V1022390504157884413omplex @ Z4 ) )
% 5.25/5.56 => ( ord_less_eq_real
% 5.25/5.56 @ ( real_V1022390504157884413omplex
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 @ ( times_times_real @ E @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( suc @ N ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_extremal_lemma
% 5.25/5.56 thf(fact_8031_polyfun__extremal__lemma,axiom,
% 5.25/5.56 ! [E: real,C: nat > real,N: nat] :
% 5.25/5.56 ( ( ord_less_real @ zero_zero_real @ E )
% 5.25/5.56 => ? [M8: real] :
% 5.25/5.56 ! [Z4: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ M8 @ ( real_V7735802525324610683m_real @ Z4 ) )
% 5.25/5.56 => ( ord_less_eq_real
% 5.25/5.56 @ ( real_V7735802525324610683m_real
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 @ ( times_times_real @ E @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z4 ) @ ( suc @ N ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_extremal_lemma
% 5.25/5.56 thf(fact_8032_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.56 => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 5.25/5.56 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.25/5.56 thf(fact_8033_polyfun__diff,axiom,
% 5.25/5.56 ! [N: nat,A: nat > complex,X3: complex,Y: complex] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.25/5.56 => ( ( minus_minus_complex
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( times_times_complex @ ( minus_minus_complex @ X3 @ Y )
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [J3: nat] :
% 5.25/5.56 ( times_times_complex
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 5.25/5.56 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.25/5.56 @ ( power_power_complex @ X3 @ J3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_diff
% 5.25/5.56 thf(fact_8034_polyfun__diff,axiom,
% 5.25/5.56 ! [N: nat,A: nat > rat,X3: rat,Y: rat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.25/5.56 => ( ( minus_minus_rat
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( times_times_rat @ ( minus_minus_rat @ X3 @ Y )
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [J3: nat] :
% 5.25/5.56 ( times_times_rat
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 5.25/5.56 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.25/5.56 @ ( power_power_rat @ X3 @ J3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_diff
% 5.25/5.56 thf(fact_8035_polyfun__diff,axiom,
% 5.25/5.56 ! [N: nat,A: nat > int,X3: int,Y: int] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.25/5.56 => ( ( minus_minus_int
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( times_times_int @ ( minus_minus_int @ X3 @ Y )
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [J3: nat] :
% 5.25/5.56 ( times_times_int
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 5.25/5.56 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.25/5.56 @ ( power_power_int @ X3 @ J3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_diff
% 5.25/5.56 thf(fact_8036_polyfun__diff,axiom,
% 5.25/5.56 ! [N: nat,A: nat > real,X3: real,Y: real] :
% 5.25/5.56 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.25/5.56 => ( ( minus_minus_real
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X3 @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ I3 ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( times_times_real @ ( minus_minus_real @ X3 @ Y )
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [J3: nat] :
% 5.25/5.56 ( times_times_real
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 5.25/5.56 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.25/5.56 @ ( power_power_real @ X3 @ J3 ) )
% 5.25/5.56 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % polyfun_diff
% 5.25/5.56 thf(fact_8037_gbinomial__r__part__sum,axiom,
% 5.25/5.56 ! [M: nat] :
% 5.25/5.56 ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_r_part_sum
% 5.25/5.56 thf(fact_8038_gbinomial__r__part__sum,axiom,
% 5.25/5.56 ! [M: nat] :
% 5.25/5.56 ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.25/5.56 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_r_part_sum
% 5.25/5.56 thf(fact_8039_gbinomial__r__part__sum,axiom,
% 5.25/5.56 ! [M: nat] :
% 5.25/5.56 ( ( 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 ) )
% 5.25/5.56 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % gbinomial_r_part_sum
% 5.25/5.56 thf(fact_8040_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.56 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X3 ) ) @ X3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_ln_one_plus_x_minus_x_bound
% 5.25/5.56 thf(fact_8041_choose__odd__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] :
% 5.25/5.56 ( if_complex
% 5.25/5.56 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 5.25/5.56 @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I3 ) )
% 5.25/5.56 @ zero_zero_complex )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_odd_sum
% 5.25/5.56 thf(fact_8042_choose__odd__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] :
% 5.25/5.56 ( if_int
% 5.25/5.56 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 5.25/5.56 @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) )
% 5.25/5.56 @ zero_zero_int )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_odd_sum
% 5.25/5.56 thf(fact_8043_choose__odd__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] :
% 5.25/5.56 ( if_rat
% 5.25/5.56 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 5.25/5.56 @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) )
% 5.25/5.56 @ zero_zero_rat )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_odd_sum
% 5.25/5.56 thf(fact_8044_choose__odd__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] :
% 5.25/5.56 ( if_real
% 5.25/5.56 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 5.25/5.56 @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I3 ) )
% 5.25/5.56 @ zero_zero_real )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_odd_sum
% 5.25/5.56 thf(fact_8045_choose__even__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.25/5.56 @ ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I3 ) ) @ zero_zero_complex )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_even_sum
% 5.25/5.56 thf(fact_8046_choose__even__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.25/5.56 @ ( groups3539618377306564664at_int
% 5.25/5.56 @ ^ [I3: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) ) @ zero_zero_int )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_even_sum
% 5.25/5.56 thf(fact_8047_choose__even__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.25/5.56 @ ( groups2906978787729119204at_rat
% 5.25/5.56 @ ^ [I3: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) ) @ zero_zero_rat )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_even_sum
% 5.25/5.56 thf(fact_8048_choose__even__sum,axiom,
% 5.25/5.56 ! [N: nat] :
% 5.25/5.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.56 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.25/5.56 @ ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I3 ) ) @ zero_zero_real )
% 5.25/5.56 @ ( set_ord_atMost_nat @ N ) ) )
% 5.25/5.56 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % choose_even_sum
% 5.25/5.56 thf(fact_8049_abs__sqrt__wlog,axiom,
% 5.25/5.56 ! [P: code_integer > code_integer > $o,X3: code_integer] :
% 5.25/5.56 ( ! [X5: code_integer] :
% 5.25/5.56 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X5 )
% 5.25/5.56 => ( P @ X5 @ ( power_8256067586552552935nteger @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.56 => ( P @ ( abs_abs_Code_integer @ X3 ) @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_sqrt_wlog
% 5.25/5.56 thf(fact_8050_abs__sqrt__wlog,axiom,
% 5.25/5.56 ! [P: real > real > $o,X3: real] :
% 5.25/5.56 ( ! [X5: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.25/5.56 => ( P @ X5 @ ( power_power_real @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.56 => ( P @ ( abs_abs_real @ X3 ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_sqrt_wlog
% 5.25/5.56 thf(fact_8051_abs__sqrt__wlog,axiom,
% 5.25/5.56 ! [P: rat > rat > $o,X3: rat] :
% 5.25/5.56 ( ! [X5: rat] :
% 5.25/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ X5 )
% 5.25/5.56 => ( P @ X5 @ ( power_power_rat @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.56 => ( P @ ( abs_abs_rat @ X3 ) @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_sqrt_wlog
% 5.25/5.56 thf(fact_8052_abs__sqrt__wlog,axiom,
% 5.25/5.56 ! [P: int > int > $o,X3: int] :
% 5.25/5.56 ( ! [X5: int] :
% 5.25/5.56 ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 5.25/5.56 => ( P @ X5 @ ( power_power_int @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.56 => ( P @ ( abs_abs_int @ X3 ) @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_sqrt_wlog
% 5.25/5.56 thf(fact_8053_monoseq__arctan__series,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.56 => ( topolo6980174941875973593q_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % monoseq_arctan_series
% 5.25/5.56 thf(fact_8054_arctan__series,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.56 => ( ( arctan @ X3 )
% 5.25/5.56 = ( suminf_real
% 5.25/5.56 @ ^ [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 @ X3 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % arctan_series
% 5.25/5.56 thf(fact_8055_pi__series,axiom,
% 5.25/5.56 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.25/5.56 = ( suminf_real
% 5.25/5.56 @ ^ [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 ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % pi_series
% 5.25/5.56 thf(fact_8056_summable__arctan__series,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.56 => ( summable_real
% 5.25/5.56 @ ^ [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 @ X3 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_arctan_series
% 5.25/5.56 thf(fact_8057_of__nat__id,axiom,
% 5.25/5.56 ( semiri1316708129612266289at_nat
% 5.25/5.56 = ( ^ [N2: nat] : N2 ) ) ).
% 5.25/5.56
% 5.25/5.56 % of_nat_id
% 5.25/5.56 thf(fact_8058_zdvd1__eq,axiom,
% 5.25/5.56 ! [X3: int] :
% 5.25/5.56 ( ( dvd_dvd_int @ X3 @ one_one_int )
% 5.25/5.56 = ( ( abs_abs_int @ X3 )
% 5.25/5.56 = one_one_int ) ) ).
% 5.25/5.56
% 5.25/5.56 % zdvd1_eq
% 5.25/5.56 thf(fact_8059_summable__iff__shift,axiom,
% 5.25/5.56 ! [F: nat > real,K: nat] :
% 5.25/5.56 ( ( summable_real
% 5.25/5.56 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.25/5.56 = ( summable_real @ F ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_iff_shift
% 5.25/5.56 thf(fact_8060_zabs__less__one__iff,axiom,
% 5.25/5.56 ! [Z: int] :
% 5.25/5.56 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 5.25/5.56 = ( Z = zero_zero_int ) ) ).
% 5.25/5.56
% 5.25/5.56 % zabs_less_one_iff
% 5.25/5.56 thf(fact_8061_zero__le__arctan__iff,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X3 ) )
% 5.25/5.56 = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 5.25/5.56
% 5.25/5.56 % zero_le_arctan_iff
% 5.25/5.56 thf(fact_8062_arctan__le__zero__iff,axiom,
% 5.25/5.56 ! [X3: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( arctan @ X3 ) @ zero_zero_real )
% 5.25/5.56 = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % arctan_le_zero_iff
% 5.25/5.56 thf(fact_8063_summable__cmult__iff,axiom,
% 5.25/5.56 ! [C: complex,F: nat > complex] :
% 5.25/5.56 ( ( summable_complex
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 5.25/5.56 = ( ( C = zero_zero_complex )
% 5.25/5.56 | ( summable_complex @ F ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_cmult_iff
% 5.25/5.56 thf(fact_8064_summable__cmult__iff,axiom,
% 5.25/5.56 ! [C: real,F: nat > real] :
% 5.25/5.56 ( ( summable_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.25/5.56 = ( ( C = zero_zero_real )
% 5.25/5.56 | ( summable_real @ F ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_cmult_iff
% 5.25/5.56 thf(fact_8065_summable__divide__iff,axiom,
% 5.25/5.56 ! [F: nat > complex,C: complex] :
% 5.25/5.56 ( ( summable_complex
% 5.25/5.56 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 5.25/5.56 = ( ( C = zero_zero_complex )
% 5.25/5.56 | ( summable_complex @ F ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_divide_iff
% 5.25/5.56 thf(fact_8066_summable__divide__iff,axiom,
% 5.25/5.56 ! [F: nat > real,C: real] :
% 5.25/5.56 ( ( summable_real
% 5.25/5.56 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 5.25/5.56 = ( ( C = zero_zero_real )
% 5.25/5.56 | ( summable_real @ F ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_divide_iff
% 5.25/5.56 thf(fact_8067_summable__geometric__iff,axiom,
% 5.25/5.56 ! [C: real] :
% 5.25/5.56 ( ( summable_real @ ( power_power_real @ C ) )
% 5.25/5.56 = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_geometric_iff
% 5.25/5.56 thf(fact_8068_summable__geometric__iff,axiom,
% 5.25/5.56 ! [C: complex] :
% 5.25/5.56 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.25/5.56 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_geometric_iff
% 5.25/5.56 thf(fact_8069_arctan__le__iff,axiom,
% 5.25/5.56 ! [X3: real,Y: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ ( arctan @ X3 ) @ ( arctan @ Y ) )
% 5.25/5.56 = ( ord_less_eq_real @ X3 @ Y ) ) ).
% 5.25/5.56
% 5.25/5.56 % arctan_le_iff
% 5.25/5.56 thf(fact_8070_arctan__monotone_H,axiom,
% 5.25/5.56 ! [X3: real,Y: real] :
% 5.25/5.56 ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.56 => ( ord_less_eq_real @ ( arctan @ X3 ) @ ( arctan @ Y ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % arctan_monotone'
% 5.25/5.56 thf(fact_8071_summable__comparison__test_H,axiom,
% 5.25/5.56 ! [G: nat > real,N5: nat,F: nat > real] :
% 5.25/5.56 ( ( summable_real @ G )
% 5.25/5.56 => ( ! [N3: nat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ N5 @ N3 )
% 5.25/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.25/5.56 => ( summable_real @ F ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_comparison_test'
% 5.25/5.56 thf(fact_8072_summable__comparison__test_H,axiom,
% 5.25/5.56 ! [G: nat > real,N5: nat,F: nat > complex] :
% 5.25/5.56 ( ( summable_real @ G )
% 5.25/5.56 => ( ! [N3: nat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ N5 @ N3 )
% 5.25/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.25/5.56 => ( summable_complex @ F ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_comparison_test'
% 5.25/5.56 thf(fact_8073_summable__comparison__test,axiom,
% 5.25/5.56 ! [F: nat > real,G: nat > real] :
% 5.25/5.56 ( ? [N6: nat] :
% 5.25/5.56 ! [N3: nat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ N6 @ N3 )
% 5.25/5.56 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.25/5.56 => ( ( summable_real @ G )
% 5.25/5.56 => ( summable_real @ F ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_comparison_test
% 5.25/5.56 thf(fact_8074_summable__comparison__test,axiom,
% 5.25/5.56 ! [F: nat > complex,G: nat > real] :
% 5.25/5.56 ( ? [N6: nat] :
% 5.25/5.56 ! [N3: nat] :
% 5.25/5.56 ( ( ord_less_eq_nat @ N6 @ N3 )
% 5.25/5.56 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.25/5.56 => ( ( summable_real @ G )
% 5.25/5.56 => ( summable_complex @ F ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_comparison_test
% 5.25/5.56 thf(fact_8075_summable__mult,axiom,
% 5.25/5.56 ! [F: nat > real,C: real] :
% 5.25/5.56 ( ( summable_real @ F )
% 5.25/5.56 => ( summable_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_mult
% 5.25/5.56 thf(fact_8076_summable__mult2,axiom,
% 5.25/5.56 ! [F: nat > real,C: real] :
% 5.25/5.56 ( ( summable_real @ F )
% 5.25/5.56 => ( summable_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_mult2
% 5.25/5.56 thf(fact_8077_summable__add,axiom,
% 5.25/5.56 ! [F: nat > real,G: nat > real] :
% 5.25/5.56 ( ( summable_real @ F )
% 5.25/5.56 => ( ( summable_real @ G )
% 5.25/5.56 => ( summable_real
% 5.25/5.56 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_add
% 5.25/5.56 thf(fact_8078_summable__add,axiom,
% 5.25/5.56 ! [F: nat > nat,G: nat > nat] :
% 5.25/5.56 ( ( summable_nat @ F )
% 5.25/5.56 => ( ( summable_nat @ G )
% 5.25/5.56 => ( summable_nat
% 5.25/5.56 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_add
% 5.25/5.56 thf(fact_8079_summable__add,axiom,
% 5.25/5.56 ! [F: nat > int,G: nat > int] :
% 5.25/5.56 ( ( summable_int @ F )
% 5.25/5.56 => ( ( summable_int @ G )
% 5.25/5.56 => ( summable_int
% 5.25/5.56 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_add
% 5.25/5.56 thf(fact_8080_summable__divide,axiom,
% 5.25/5.56 ! [F: nat > complex,C: complex] :
% 5.25/5.56 ( ( summable_complex @ F )
% 5.25/5.56 => ( summable_complex
% 5.25/5.56 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_divide
% 5.25/5.56 thf(fact_8081_summable__divide,axiom,
% 5.25/5.56 ! [F: nat > real,C: real] :
% 5.25/5.56 ( ( summable_real @ F )
% 5.25/5.56 => ( summable_real
% 5.25/5.56 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_divide
% 5.25/5.56 thf(fact_8082_summable__Suc__iff,axiom,
% 5.25/5.56 ! [F: nat > real] :
% 5.25/5.56 ( ( summable_real
% 5.25/5.56 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 5.25/5.56 = ( summable_real @ F ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_Suc_iff
% 5.25/5.56 thf(fact_8083_summable__ignore__initial__segment,axiom,
% 5.25/5.56 ! [F: nat > real,K: nat] :
% 5.25/5.56 ( ( summable_real @ F )
% 5.25/5.56 => ( summable_real
% 5.25/5.56 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_ignore_initial_segment
% 5.25/5.56 thf(fact_8084_powser__insidea,axiom,
% 5.25/5.56 ! [F: nat > real,X3: real,Z: real] :
% 5.25/5.56 ( ( summable_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) )
% 5.25/5.56 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X3 ) )
% 5.25/5.56 => ( summable_real
% 5.25/5.56 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % powser_insidea
% 5.25/5.56 thf(fact_8085_powser__insidea,axiom,
% 5.25/5.56 ! [F: nat > complex,X3: complex,Z: complex] :
% 5.25/5.56 ( ( summable_complex
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) )
% 5.25/5.56 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X3 ) )
% 5.25/5.56 => ( summable_real
% 5.25/5.56 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % powser_insidea
% 5.25/5.56 thf(fact_8086_suminf__le,axiom,
% 5.25/5.56 ! [F: nat > real,G: nat > real] :
% 5.25/5.56 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.25/5.56 => ( ( summable_real @ F )
% 5.25/5.56 => ( ( summable_real @ G )
% 5.25/5.56 => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % suminf_le
% 5.25/5.56 thf(fact_8087_suminf__le,axiom,
% 5.25/5.56 ! [F: nat > nat,G: nat > nat] :
% 5.25/5.56 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.25/5.56 => ( ( summable_nat @ F )
% 5.25/5.56 => ( ( summable_nat @ G )
% 5.25/5.56 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % suminf_le
% 5.25/5.56 thf(fact_8088_suminf__le,axiom,
% 5.25/5.56 ! [F: nat > int,G: nat > int] :
% 5.25/5.56 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.25/5.56 => ( ( summable_int @ F )
% 5.25/5.56 => ( ( summable_int @ G )
% 5.25/5.56 => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % suminf_le
% 5.25/5.56 thf(fact_8089_summable__mult__D,axiom,
% 5.25/5.56 ! [C: complex,F: nat > complex] :
% 5.25/5.56 ( ( summable_complex
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 5.25/5.56 => ( ( C != zero_zero_complex )
% 5.25/5.56 => ( summable_complex @ F ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_mult_D
% 5.25/5.56 thf(fact_8090_summable__mult__D,axiom,
% 5.25/5.56 ! [C: real,F: nat > real] :
% 5.25/5.56 ( ( summable_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.25/5.56 => ( ( C != zero_zero_real )
% 5.25/5.56 => ( summable_real @ F ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_mult_D
% 5.25/5.56 thf(fact_8091_abs__zmult__eq__1,axiom,
% 5.25/5.56 ! [M: int,N: int] :
% 5.25/5.56 ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 5.25/5.56 = one_one_int )
% 5.25/5.56 => ( ( abs_abs_int @ M )
% 5.25/5.56 = one_one_int ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_zmult_eq_1
% 5.25/5.56 thf(fact_8092_summable__zero__power,axiom,
% 5.25/5.56 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 5.25/5.56
% 5.25/5.56 % summable_zero_power
% 5.25/5.56 thf(fact_8093_summable__zero__power,axiom,
% 5.25/5.56 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 5.25/5.56
% 5.25/5.56 % summable_zero_power
% 5.25/5.56 thf(fact_8094_summable__zero__power,axiom,
% 5.25/5.56 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 5.25/5.56
% 5.25/5.56 % summable_zero_power
% 5.25/5.56 thf(fact_8095_pi__ge__zero,axiom,
% 5.25/5.56 ord_less_eq_real @ zero_zero_real @ pi ).
% 5.25/5.56
% 5.25/5.56 % pi_ge_zero
% 5.25/5.56 thf(fact_8096_abs__div,axiom,
% 5.25/5.56 ! [Y: int,X3: int] :
% 5.25/5.56 ( ( dvd_dvd_int @ Y @ X3 )
% 5.25/5.56 => ( ( abs_abs_int @ ( divide_divide_int @ X3 @ Y ) )
% 5.25/5.56 = ( divide_divide_int @ ( abs_abs_int @ X3 ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % abs_div
% 5.25/5.56 thf(fact_8097_suminf__mult2,axiom,
% 5.25/5.56 ! [F: nat > real,C: real] :
% 5.25/5.56 ( ( summable_real @ F )
% 5.25/5.56 => ( ( times_times_real @ ( suminf_real @ F ) @ C )
% 5.25/5.56 = ( suminf_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % suminf_mult2
% 5.25/5.56 thf(fact_8098_suminf__mult,axiom,
% 5.25/5.56 ! [F: nat > real,C: real] :
% 5.25/5.56 ( ( summable_real @ F )
% 5.25/5.56 => ( ( suminf_real
% 5.25/5.56 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.25/5.56 = ( times_times_real @ C @ ( suminf_real @ F ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % suminf_mult
% 5.25/5.56 thf(fact_8099_suminf__add,axiom,
% 5.25/5.56 ! [F: nat > real,G: nat > real] :
% 5.25/5.56 ( ( summable_real @ F )
% 5.25/5.56 => ( ( summable_real @ G )
% 5.25/5.56 => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.25/5.56 = ( suminf_real
% 5.25/5.56 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % suminf_add
% 5.25/5.56 thf(fact_8100_suminf__add,axiom,
% 5.25/5.56 ! [F: nat > nat,G: nat > nat] :
% 5.25/5.56 ( ( summable_nat @ F )
% 5.25/5.56 => ( ( summable_nat @ G )
% 5.25/5.56 => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 5.25/5.56 = ( suminf_nat
% 5.25/5.56 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % suminf_add
% 5.25/5.56 thf(fact_8101_suminf__add,axiom,
% 5.25/5.56 ! [F: nat > int,G: nat > int] :
% 5.25/5.56 ( ( summable_int @ F )
% 5.25/5.56 => ( ( summable_int @ G )
% 5.25/5.56 => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 5.25/5.56 = ( suminf_int
% 5.25/5.56 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % suminf_add
% 5.25/5.56 thf(fact_8102_suminf__divide,axiom,
% 5.25/5.56 ! [F: nat > complex,C: complex] :
% 5.25/5.56 ( ( summable_complex @ F )
% 5.25/5.56 => ( ( suminf_complex
% 5.25/5.56 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 5.25/5.56 = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % suminf_divide
% 5.25/5.56 thf(fact_8103_suminf__divide,axiom,
% 5.25/5.56 ! [F: nat > real,C: real] :
% 5.25/5.56 ( ( summable_real @ F )
% 5.25/5.56 => ( ( suminf_real
% 5.25/5.56 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 5.25/5.56 = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % suminf_divide
% 5.25/5.56 thf(fact_8104_summable__Cauchy__product,axiom,
% 5.25/5.56 ! [A: nat > complex,B: nat > complex] :
% 5.25/5.56 ( ( summable_real
% 5.25/5.56 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.25/5.56 => ( ( summable_real
% 5.25/5.56 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.25/5.56 => ( summable_complex
% 5.25/5.56 @ ^ [K3: nat] :
% 5.25/5.56 ( groups2073611262835488442omplex
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( B @ ( minus_minus_nat @ K3 @ I3 ) ) )
% 5.25/5.56 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ).
% 5.25/5.56
% 5.25/5.56 % summable_Cauchy_product
% 5.25/5.56 thf(fact_8105_summable__Cauchy__product,axiom,
% 5.25/5.56 ! [A: nat > real,B: nat > real] :
% 5.25/5.56 ( ( summable_real
% 5.25/5.56 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.25/5.56 => ( ( summable_real
% 5.25/5.56 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.25/5.56 => ( summable_real
% 5.25/5.56 @ ^ [K3: nat] :
% 5.25/5.56 ( groups6591440286371151544t_real
% 5.25/5.56 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( B @ ( minus_minus_nat @ K3 @ I3 ) ) )
% 5.25/5.57 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_Cauchy_product
% 5.25/5.57 thf(fact_8106_arctan__ubound,axiom,
% 5.25/5.57 ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % arctan_ubound
% 5.25/5.57 thf(fact_8107_arctan__one,axiom,
% 5.25/5.57 ( ( arctan @ one_one_real )
% 5.25/5.57 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % arctan_one
% 5.25/5.57 thf(fact_8108_suminf__nonneg,axiom,
% 5.25/5.57 ! [F: nat > real] :
% 5.25/5.57 ( ( summable_real @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.25/5.57 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_nonneg
% 5.25/5.57 thf(fact_8109_suminf__nonneg,axiom,
% 5.25/5.57 ! [F: nat > nat] :
% 5.25/5.57 ( ( summable_nat @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.25/5.57 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_nonneg
% 5.25/5.57 thf(fact_8110_suminf__nonneg,axiom,
% 5.25/5.57 ! [F: nat > int] :
% 5.25/5.57 ( ( summable_int @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.25/5.57 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_nonneg
% 5.25/5.57 thf(fact_8111_suminf__eq__zero__iff,axiom,
% 5.25/5.57 ! [F: nat > real] :
% 5.25/5.57 ( ( summable_real @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.25/5.57 => ( ( ( suminf_real @ F )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 = ( ! [N2: nat] :
% 5.25/5.57 ( ( F @ N2 )
% 5.25/5.57 = zero_zero_real ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_eq_zero_iff
% 5.25/5.57 thf(fact_8112_suminf__eq__zero__iff,axiom,
% 5.25/5.57 ! [F: nat > nat] :
% 5.25/5.57 ( ( summable_nat @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.25/5.57 => ( ( ( suminf_nat @ F )
% 5.25/5.57 = zero_zero_nat )
% 5.25/5.57 = ( ! [N2: nat] :
% 5.25/5.57 ( ( F @ N2 )
% 5.25/5.57 = zero_zero_nat ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_eq_zero_iff
% 5.25/5.57 thf(fact_8113_suminf__eq__zero__iff,axiom,
% 5.25/5.57 ! [F: nat > int] :
% 5.25/5.57 ( ( summable_int @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.25/5.57 => ( ( ( suminf_int @ F )
% 5.25/5.57 = zero_zero_int )
% 5.25/5.57 = ( ! [N2: nat] :
% 5.25/5.57 ( ( F @ N2 )
% 5.25/5.57 = zero_zero_int ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_eq_zero_iff
% 5.25/5.57 thf(fact_8114_suminf__pos,axiom,
% 5.25/5.57 ! [F: nat > real] :
% 5.25/5.57 ( ( summable_real @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 5.25/5.57 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_pos
% 5.25/5.57 thf(fact_8115_suminf__pos,axiom,
% 5.25/5.57 ! [F: nat > nat] :
% 5.25/5.57 ( ( summable_nat @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.25/5.57 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_pos
% 5.25/5.57 thf(fact_8116_suminf__pos,axiom,
% 5.25/5.57 ! [F: nat > int] :
% 5.25/5.57 ( ( summable_int @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 5.25/5.57 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_pos
% 5.25/5.57 thf(fact_8117_summable__0__powser,axiom,
% 5.25/5.57 ! [F: nat > complex] :
% 5.25/5.57 ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_0_powser
% 5.25/5.57 thf(fact_8118_summable__0__powser,axiom,
% 5.25/5.57 ! [F: nat > real] :
% 5.25/5.57 ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_0_powser
% 5.25/5.57 thf(fact_8119_summable__zero__power_H,axiom,
% 5.25/5.57 ! [F: nat > complex] :
% 5.25/5.57 ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_zero_power'
% 5.25/5.57 thf(fact_8120_summable__zero__power_H,axiom,
% 5.25/5.57 ! [F: nat > real] :
% 5.25/5.57 ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_zero_power'
% 5.25/5.57 thf(fact_8121_summable__zero__power_H,axiom,
% 5.25/5.57 ! [F: nat > int] :
% 5.25/5.57 ( summable_int
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_int @ ( F @ N2 ) @ ( power_power_int @ zero_zero_int @ N2 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_zero_power'
% 5.25/5.57 thf(fact_8122_summable__powser__split__head,axiom,
% 5.25/5.57 ! [F: nat > complex,Z: complex] :
% 5.25/5.57 ( ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.25/5.57 = ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_powser_split_head
% 5.25/5.57 thf(fact_8123_summable__powser__split__head,axiom,
% 5.25/5.57 ! [F: nat > real,Z: real] :
% 5.25/5.57 ( ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.25/5.57 = ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_powser_split_head
% 5.25/5.57 thf(fact_8124_powser__split__head_I3_J,axiom,
% 5.25/5.57 ! [F: nat > complex,Z: complex] :
% 5.25/5.57 ( ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.25/5.57 => ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % powser_split_head(3)
% 5.25/5.57 thf(fact_8125_powser__split__head_I3_J,axiom,
% 5.25/5.57 ! [F: nat > real,Z: real] :
% 5.25/5.57 ( ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.25/5.57 => ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % powser_split_head(3)
% 5.25/5.57 thf(fact_8126_arctan__lbound,axiom,
% 5.25/5.57 ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 5.25/5.57
% 5.25/5.57 % arctan_lbound
% 5.25/5.57 thf(fact_8127_arctan__bounded,axiom,
% 5.25/5.57 ! [Y: real] :
% 5.25/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.25/5.57 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % arctan_bounded
% 5.25/5.57 thf(fact_8128_summable__powser__ignore__initial__segment,axiom,
% 5.25/5.57 ! [F: nat > complex,M: nat,Z: complex] :
% 5.25/5.57 ( ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N2 @ M ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.25/5.57 = ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_powser_ignore_initial_segment
% 5.25/5.57 thf(fact_8129_summable__powser__ignore__initial__segment,axiom,
% 5.25/5.57 ! [F: nat > real,M: nat,Z: real] :
% 5.25/5.57 ( ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N2 @ M ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.25/5.57 = ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_powser_ignore_initial_segment
% 5.25/5.57 thf(fact_8130_dvd__imp__le__int,axiom,
% 5.25/5.57 ! [I2: int,D: int] :
% 5.25/5.57 ( ( I2 != zero_zero_int )
% 5.25/5.57 => ( ( dvd_dvd_int @ D @ I2 )
% 5.25/5.57 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % dvd_imp_le_int
% 5.25/5.57 thf(fact_8131_summable__norm__comparison__test,axiom,
% 5.25/5.57 ! [F: nat > complex,G: nat > real] :
% 5.25/5.57 ( ? [N6: nat] :
% 5.25/5.57 ! [N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N6 @ N3 )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.25/5.57 => ( ( summable_real @ G )
% 5.25/5.57 => ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_norm_comparison_test
% 5.25/5.57 thf(fact_8132_abs__mod__less,axiom,
% 5.25/5.57 ! [L2: int,K: int] :
% 5.25/5.57 ( ( L2 != zero_zero_int )
% 5.25/5.57 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L2 ) ) @ ( abs_abs_int @ L2 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % abs_mod_less
% 5.25/5.57 thf(fact_8133_summable__rabs__comparison__test,axiom,
% 5.25/5.57 ! [F: nat > real,G: nat > real] :
% 5.25/5.57 ( ? [N6: nat] :
% 5.25/5.57 ! [N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N6 @ N3 )
% 5.25/5.57 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.25/5.57 => ( ( summable_real @ G )
% 5.25/5.57 => ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_rabs_comparison_test
% 5.25/5.57 thf(fact_8134_summable__rabs,axiom,
% 5.25/5.57 ! [F: nat > real] :
% 5.25/5.57 ( ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) )
% 5.25/5.57 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 5.25/5.57 @ ( suminf_real
% 5.25/5.57 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_rabs
% 5.25/5.57 thf(fact_8135_suminf__pos2,axiom,
% 5.25/5.57 ! [F: nat > real,I2: nat] :
% 5.25/5.57 ( ( summable_real @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.25/5.57 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.25/5.57 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_pos2
% 5.25/5.57 thf(fact_8136_suminf__pos2,axiom,
% 5.25/5.57 ! [F: nat > nat,I2: nat] :
% 5.25/5.57 ( ( summable_nat @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.25/5.57 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.25/5.57 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_pos2
% 5.25/5.57 thf(fact_8137_suminf__pos2,axiom,
% 5.25/5.57 ! [F: nat > int,I2: nat] :
% 5.25/5.57 ( ( summable_int @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.25/5.57 => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 5.25/5.57 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_pos2
% 5.25/5.57 thf(fact_8138_suminf__pos__iff,axiom,
% 5.25/5.57 ! [F: nat > real] :
% 5.25/5.57 ( ( summable_real @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.25/5.57 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 5.25/5.57 = ( ? [I3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_pos_iff
% 5.25/5.57 thf(fact_8139_suminf__pos__iff,axiom,
% 5.25/5.57 ! [F: nat > nat] :
% 5.25/5.57 ( ( summable_nat @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.25/5.57 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 5.25/5.57 = ( ? [I3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_pos_iff
% 5.25/5.57 thf(fact_8140_suminf__pos__iff,axiom,
% 5.25/5.57 ! [F: nat > int] :
% 5.25/5.57 ( ( summable_int @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.25/5.57 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 5.25/5.57 = ( ? [I3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I3 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_pos_iff
% 5.25/5.57 thf(fact_8141_suminf__le__const,axiom,
% 5.25/5.57 ! [F: nat > int,X3: int] :
% 5.25/5.57 ( ( summable_int @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 5.25/5.57 => ( ord_less_eq_int @ ( suminf_int @ F ) @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_le_const
% 5.25/5.57 thf(fact_8142_suminf__le__const,axiom,
% 5.25/5.57 ! [F: nat > nat,X3: nat] :
% 5.25/5.57 ( ( summable_nat @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 5.25/5.57 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_le_const
% 5.25/5.57 thf(fact_8143_suminf__le__const,axiom,
% 5.25/5.57 ! [F: nat > real,X3: real] :
% 5.25/5.57 ( ( summable_real @ F )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 5.25/5.57 => ( ord_less_eq_real @ ( suminf_real @ F ) @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_le_const
% 5.25/5.57 thf(fact_8144_powser__inside,axiom,
% 5.25/5.57 ! [F: nat > real,X3: real,Z: real] :
% 5.25/5.57 ( ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) )
% 5.25/5.57 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X3 ) )
% 5.25/5.57 => ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % powser_inside
% 5.25/5.57 thf(fact_8145_powser__inside,axiom,
% 5.25/5.57 ! [F: nat > complex,X3: complex,Z: complex] :
% 5.25/5.57 ( ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) )
% 5.25/5.57 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X3 ) )
% 5.25/5.57 => ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % powser_inside
% 5.25/5.57 thf(fact_8146_summableI__nonneg__bounded,axiom,
% 5.25/5.57 ! [F: nat > int,X3: int] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 5.25/5.57 => ( summable_int @ F ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summableI_nonneg_bounded
% 5.25/5.57 thf(fact_8147_summableI__nonneg__bounded,axiom,
% 5.25/5.57 ! [F: nat > nat,X3: nat] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 5.25/5.57 => ( summable_nat @ F ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summableI_nonneg_bounded
% 5.25/5.57 thf(fact_8148_summableI__nonneg__bounded,axiom,
% 5.25/5.57 ! [F: nat > real,X3: real] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X3 )
% 5.25/5.57 => ( summable_real @ F ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summableI_nonneg_bounded
% 5.25/5.57 thf(fact_8149_bounded__imp__summable,axiom,
% 5.25/5.57 ! [A: nat > int,B3: int] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N3 ) )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 5.25/5.57 => ( summable_int @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % bounded_imp_summable
% 5.25/5.57 thf(fact_8150_bounded__imp__summable,axiom,
% 5.25/5.57 ! [A: nat > nat,B3: nat] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N3 ) )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 5.25/5.57 => ( summable_nat @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % bounded_imp_summable
% 5.25/5.57 thf(fact_8151_bounded__imp__summable,axiom,
% 5.25/5.57 ! [A: nat > real,B3: real] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 5.25/5.57 => ( summable_real @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % bounded_imp_summable
% 5.25/5.57 thf(fact_8152_complete__algebra__summable__geometric,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ one_one_real )
% 5.25/5.57 => ( summable_real @ ( power_power_real @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % complete_algebra_summable_geometric
% 5.25/5.57 thf(fact_8153_complete__algebra__summable__geometric,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ one_one_real )
% 5.25/5.57 => ( summable_complex @ ( power_power_complex @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % complete_algebra_summable_geometric
% 5.25/5.57 thf(fact_8154_summable__geometric,axiom,
% 5.25/5.57 ! [C: real] :
% 5.25/5.57 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.25/5.57 => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_geometric
% 5.25/5.57 thf(fact_8155_summable__geometric,axiom,
% 5.25/5.57 ! [C: complex] :
% 5.25/5.57 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.25/5.57 => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_geometric
% 5.25/5.57 thf(fact_8156_suminf__split__head,axiom,
% 5.25/5.57 ! [F: nat > real] :
% 5.25/5.57 ( ( summable_real @ F )
% 5.25/5.57 => ( ( suminf_real
% 5.25/5.57 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 5.25/5.57 = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_split_head
% 5.25/5.57 thf(fact_8157_machin__Euler,axiom,
% 5.25/5.57 ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.25/5.57 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % machin_Euler
% 5.25/5.57 thf(fact_8158_machin,axiom,
% 5.25/5.57 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.25/5.57 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % machin
% 5.25/5.57 thf(fact_8159_pi__less__4,axiom,
% 5.25/5.57 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % pi_less_4
% 5.25/5.57 thf(fact_8160_pi__ge__two,axiom,
% 5.25/5.57 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.25/5.57
% 5.25/5.57 % pi_ge_two
% 5.25/5.57 thf(fact_8161_zdvd__mult__cancel1,axiom,
% 5.25/5.57 ! [M: int,N: int] :
% 5.25/5.57 ( ( M != zero_zero_int )
% 5.25/5.57 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 5.25/5.57 = ( ( abs_abs_int @ N )
% 5.25/5.57 = one_one_int ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % zdvd_mult_cancel1
% 5.25/5.57 thf(fact_8162_pi__half__neq__two,axiom,
% 5.25/5.57 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.25/5.57 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % pi_half_neq_two
% 5.25/5.57 thf(fact_8163_summable__norm,axiom,
% 5.25/5.57 ! [F: nat > real] :
% 5.25/5.57 ( ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( F @ N2 ) ) )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 5.25/5.57 @ ( suminf_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( F @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_norm
% 5.25/5.57 thf(fact_8164_summable__norm,axiom,
% 5.25/5.57 ! [F: nat > complex] :
% 5.25/5.57 ( ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 5.25/5.57 @ ( suminf_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_norm
% 5.25/5.57 thf(fact_8165_suminf__split__initial__segment,axiom,
% 5.25/5.57 ! [F: nat > real,K: nat] :
% 5.25/5.57 ( ( summable_real @ F )
% 5.25/5.57 => ( ( suminf_real @ F )
% 5.25/5.57 = ( plus_plus_real
% 5.25/5.57 @ ( suminf_real
% 5.25/5.57 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.25/5.57 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_split_initial_segment
% 5.25/5.57 thf(fact_8166_suminf__minus__initial__segment,axiom,
% 5.25/5.57 ! [F: nat > real,K: nat] :
% 5.25/5.57 ( ( summable_real @ F )
% 5.25/5.57 => ( ( suminf_real
% 5.25/5.57 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.25/5.57 = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_minus_initial_segment
% 5.25/5.57 thf(fact_8167_even__abs__add__iff,axiom,
% 5.25/5.57 ! [K: int,L2: int] :
% 5.25/5.57 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L2 ) )
% 5.25/5.57 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % even_abs_add_iff
% 5.25/5.57 thf(fact_8168_even__add__abs__iff,axiom,
% 5.25/5.57 ! [K: int,L2: int] :
% 5.25/5.57 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L2 ) ) )
% 5.25/5.57 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % even_add_abs_iff
% 5.25/5.57 thf(fact_8169_pi__half__neq__zero,axiom,
% 5.25/5.57 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.25/5.57 != zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % pi_half_neq_zero
% 5.25/5.57 thf(fact_8170_pi__half__less__two,axiom,
% 5.25/5.57 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.25/5.57
% 5.25/5.57 % pi_half_less_two
% 5.25/5.57 thf(fact_8171_pi__half__le__two,axiom,
% 5.25/5.57 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.25/5.57
% 5.25/5.57 % pi_half_le_two
% 5.25/5.57 thf(fact_8172_sum__less__suminf,axiom,
% 5.25/5.57 ! [F: nat > int,N: nat] :
% 5.25/5.57 ( ( summable_int @ F )
% 5.25/5.57 => ( ! [M5: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N @ M5 )
% 5.25/5.57 => ( ord_less_int @ zero_zero_int @ ( F @ M5 ) ) )
% 5.25/5.57 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sum_less_suminf
% 5.25/5.57 thf(fact_8173_sum__less__suminf,axiom,
% 5.25/5.57 ! [F: nat > nat,N: nat] :
% 5.25/5.57 ( ( summable_nat @ F )
% 5.25/5.57 => ( ! [M5: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N @ M5 )
% 5.25/5.57 => ( ord_less_nat @ zero_zero_nat @ ( F @ M5 ) ) )
% 5.25/5.57 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sum_less_suminf
% 5.25/5.57 thf(fact_8174_sum__less__suminf,axiom,
% 5.25/5.57 ! [F: nat > real,N: nat] :
% 5.25/5.57 ( ( summable_real @ F )
% 5.25/5.57 => ( ! [M5: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N @ M5 )
% 5.25/5.57 => ( ord_less_real @ zero_zero_real @ ( F @ M5 ) ) )
% 5.25/5.57 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sum_less_suminf
% 5.25/5.57 thf(fact_8175_powser__split__head_I1_J,axiom,
% 5.25/5.57 ! [F: nat > complex,Z: complex] :
% 5.25/5.57 ( ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.25/5.57 => ( ( suminf_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.25/5.57 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 5.25/5.57 @ ( times_times_complex
% 5.25/5.57 @ ( suminf_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.25/5.57 @ Z ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % powser_split_head(1)
% 5.25/5.57 thf(fact_8176_powser__split__head_I1_J,axiom,
% 5.25/5.57 ! [F: nat > real,Z: real] :
% 5.25/5.57 ( ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.25/5.57 => ( ( suminf_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.25/5.57 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 5.25/5.57 @ ( times_times_real
% 5.25/5.57 @ ( suminf_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.25/5.57 @ Z ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % powser_split_head(1)
% 5.25/5.57 thf(fact_8177_powser__split__head_I2_J,axiom,
% 5.25/5.57 ! [F: nat > complex,Z: complex] :
% 5.25/5.57 ( ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.25/5.57 => ( ( times_times_complex
% 5.25/5.57 @ ( suminf_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.25/5.57 @ Z )
% 5.25/5.57 = ( minus_minus_complex
% 5.25/5.57 @ ( suminf_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.25/5.57 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % powser_split_head(2)
% 5.25/5.57 thf(fact_8178_powser__split__head_I2_J,axiom,
% 5.25/5.57 ! [F: nat > real,Z: real] :
% 5.25/5.57 ( ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.25/5.57 => ( ( times_times_real
% 5.25/5.57 @ ( suminf_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.25/5.57 @ Z )
% 5.25/5.57 = ( minus_minus_real
% 5.25/5.57 @ ( suminf_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.25/5.57 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % powser_split_head(2)
% 5.25/5.57 thf(fact_8179_monoseq__realpow,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 5.25/5.57 => ( topolo6980174941875973593q_real @ ( power_power_real @ X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoseq_realpow
% 5.25/5.57 thf(fact_8180_summable__partial__sum__bound,axiom,
% 5.25/5.57 ! [F: nat > complex,E: real] :
% 5.25/5.57 ( ( summable_complex @ F )
% 5.25/5.57 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.25/5.57 => ~ ! [N7: nat] :
% 5.25/5.57 ~ ! [M2: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N7 @ M2 )
% 5.25/5.57 => ! [N8: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M2 @ N8 ) ) ) @ E ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_partial_sum_bound
% 5.25/5.57 thf(fact_8181_summable__partial__sum__bound,axiom,
% 5.25/5.57 ! [F: nat > real,E: real] :
% 5.25/5.57 ( ( summable_real @ F )
% 5.25/5.57 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.25/5.57 => ~ ! [N7: nat] :
% 5.25/5.57 ~ ! [M2: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N7 @ M2 )
% 5.25/5.57 => ! [N8: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M2 @ N8 ) ) ) @ E ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_partial_sum_bound
% 5.25/5.57 thf(fact_8182_suminf__exist__split,axiom,
% 5.25/5.57 ! [R2: real,F: nat > real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.25/5.57 => ( ( summable_real @ F )
% 5.25/5.57 => ? [N7: nat] :
% 5.25/5.57 ! [N8: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N7 @ N8 )
% 5.25/5.57 => ( ord_less_real
% 5.25/5.57 @ ( real_V7735802525324610683m_real
% 5.25/5.57 @ ( suminf_real
% 5.25/5.57 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N8 ) ) ) )
% 5.25/5.57 @ R2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_exist_split
% 5.25/5.57 thf(fact_8183_suminf__exist__split,axiom,
% 5.25/5.57 ! [R2: real,F: nat > complex] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.25/5.57 => ( ( summable_complex @ F )
% 5.25/5.57 => ? [N7: nat] :
% 5.25/5.57 ! [N8: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N7 @ N8 )
% 5.25/5.57 => ( ord_less_real
% 5.25/5.57 @ ( real_V1022390504157884413omplex
% 5.25/5.57 @ ( suminf_complex
% 5.25/5.57 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N8 ) ) ) )
% 5.25/5.57 @ R2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % suminf_exist_split
% 5.25/5.57 thf(fact_8184_summable__power__series,axiom,
% 5.25/5.57 ! [F: nat > real,Z: real] :
% 5.25/5.57 ( ! [I4: nat] : ( ord_less_eq_real @ ( F @ I4 ) @ one_one_real )
% 5.25/5.57 => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.25/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.25/5.57 => ( ( ord_less_real @ Z @ one_one_real )
% 5.25/5.57 => ( summable_real
% 5.25/5.57 @ ^ [I3: nat] : ( times_times_real @ ( F @ I3 ) @ ( power_power_real @ Z @ I3 ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_power_series
% 5.25/5.57 thf(fact_8185_Abel__lemma,axiom,
% 5.25/5.57 ! [R2: real,R0: real,A: nat > complex,M7: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.25/5.57 => ( ( ord_less_real @ R2 @ R0 )
% 5.25/5.57 => ( ! [N3: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R0 @ N3 ) ) @ M7 )
% 5.25/5.57 => ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N2 ) ) @ ( power_power_real @ R2 @ N2 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Abel_lemma
% 5.25/5.57 thf(fact_8186_nat__intermed__int__val,axiom,
% 5.25/5.57 ! [M: nat,N: nat,F: nat > int,K: int] :
% 5.25/5.57 ( ! [I4: nat] :
% 5.25/5.57 ( ( ( ord_less_eq_nat @ M @ I4 )
% 5.25/5.57 & ( ord_less_nat @ I4 @ N ) )
% 5.25/5.57 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.25/5.57 => ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.57 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.25/5.57 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.25/5.57 => ? [I4: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M @ I4 )
% 5.25/5.57 & ( ord_less_eq_nat @ I4 @ N )
% 5.25/5.57 & ( ( F @ I4 )
% 5.25/5.57 = K ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % nat_intermed_int_val
% 5.25/5.57 thf(fact_8187_Cauchy__product,axiom,
% 5.25/5.57 ! [A: nat > complex,B: nat > complex] :
% 5.25/5.57 ( ( summable_real
% 5.25/5.57 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.25/5.57 => ( ( summable_real
% 5.25/5.57 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.25/5.57 => ( ( times_times_complex @ ( suminf_complex @ A ) @ ( suminf_complex @ B ) )
% 5.25/5.57 = ( suminf_complex
% 5.25/5.57 @ ^ [K3: nat] :
% 5.25/5.57 ( groups2073611262835488442omplex
% 5.25/5.57 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( B @ ( minus_minus_nat @ K3 @ I3 ) ) )
% 5.25/5.57 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Cauchy_product
% 5.25/5.57 thf(fact_8188_Cauchy__product,axiom,
% 5.25/5.57 ! [A: nat > real,B: nat > real] :
% 5.25/5.57 ( ( summable_real
% 5.25/5.57 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.25/5.57 => ( ( summable_real
% 5.25/5.57 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.25/5.57 => ( ( times_times_real @ ( suminf_real @ A ) @ ( suminf_real @ B ) )
% 5.25/5.57 = ( suminf_real
% 5.25/5.57 @ ^ [K3: nat] :
% 5.25/5.57 ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( B @ ( minus_minus_nat @ K3 @ I3 ) ) )
% 5.25/5.57 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Cauchy_product
% 5.25/5.57 thf(fact_8189_incr__lemma,axiom,
% 5.25/5.57 ! [D: int,Z: int,X3: int] :
% 5.25/5.57 ( ( ord_less_int @ zero_zero_int @ D )
% 5.25/5.57 => ( ord_less_int @ Z @ ( plus_plus_int @ X3 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % incr_lemma
% 5.25/5.57 thf(fact_8190_decr__lemma,axiom,
% 5.25/5.57 ! [D: int,X3: int,Z: int] :
% 5.25/5.57 ( ( ord_less_int @ zero_zero_int @ D )
% 5.25/5.57 => ( ord_less_int @ ( minus_minus_int @ X3 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X3 @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 5.25/5.57
% 5.25/5.57 % decr_lemma
% 5.25/5.57 thf(fact_8191_pi__half__gt__zero,axiom,
% 5.25/5.57 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % pi_half_gt_zero
% 5.25/5.57 thf(fact_8192_pi__half__ge__zero,axiom,
% 5.25/5.57 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % pi_half_ge_zero
% 5.25/5.57 thf(fact_8193_m2pi__less__pi,axiom,
% 5.25/5.57 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.25/5.57
% 5.25/5.57 % m2pi_less_pi
% 5.25/5.57 thf(fact_8194_summable__ratio__test,axiom,
% 5.25/5.57 ! [C: real,N5: nat,F: nat > real] :
% 5.25/5.57 ( ( ord_less_real @ C @ one_one_real )
% 5.25/5.57 => ( ! [N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N5 @ N3 )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 5.25/5.57 => ( summable_real @ F ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_ratio_test
% 5.25/5.57 thf(fact_8195_summable__ratio__test,axiom,
% 5.25/5.57 ! [C: real,N5: nat,F: nat > complex] :
% 5.25/5.57 ( ( ord_less_real @ C @ one_one_real )
% 5.25/5.57 => ( ! [N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N5 @ N3 )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 5.25/5.57 => ( summable_complex @ F ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_ratio_test
% 5.25/5.57 thf(fact_8196_sum__less__suminf2,axiom,
% 5.25/5.57 ! [F: nat > int,N: nat,I2: nat] :
% 5.25/5.57 ( ( summable_int @ F )
% 5.25/5.57 => ( ! [M5: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N @ M5 )
% 5.25/5.57 => ( ord_less_eq_int @ zero_zero_int @ ( F @ M5 ) ) )
% 5.25/5.57 => ( ( ord_less_eq_nat @ N @ I2 )
% 5.25/5.57 => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 5.25/5.57 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sum_less_suminf2
% 5.25/5.57 thf(fact_8197_sum__less__suminf2,axiom,
% 5.25/5.57 ! [F: nat > nat,N: nat,I2: nat] :
% 5.25/5.57 ( ( summable_nat @ F )
% 5.25/5.57 => ( ! [M5: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N @ M5 )
% 5.25/5.57 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M5 ) ) )
% 5.25/5.57 => ( ( ord_less_eq_nat @ N @ I2 )
% 5.25/5.57 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.25/5.57 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sum_less_suminf2
% 5.25/5.57 thf(fact_8198_sum__less__suminf2,axiom,
% 5.25/5.57 ! [F: nat > real,N: nat,I2: nat] :
% 5.25/5.57 ( ( summable_real @ F )
% 5.25/5.57 => ( ! [M5: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N @ M5 )
% 5.25/5.57 => ( ord_less_eq_real @ zero_zero_real @ ( F @ M5 ) ) )
% 5.25/5.57 => ( ( ord_less_eq_nat @ N @ I2 )
% 5.25/5.57 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.25/5.57 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sum_less_suminf2
% 5.25/5.57 thf(fact_8199_nat__ivt__aux,axiom,
% 5.25/5.57 ! [N: nat,F: nat > int,K: int] :
% 5.25/5.57 ( ! [I4: nat] :
% 5.25/5.57 ( ( ord_less_nat @ I4 @ N )
% 5.25/5.57 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.25/5.57 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.25/5.57 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.25/5.57 => ? [I4: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ I4 @ N )
% 5.25/5.57 & ( ( F @ I4 )
% 5.25/5.57 = K ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % nat_ivt_aux
% 5.25/5.57 thf(fact_8200_Cauchy__product__sums,axiom,
% 5.25/5.57 ! [A: nat > complex,B: nat > complex] :
% 5.25/5.57 ( ( summable_real
% 5.25/5.57 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.25/5.57 => ( ( summable_real
% 5.25/5.57 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.25/5.57 => ( sums_complex
% 5.25/5.57 @ ^ [K3: nat] :
% 5.25/5.57 ( groups2073611262835488442omplex
% 5.25/5.57 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( B @ ( minus_minus_nat @ K3 @ I3 ) ) )
% 5.25/5.57 @ ( set_ord_atMost_nat @ K3 ) )
% 5.25/5.57 @ ( times_times_complex @ ( suminf_complex @ A ) @ ( suminf_complex @ B ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Cauchy_product_sums
% 5.25/5.57 thf(fact_8201_Cauchy__product__sums,axiom,
% 5.25/5.57 ! [A: nat > real,B: nat > real] :
% 5.25/5.57 ( ( summable_real
% 5.25/5.57 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.25/5.57 => ( ( summable_real
% 5.25/5.57 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.25/5.57 => ( sums_real
% 5.25/5.57 @ ^ [K3: nat] :
% 5.25/5.57 ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( B @ ( minus_minus_nat @ K3 @ I3 ) ) )
% 5.25/5.57 @ ( set_ord_atMost_nat @ K3 ) )
% 5.25/5.57 @ ( times_times_real @ ( suminf_real @ A ) @ ( suminf_real @ B ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Cauchy_product_sums
% 5.25/5.57 thf(fact_8202_complex__mod__minus__le__complex__mod,axiom,
% 5.25/5.57 ! [X3: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X3 ) ) @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % complex_mod_minus_le_complex_mod
% 5.25/5.57 thf(fact_8203_minus__pi__half__less__zero,axiom,
% 5.25/5.57 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.25/5.57
% 5.25/5.57 % minus_pi_half_less_zero
% 5.25/5.57 thf(fact_8204_complex__mod__triangle__ineq2,axiom,
% 5.25/5.57 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % complex_mod_triangle_ineq2
% 5.25/5.57 thf(fact_8205_nat0__intermed__int__val,axiom,
% 5.25/5.57 ! [N: nat,F: nat > int,K: int] :
% 5.25/5.57 ( ! [I4: nat] :
% 5.25/5.57 ( ( ord_less_nat @ I4 @ N )
% 5.25/5.57 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I4 @ one_one_nat ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.25/5.57 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.25/5.57 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.25/5.57 => ? [I4: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ I4 @ N )
% 5.25/5.57 & ( ( F @ I4 )
% 5.25/5.57 = K ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % nat0_intermed_int_val
% 5.25/5.57 thf(fact_8206_sum__roots__unity,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( ord_less_nat @ one_one_nat @ N )
% 5.25/5.57 => ( ( groups7754918857620584856omplex
% 5.25/5.57 @ ^ [X2: complex] : X2
% 5.25/5.57 @ ( collect_complex
% 5.25/5.57 @ ^ [Z5: complex] :
% 5.25/5.57 ( ( power_power_complex @ Z5 @ N )
% 5.25/5.57 = one_one_complex ) ) )
% 5.25/5.57 = zero_zero_complex ) ) ).
% 5.25/5.57
% 5.25/5.57 % sum_roots_unity
% 5.25/5.57 thf(fact_8207_sum__nth__roots,axiom,
% 5.25/5.57 ! [N: nat,C: complex] :
% 5.25/5.57 ( ( ord_less_nat @ one_one_nat @ N )
% 5.25/5.57 => ( ( groups7754918857620584856omplex
% 5.25/5.57 @ ^ [X2: complex] : X2
% 5.25/5.57 @ ( collect_complex
% 5.25/5.57 @ ^ [Z5: complex] :
% 5.25/5.57 ( ( power_power_complex @ Z5 @ N )
% 5.25/5.57 = C ) ) )
% 5.25/5.57 = zero_zero_complex ) ) ).
% 5.25/5.57
% 5.25/5.57 % sum_nth_roots
% 5.25/5.57 thf(fact_8208_arctan__add,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.57 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.25/5.57 => ( ( plus_plus_real @ ( arctan @ X3 ) @ ( arctan @ Y ) )
% 5.25/5.57 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X3 @ Y ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % arctan_add
% 5.25/5.57 thf(fact_8209_sum__pos__lt__pair,axiom,
% 5.25/5.57 ! [F: nat > real,K: nat] :
% 5.25/5.57 ( ( summable_real @ F )
% 5.25/5.57 => ( ! [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 ) ) ) ) )
% 5.25/5.57 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sum_pos_lt_pair
% 5.25/5.57 thf(fact_8210_arctan__double,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.57 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X3 ) )
% 5.25/5.57 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % arctan_double
% 5.25/5.57 thf(fact_8211_sin__cos__npi,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_cos_npi
% 5.25/5.57 thf(fact_8212_diffs__equiv,axiom,
% 5.25/5.57 ! [C: nat > complex,X3: complex] :
% 5.25/5.57 ( ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) )
% 5.25/5.57 => ( sums_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( C @ N2 ) ) @ ( power_power_complex @ X3 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.25/5.57 @ ( suminf_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % diffs_equiv
% 5.25/5.57 thf(fact_8213_diffs__equiv,axiom,
% 5.25/5.57 ! [C: nat > real,X3: real] :
% 5.25/5.57 ( ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) )
% 5.25/5.57 => ( sums_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( C @ N2 ) ) @ ( power_power_real @ X3 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.25/5.57 @ ( suminf_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % diffs_equiv
% 5.25/5.57 thf(fact_8214_cos__pi__eq__zero,axiom,
% 5.25/5.57 ! [M: nat] :
% 5.25/5.57 ( ( 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 ) ) ) )
% 5.25/5.57 = zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % cos_pi_eq_zero
% 5.25/5.57 thf(fact_8215_monoseq__def,axiom,
% 5.25/5.57 ( topolo6980174941875973593q_real
% 5.25/5.57 = ( ^ [X4: nat > real] :
% 5.25/5.57 ( ! [M6: nat,N2: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.25/5.57 => ( ord_less_eq_real @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 5.25/5.57 | ! [M6: nat,N2: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.25/5.57 => ( ord_less_eq_real @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoseq_def
% 5.25/5.57 thf(fact_8216_monoseq__def,axiom,
% 5.25/5.57 ( topolo3100542954746470799et_int
% 5.25/5.57 = ( ^ [X4: nat > set_int] :
% 5.25/5.57 ( ! [M6: nat,N2: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.25/5.57 => ( ord_less_eq_set_int @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 5.25/5.57 | ! [M6: nat,N2: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.25/5.57 => ( ord_less_eq_set_int @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoseq_def
% 5.25/5.57 thf(fact_8217_monoseq__def,axiom,
% 5.25/5.57 ( topolo4267028734544971653eq_rat
% 5.25/5.57 = ( ^ [X4: nat > rat] :
% 5.25/5.57 ( ! [M6: nat,N2: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.25/5.57 => ( ord_less_eq_rat @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 5.25/5.57 | ! [M6: nat,N2: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.25/5.57 => ( ord_less_eq_rat @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoseq_def
% 5.25/5.57 thf(fact_8218_monoseq__def,axiom,
% 5.25/5.57 ( topolo1459490580787246023eq_num
% 5.25/5.57 = ( ^ [X4: nat > num] :
% 5.25/5.57 ( ! [M6: nat,N2: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.25/5.57 => ( ord_less_eq_num @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 5.25/5.57 | ! [M6: nat,N2: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.25/5.57 => ( ord_less_eq_num @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoseq_def
% 5.25/5.57 thf(fact_8219_monoseq__def,axiom,
% 5.25/5.57 ( topolo4902158794631467389eq_nat
% 5.25/5.57 = ( ^ [X4: nat > nat] :
% 5.25/5.57 ( ! [M6: nat,N2: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.25/5.57 => ( ord_less_eq_nat @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 5.25/5.57 | ! [M6: nat,N2: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.25/5.57 => ( ord_less_eq_nat @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoseq_def
% 5.25/5.57 thf(fact_8220_monoseq__def,axiom,
% 5.25/5.57 ( topolo4899668324122417113eq_int
% 5.25/5.57 = ( ^ [X4: nat > int] :
% 5.25/5.57 ( ! [M6: nat,N2: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.25/5.57 => ( ord_less_eq_int @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) )
% 5.25/5.57 | ! [M6: nat,N2: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.25/5.57 => ( ord_less_eq_int @ ( X4 @ N2 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoseq_def
% 5.25/5.57 thf(fact_8221_monoI2,axiom,
% 5.25/5.57 ! [X8: nat > real] :
% 5.25/5.57 ( ! [M5: nat,N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.25/5.57 => ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.25/5.57 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoI2
% 5.25/5.57 thf(fact_8222_monoI2,axiom,
% 5.25/5.57 ! [X8: nat > set_int] :
% 5.25/5.57 ( ! [M5: nat,N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.25/5.57 => ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.25/5.57 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoI2
% 5.25/5.57 thf(fact_8223_monoI2,axiom,
% 5.25/5.57 ! [X8: nat > rat] :
% 5.25/5.57 ( ! [M5: nat,N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.25/5.57 => ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.25/5.57 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoI2
% 5.25/5.57 thf(fact_8224_monoI2,axiom,
% 5.25/5.57 ! [X8: nat > num] :
% 5.25/5.57 ( ! [M5: nat,N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.25/5.57 => ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.25/5.57 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoI2
% 5.25/5.57 thf(fact_8225_monoI2,axiom,
% 5.25/5.57 ! [X8: nat > nat] :
% 5.25/5.57 ( ! [M5: nat,N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.25/5.57 => ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.25/5.57 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoI2
% 5.25/5.57 thf(fact_8226_monoI2,axiom,
% 5.25/5.57 ! [X8: nat > int] :
% 5.25/5.57 ( ! [M5: nat,N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.25/5.57 => ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.25/5.57 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoI2
% 5.25/5.57 thf(fact_8227_cos__zero,axiom,
% 5.25/5.57 ( ( cos_complex @ zero_zero_complex )
% 5.25/5.57 = one_one_complex ) ).
% 5.25/5.57
% 5.25/5.57 % cos_zero
% 5.25/5.57 thf(fact_8228_cos__zero,axiom,
% 5.25/5.57 ( ( cos_real @ zero_zero_real )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % cos_zero
% 5.25/5.57 thf(fact_8229_cos__pi,axiom,
% 5.25/5.57 ( ( cos_real @ pi )
% 5.25/5.57 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_pi
% 5.25/5.57 thf(fact_8230_cos__periodic__pi2,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( cos_real @ ( plus_plus_real @ pi @ X3 ) )
% 5.25/5.57 = ( uminus_uminus_real @ ( cos_real @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_periodic_pi2
% 5.25/5.57 thf(fact_8231_cos__periodic__pi,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( cos_real @ ( plus_plus_real @ X3 @ pi ) )
% 5.25/5.57 = ( uminus_uminus_real @ ( cos_real @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_periodic_pi
% 5.25/5.57 thf(fact_8232_sin__periodic__pi,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( sin_real @ ( plus_plus_real @ X3 @ pi ) )
% 5.25/5.57 = ( uminus_uminus_real @ ( sin_real @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_periodic_pi
% 5.25/5.57 thf(fact_8233_sin__periodic__pi2,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( sin_real @ ( plus_plus_real @ pi @ X3 ) )
% 5.25/5.57 = ( uminus_uminus_real @ ( sin_real @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_periodic_pi2
% 5.25/5.57 thf(fact_8234_sin__cos__squared__add3,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X3 ) @ ( cos_complex @ X3 ) ) @ ( times_times_complex @ ( sin_complex @ X3 ) @ ( sin_complex @ X3 ) ) )
% 5.25/5.57 = one_one_complex ) ).
% 5.25/5.57
% 5.25/5.57 % sin_cos_squared_add3
% 5.25/5.57 thf(fact_8235_sin__cos__squared__add3,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X3 ) @ ( cos_real @ X3 ) ) @ ( times_times_real @ ( sin_real @ X3 ) @ ( sin_real @ X3 ) ) )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % sin_cos_squared_add3
% 5.25/5.57 thf(fact_8236_sin__npi,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.25/5.57 = zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % sin_npi
% 5.25/5.57 thf(fact_8237_sin__npi2,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.25/5.57 = zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % sin_npi2
% 5.25/5.57 thf(fact_8238_sin__npi__int,axiom,
% 5.25/5.57 ! [N: int] :
% 5.25/5.57 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.25/5.57 = zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % sin_npi_int
% 5.25/5.57 thf(fact_8239_cos__pi__half,axiom,
% 5.25/5.57 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 = zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % cos_pi_half
% 5.25/5.57 thf(fact_8240_sin__two__pi,axiom,
% 5.25/5.57 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.25/5.57 = zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % sin_two_pi
% 5.25/5.57 thf(fact_8241_sin__pi__half,axiom,
% 5.25/5.57 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % sin_pi_half
% 5.25/5.57 thf(fact_8242_cos__two__pi,axiom,
% 5.25/5.57 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % cos_two_pi
% 5.25/5.57 thf(fact_8243_cos__periodic,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( cos_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.25/5.57 = ( cos_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_periodic
% 5.25/5.57 thf(fact_8244_sin__periodic,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( sin_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.25/5.57 = ( sin_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_periodic
% 5.25/5.57 thf(fact_8245_cos__2pi__minus,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X3 ) )
% 5.25/5.57 = ( cos_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_2pi_minus
% 5.25/5.57 thf(fact_8246_cos__npi2,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.25/5.57 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_npi2
% 5.25/5.57 thf(fact_8247_cos__npi,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.25/5.57 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_npi
% 5.25/5.57 thf(fact_8248_sin__cos__squared__add,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % sin_cos_squared_add
% 5.25/5.57 thf(fact_8249_sin__cos__squared__add,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.57 = one_one_complex ) ).
% 5.25/5.57
% 5.25/5.57 % sin_cos_squared_add
% 5.25/5.57 thf(fact_8250_sin__cos__squared__add2,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % sin_cos_squared_add2
% 5.25/5.57 thf(fact_8251_sin__cos__squared__add2,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.57 = one_one_complex ) ).
% 5.25/5.57
% 5.25/5.57 % sin_cos_squared_add2
% 5.25/5.57 thf(fact_8252_sin__2npi,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.25/5.57 = zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % sin_2npi
% 5.25/5.57 thf(fact_8253_cos__2npi,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % cos_2npi
% 5.25/5.57 thf(fact_8254_sin__2pi__minus,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X3 ) )
% 5.25/5.57 = ( uminus_uminus_real @ ( sin_real @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_2pi_minus
% 5.25/5.57 thf(fact_8255_sin__int__2pin,axiom,
% 5.25/5.57 ! [N: int] :
% 5.25/5.57 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.25/5.57 = zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % sin_int_2pin
% 5.25/5.57 thf(fact_8256_cos__int__2pin,axiom,
% 5.25/5.57 ! [N: int] :
% 5.25/5.57 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % cos_int_2pin
% 5.25/5.57 thf(fact_8257_cos__3over2__pi,axiom,
% 5.25/5.57 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.25/5.57 = zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % cos_3over2_pi
% 5.25/5.57 thf(fact_8258_sin__3over2__pi,axiom,
% 5.25/5.57 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.25/5.57 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_3over2_pi
% 5.25/5.57 thf(fact_8259_cos__npi__int,axiom,
% 5.25/5.57 ! [N: int] :
% 5.25/5.57 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.25/5.57 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.25/5.57 = one_one_real ) )
% 5.25/5.57 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.25/5.57 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.25/5.57 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_npi_int
% 5.25/5.57 thf(fact_8260_sin__diff,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( sin_real @ ( minus_minus_real @ X3 @ Y ) )
% 5.25/5.57 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X3 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X3 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_diff
% 5.25/5.57 thf(fact_8261_polar__Ex,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ? [R3: real,A5: real] :
% 5.25/5.57 ( ( X3
% 5.25/5.57 = ( times_times_real @ R3 @ ( cos_real @ A5 ) ) )
% 5.25/5.57 & ( Y
% 5.25/5.57 = ( times_times_real @ R3 @ ( sin_real @ A5 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % polar_Ex
% 5.25/5.57 thf(fact_8262_sin__add,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( sin_real @ ( plus_plus_real @ X3 @ Y ) )
% 5.25/5.57 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X3 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X3 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_add
% 5.25/5.57 thf(fact_8263_cos__one__sin__zero,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( ( cos_complex @ X3 )
% 5.25/5.57 = one_one_complex )
% 5.25/5.57 => ( ( sin_complex @ X3 )
% 5.25/5.57 = zero_zero_complex ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_one_sin_zero
% 5.25/5.57 thf(fact_8264_cos__one__sin__zero,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( cos_real @ X3 )
% 5.25/5.57 = one_one_real )
% 5.25/5.57 => ( ( sin_real @ X3 )
% 5.25/5.57 = zero_zero_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_one_sin_zero
% 5.25/5.57 thf(fact_8265_cos__add,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( cos_real @ ( plus_plus_real @ X3 @ Y ) )
% 5.25/5.57 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X3 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X3 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_add
% 5.25/5.57 thf(fact_8266_cos__diff,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( cos_real @ ( minus_minus_real @ X3 @ Y ) )
% 5.25/5.57 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X3 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X3 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_diff
% 5.25/5.57 thf(fact_8267_sin__zero__norm__cos__one,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( sin_real @ X3 )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X3 ) )
% 5.25/5.57 = one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_zero_norm_cos_one
% 5.25/5.57 thf(fact_8268_sin__zero__norm__cos__one,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( ( sin_complex @ X3 )
% 5.25/5.57 = zero_zero_complex )
% 5.25/5.57 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X3 ) )
% 5.25/5.57 = one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_zero_norm_cos_one
% 5.25/5.57 thf(fact_8269_sin__zero__abs__cos__one,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( sin_real @ X3 )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 => ( ( abs_abs_real @ ( cos_real @ X3 ) )
% 5.25/5.57 = one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_zero_abs_cos_one
% 5.25/5.57 thf(fact_8270_sin__double,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) )
% 5.25/5.57 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X3 ) ) @ ( cos_complex @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_double
% 5.25/5.57 thf(fact_8271_sin__double,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) )
% 5.25/5.57 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X3 ) ) @ ( cos_real @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_double
% 5.25/5.57 thf(fact_8272_sincos__principal__value,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ? [Y3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.25/5.57 & ( ord_less_eq_real @ Y3 @ pi )
% 5.25/5.57 & ( ( sin_real @ Y3 )
% 5.25/5.57 = ( sin_real @ X3 ) )
% 5.25/5.57 & ( ( cos_real @ Y3 )
% 5.25/5.57 = ( cos_real @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sincos_principal_value
% 5.25/5.57 thf(fact_8273_sin__x__le__x,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ord_less_eq_real @ ( sin_real @ X3 ) @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_x_le_x
% 5.25/5.57 thf(fact_8274_sin__le__one,axiom,
% 5.25/5.57 ! [X3: real] : ( ord_less_eq_real @ ( sin_real @ X3 ) @ one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % sin_le_one
% 5.25/5.57 thf(fact_8275_cos__le__one,axiom,
% 5.25/5.57 ! [X3: real] : ( ord_less_eq_real @ ( cos_real @ X3 ) @ one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % cos_le_one
% 5.25/5.57 thf(fact_8276_abs__sin__x__le__abs__x,axiom,
% 5.25/5.57 ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X3 ) ) @ ( abs_abs_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % abs_sin_x_le_abs_x
% 5.25/5.57 thf(fact_8277_sin__cos__le1,axiom,
% 5.25/5.57 ! [X3: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X3 ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X3 ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % sin_cos_le1
% 5.25/5.57 thf(fact_8278_cos__squared__eq,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.57 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_squared_eq
% 5.25/5.57 thf(fact_8279_cos__squared__eq,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.57 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_squared_eq
% 5.25/5.57 thf(fact_8280_sin__squared__eq,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.57 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_squared_eq
% 5.25/5.57 thf(fact_8281_sin__squared__eq,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.57 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_squared_eq
% 5.25/5.57 thf(fact_8282_sin__x__ge__neg__x,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ord_less_eq_real @ ( uminus_uminus_real @ X3 ) @ ( sin_real @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_x_ge_neg_x
% 5.25/5.57 thf(fact_8283_sin__ge__zero,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ pi )
% 5.25/5.57 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_ge_zero
% 5.25/5.57 thf(fact_8284_sin__ge__minus__one,axiom,
% 5.25/5.57 ! [X3: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_ge_minus_one
% 5.25/5.57 thf(fact_8285_cos__inj__pi,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ pi )
% 5.25/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.57 => ( ( ord_less_eq_real @ Y @ pi )
% 5.25/5.57 => ( ( ( cos_real @ X3 )
% 5.25/5.57 = ( cos_real @ Y ) )
% 5.25/5.57 => ( X3 = Y ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_inj_pi
% 5.25/5.57 thf(fact_8286_cos__mono__le__eq,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ pi )
% 5.25/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.57 => ( ( ord_less_eq_real @ Y @ pi )
% 5.25/5.57 => ( ( ord_less_eq_real @ ( cos_real @ X3 ) @ ( cos_real @ Y ) )
% 5.25/5.57 = ( ord_less_eq_real @ Y @ X3 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_mono_le_eq
% 5.25/5.57 thf(fact_8287_cos__monotone__0__pi__le,axiom,
% 5.25/5.57 ! [Y: real,X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.57 => ( ( ord_less_eq_real @ Y @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ pi )
% 5.25/5.57 => ( ord_less_eq_real @ ( cos_real @ X3 ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_monotone_0_pi_le
% 5.25/5.57 thf(fact_8288_cos__ge__minus__one,axiom,
% 5.25/5.57 ! [X3: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_ge_minus_one
% 5.25/5.57 thf(fact_8289_abs__sin__le__one,axiom,
% 5.25/5.57 ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X3 ) ) @ one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % abs_sin_le_one
% 5.25/5.57 thf(fact_8290_abs__cos__le__one,axiom,
% 5.25/5.57 ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X3 ) ) @ one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % abs_cos_le_one
% 5.25/5.57 thf(fact_8291_sin__times__sin,axiom,
% 5.25/5.57 ! [W: complex,Z: complex] :
% 5.25/5.57 ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_times_sin
% 5.25/5.57 thf(fact_8292_sin__times__sin,axiom,
% 5.25/5.57 ! [W: real,Z: real] :
% 5.25/5.57 ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.25/5.57 = ( 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 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_times_sin
% 5.25/5.57 thf(fact_8293_sin__times__cos,axiom,
% 5.25/5.57 ! [W: complex,Z: complex] :
% 5.25/5.57 ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_times_cos
% 5.25/5.57 thf(fact_8294_sin__times__cos,axiom,
% 5.25/5.57 ! [W: real,Z: real] :
% 5.25/5.57 ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 5.25/5.57 = ( 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 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_times_cos
% 5.25/5.57 thf(fact_8295_cos__times__sin,axiom,
% 5.25/5.57 ! [W: complex,Z: complex] :
% 5.25/5.57 ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_times_sin
% 5.25/5.57 thf(fact_8296_cos__times__sin,axiom,
% 5.25/5.57 ! [W: real,Z: real] :
% 5.25/5.57 ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 5.25/5.57 = ( 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 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_times_sin
% 5.25/5.57 thf(fact_8297_sin__plus__sin,axiom,
% 5.25/5.57 ! [W: complex,Z: complex] :
% 5.25/5.57 ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.25/5.57 = ( 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 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_plus_sin
% 5.25/5.57 thf(fact_8298_sin__plus__sin,axiom,
% 5.25/5.57 ! [W: real,Z: real] :
% 5.25/5.57 ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.25/5.57 = ( 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 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_plus_sin
% 5.25/5.57 thf(fact_8299_sin__diff__sin,axiom,
% 5.25/5.57 ! [W: complex,Z: complex] :
% 5.25/5.57 ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.25/5.57 = ( 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 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_diff_sin
% 5.25/5.57 thf(fact_8300_sin__diff__sin,axiom,
% 5.25/5.57 ! [W: real,Z: real] :
% 5.25/5.57 ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.25/5.57 = ( 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 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_diff_sin
% 5.25/5.57 thf(fact_8301_cos__diff__cos,axiom,
% 5.25/5.57 ! [W: complex,Z: complex] :
% 5.25/5.57 ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.25/5.57 = ( 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 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_diff_cos
% 5.25/5.57 thf(fact_8302_cos__diff__cos,axiom,
% 5.25/5.57 ! [W: real,Z: real] :
% 5.25/5.57 ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.25/5.57 = ( 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 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_diff_cos
% 5.25/5.57 thf(fact_8303_cos__double,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) )
% 5.25/5.57 = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_double
% 5.25/5.57 thf(fact_8304_cos__double,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) )
% 5.25/5.57 = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_double
% 5.25/5.57 thf(fact_8305_cos__double__sin,axiom,
% 5.25/5.57 ! [W: complex] :
% 5.25/5.57 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.25/5.57 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_double_sin
% 5.25/5.57 thf(fact_8306_cos__double__sin,axiom,
% 5.25/5.57 ! [W: real] :
% 5.25/5.57 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.25/5.57 = ( 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 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_double_sin
% 5.25/5.57 thf(fact_8307_cos__two__neq__zero,axiom,
% 5.25/5.57 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.25/5.57 != zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % cos_two_neq_zero
% 5.25/5.57 thf(fact_8308_cos__mono__less__eq,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ pi )
% 5.25/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.57 => ( ( ord_less_eq_real @ Y @ pi )
% 5.25/5.57 => ( ( ord_less_real @ ( cos_real @ X3 ) @ ( cos_real @ Y ) )
% 5.25/5.57 = ( ord_less_real @ Y @ X3 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_mono_less_eq
% 5.25/5.57 thf(fact_8309_cos__monotone__0__pi,axiom,
% 5.25/5.57 ! [Y: real,X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.57 => ( ( ord_less_real @ Y @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ pi )
% 5.25/5.57 => ( ord_less_real @ ( cos_real @ X3 ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_monotone_0_pi
% 5.25/5.57 thf(fact_8310_cos__monotone__minus__pi__0_H,axiom,
% 5.25/5.57 ! [Y: real,X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.25/5.57 => ( ( ord_less_eq_real @ Y @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.57 => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X3 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_monotone_minus_pi_0'
% 5.25/5.57 thf(fact_8311_sin__zero__iff__int2,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( sin_real @ X3 )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 = ( ? [I3: int] :
% 5.25/5.57 ( X3
% 5.25/5.57 = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ pi ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_zero_iff_int2
% 5.25/5.57 thf(fact_8312_diffs__def,axiom,
% 5.25/5.57 ( diffs_int
% 5.25/5.57 = ( ^ [C2: nat > int,N2: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( C2 @ ( suc @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % diffs_def
% 5.25/5.57 thf(fact_8313_diffs__def,axiom,
% 5.25/5.57 ( diffs_real
% 5.25/5.57 = ( ^ [C2: nat > real,N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( C2 @ ( suc @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % diffs_def
% 5.25/5.57 thf(fact_8314_diffs__def,axiom,
% 5.25/5.57 ( diffs_rat
% 5.25/5.57 = ( ^ [C2: nat > rat,N2: nat] : ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) @ ( C2 @ ( suc @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % diffs_def
% 5.25/5.57 thf(fact_8315_sincos__total__pi,axiom,
% 5.25/5.57 ! [Y: real,X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.57 => ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.57 = one_one_real )
% 5.25/5.57 => ? [T3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.25/5.57 & ( ord_less_eq_real @ T3 @ pi )
% 5.25/5.57 & ( X3
% 5.25/5.57 = ( cos_real @ T3 ) )
% 5.25/5.57 & ( Y
% 5.25/5.57 = ( sin_real @ T3 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sincos_total_pi
% 5.25/5.57 thf(fact_8316_sin__expansion__lemma,axiom,
% 5.25/5.57 ! [X3: real,M: nat] :
% 5.25/5.57 ( ( sin_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.25/5.57 = ( cos_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_expansion_lemma
% 5.25/5.57 thf(fact_8317_cos__expansion__lemma,axiom,
% 5.25/5.57 ! [X3: real,M: nat] :
% 5.25/5.57 ( ( cos_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.25/5.57 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_expansion_lemma
% 5.25/5.57 thf(fact_8318_termdiff__converges__all,axiom,
% 5.25/5.57 ! [C: nat > complex,X3: complex] :
% 5.25/5.57 ( ! [X5: complex] :
% 5.25/5.57 ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X5 @ N2 ) ) )
% 5.25/5.57 => ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % termdiff_converges_all
% 5.25/5.57 thf(fact_8319_termdiff__converges__all,axiom,
% 5.25/5.57 ! [C: nat > real,X3: real] :
% 5.25/5.57 ( ! [X5: real] :
% 5.25/5.57 ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X5 @ N2 ) ) )
% 5.25/5.57 => ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % termdiff_converges_all
% 5.25/5.57 thf(fact_8320_sin__gt__zero__02,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.25/5.57 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_gt_zero_02
% 5.25/5.57 thf(fact_8321_cos__two__less__zero,axiom,
% 5.25/5.57 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.25/5.57
% 5.25/5.57 % cos_two_less_zero
% 5.25/5.57 thf(fact_8322_cos__two__le__zero,axiom,
% 5.25/5.57 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.25/5.57
% 5.25/5.57 % cos_two_le_zero
% 5.25/5.57 thf(fact_8323_cos__is__zero,axiom,
% 5.25/5.57 ? [X5: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.25/5.57 & ( ord_less_eq_real @ X5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.25/5.57 & ( ( cos_real @ X5 )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 & ! [Y4: real] :
% 5.25/5.57 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.25/5.57 & ( ord_less_eq_real @ Y4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.25/5.57 & ( ( cos_real @ Y4 )
% 5.25/5.57 = zero_zero_real ) )
% 5.25/5.57 => ( Y4 = X5 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_is_zero
% 5.25/5.57 thf(fact_8324_cos__monotone__minus__pi__0,axiom,
% 5.25/5.57 ! [Y: real,X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.25/5.57 => ( ( ord_less_real @ Y @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.57 => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X3 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_monotone_minus_pi_0
% 5.25/5.57 thf(fact_8325_cos__total,axiom,
% 5.25/5.57 ! [Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.57 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.57 => ? [X5: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.25/5.57 & ( ord_less_eq_real @ X5 @ pi )
% 5.25/5.57 & ( ( cos_real @ X5 )
% 5.25/5.57 = Y )
% 5.25/5.57 & ! [Y4: real] :
% 5.25/5.57 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.25/5.57 & ( ord_less_eq_real @ Y4 @ pi )
% 5.25/5.57 & ( ( cos_real @ Y4 )
% 5.25/5.57 = Y ) )
% 5.25/5.57 => ( Y4 = X5 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_total
% 5.25/5.57 thf(fact_8326_sincos__total__pi__half,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.57 => ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.57 = one_one_real )
% 5.25/5.57 => ? [T3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.25/5.57 & ( ord_less_eq_real @ T3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 & ( X3
% 5.25/5.57 = ( cos_real @ T3 ) )
% 5.25/5.57 & ( Y
% 5.25/5.57 = ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sincos_total_pi_half
% 5.25/5.57 thf(fact_8327_sincos__total__2pi__le,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.57 = one_one_real )
% 5.25/5.57 => ? [T3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.25/5.57 & ( ord_less_eq_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.25/5.57 & ( X3
% 5.25/5.57 = ( cos_real @ T3 ) )
% 5.25/5.57 & ( Y
% 5.25/5.57 = ( sin_real @ T3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sincos_total_2pi_le
% 5.25/5.57 thf(fact_8328_sincos__total__2pi,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.57 = one_one_real )
% 5.25/5.57 => ~ ! [T3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.25/5.57 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.25/5.57 => ( ( X3
% 5.25/5.57 = ( cos_real @ T3 ) )
% 5.25/5.57 => ( Y
% 5.25/5.57 != ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sincos_total_2pi
% 5.25/5.57 thf(fact_8329_sin__pi__divide__n__ge__0,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( N != zero_zero_nat )
% 5.25/5.57 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_pi_divide_n_ge_0
% 5.25/5.57 thf(fact_8330_cos__times__cos,axiom,
% 5.25/5.57 ! [W: complex,Z: complex] :
% 5.25/5.57 ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_times_cos
% 5.25/5.57 thf(fact_8331_cos__times__cos,axiom,
% 5.25/5.57 ! [W: real,Z: real] :
% 5.25/5.57 ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.25/5.57 = ( 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 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_times_cos
% 5.25/5.57 thf(fact_8332_cos__plus__cos,axiom,
% 5.25/5.57 ! [W: complex,Z: complex] :
% 5.25/5.57 ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.25/5.57 = ( 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 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_plus_cos
% 5.25/5.57 thf(fact_8333_cos__plus__cos,axiom,
% 5.25/5.57 ! [W: real,Z: real] :
% 5.25/5.57 ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.25/5.57 = ( 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 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_plus_cos
% 5.25/5.57 thf(fact_8334_sin__gt__zero2,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_gt_zero2
% 5.25/5.57 thf(fact_8335_sin__lt__zero,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ pi @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.25/5.57 => ( ord_less_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_lt_zero
% 5.25/5.57 thf(fact_8336_cos__double__less__one,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.25/5.57 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) ) @ one_one_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_double_less_one
% 5.25/5.57 thf(fact_8337_sin__30,axiom,
% 5.25/5.57 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.25/5.57 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_30
% 5.25/5.57 thf(fact_8338_cos__gt__zero,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_gt_zero
% 5.25/5.57 thf(fact_8339_sin__monotone__2pi__le,axiom,
% 5.25/5.57 ! [Y: real,X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.25/5.57 => ( ( ord_less_eq_real @ Y @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X3 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_monotone_2pi_le
% 5.25/5.57 thf(fact_8340_sin__mono__le__eq,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.25/5.57 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( ord_less_eq_real @ ( sin_real @ X3 ) @ ( sin_real @ Y ) )
% 5.25/5.57 = ( ord_less_eq_real @ X3 @ Y ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_mono_le_eq
% 5.25/5.57 thf(fact_8341_sin__inj__pi,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.25/5.57 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( ( sin_real @ X3 )
% 5.25/5.57 = ( sin_real @ Y ) )
% 5.25/5.57 => ( X3 = Y ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_inj_pi
% 5.25/5.57 thf(fact_8342_cos__60,axiom,
% 5.25/5.57 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.25/5.57 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_60
% 5.25/5.57 thf(fact_8343_cos__one__2pi__int,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( cos_real @ X3 )
% 5.25/5.57 = one_one_real )
% 5.25/5.57 = ( ? [X2: int] :
% 5.25/5.57 ( X3
% 5.25/5.57 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_one_2pi_int
% 5.25/5.57 thf(fact_8344_cos__double__cos,axiom,
% 5.25/5.57 ! [W: complex] :
% 5.25/5.57 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.25/5.57 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_double_cos
% 5.25/5.57 thf(fact_8345_cos__double__cos,axiom,
% 5.25/5.57 ! [W: real] :
% 5.25/5.57 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.25/5.57 = ( 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 ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_double_cos
% 5.25/5.57 thf(fact_8346_cos__treble__cos,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X3 ) )
% 5.25/5.57 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_treble_cos
% 5.25/5.57 thf(fact_8347_cos__treble__cos,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X3 ) )
% 5.25/5.57 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_treble_cos
% 5.25/5.57 thf(fact_8348_termdiff__converges,axiom,
% 5.25/5.57 ! [X3: real,K5: real,C: nat > real] :
% 5.25/5.57 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ K5 )
% 5.25/5.57 => ( ! [X5: real] :
% 5.25/5.57 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X5 ) @ K5 )
% 5.25/5.57 => ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X5 @ N2 ) ) ) )
% 5.25/5.57 => ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % termdiff_converges
% 5.25/5.57 thf(fact_8349_termdiff__converges,axiom,
% 5.25/5.57 ! [X3: complex,K5: real,C: nat > complex] :
% 5.25/5.57 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ K5 )
% 5.25/5.57 => ( ! [X5: complex] :
% 5.25/5.57 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X5 ) @ K5 )
% 5.25/5.57 => ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X5 @ N2 ) ) ) )
% 5.25/5.57 => ( summable_complex
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % termdiff_converges
% 5.25/5.57 thf(fact_8350_sin__le__zero,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ pi @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.25/5.57 => ( ord_less_eq_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_le_zero
% 5.25/5.57 thf(fact_8351_sin__less__zero,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ zero_zero_real )
% 5.25/5.57 => ( ord_less_real @ ( sin_real @ X3 ) @ zero_zero_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_less_zero
% 5.25/5.57 thf(fact_8352_sin__monotone__2pi,axiom,
% 5.25/5.57 ! [Y: real,X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.25/5.57 => ( ( ord_less_real @ Y @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X3 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_monotone_2pi
% 5.25/5.57 thf(fact_8353_sin__mono__less__eq,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.25/5.57 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( ord_less_real @ ( sin_real @ X3 ) @ ( sin_real @ Y ) )
% 5.25/5.57 = ( ord_less_real @ X3 @ Y ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_mono_less_eq
% 5.25/5.57 thf(fact_8354_sin__total,axiom,
% 5.25/5.57 ! [Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.57 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.57 => ? [X5: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.25/5.57 & ( ord_less_eq_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 & ( ( sin_real @ X5 )
% 5.25/5.57 = Y )
% 5.25/5.57 & ! [Y4: real] :
% 5.25/5.57 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.25/5.57 & ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 & ( ( sin_real @ Y4 )
% 5.25/5.57 = Y ) )
% 5.25/5.57 => ( Y4 = X5 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_total
% 5.25/5.57 thf(fact_8355_cos__gt__zero__pi,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_gt_zero_pi
% 5.25/5.57 thf(fact_8356_cos__ge__zero,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_ge_zero
% 5.25/5.57 thf(fact_8357_cos__one__2pi,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( cos_real @ X3 )
% 5.25/5.57 = one_one_real )
% 5.25/5.57 = ( ? [X2: nat] :
% 5.25/5.57 ( X3
% 5.25/5.57 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.25/5.57 | ? [X2: nat] :
% 5.25/5.57 ( X3
% 5.25/5.57 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_one_2pi
% 5.25/5.57 thf(fact_8358_sin__pi__divide__n__gt__0,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.57 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_pi_divide_n_gt_0
% 5.25/5.57 thf(fact_8359_sin__zero__iff__int,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( sin_real @ X3 )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 = ( ? [I3: int] :
% 5.25/5.57 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 5.25/5.57 & ( X3
% 5.25/5.57 = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_zero_iff_int
% 5.25/5.57 thf(fact_8360_cos__zero__iff__int,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( cos_real @ X3 )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 = ( ? [I3: int] :
% 5.25/5.57 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 5.25/5.57 & ( X3
% 5.25/5.57 = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_zero_iff_int
% 5.25/5.57 thf(fact_8361_sin__zero__lemma,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ( sin_real @ X3 )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 => ? [N3: nat] :
% 5.25/5.57 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.25/5.57 & ( X3
% 5.25/5.57 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_zero_lemma
% 5.25/5.57 thf(fact_8362_sin__zero__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( sin_real @ X3 )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 = ( ? [N2: nat] :
% 5.25/5.57 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.25/5.57 & ( X3
% 5.25/5.57 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.57 | ? [N2: nat] :
% 5.25/5.57 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.25/5.57 & ( X3
% 5.25/5.57 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_zero_iff
% 5.25/5.57 thf(fact_8363_cos__zero__lemma,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ( cos_real @ X3 )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 => ? [N3: nat] :
% 5.25/5.57 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.25/5.57 & ( X3
% 5.25/5.57 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_zero_lemma
% 5.25/5.57 thf(fact_8364_cos__zero__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( cos_real @ X3 )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 = ( ? [N2: nat] :
% 5.25/5.57 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.25/5.57 & ( X3
% 5.25/5.57 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.57 | ? [N2: nat] :
% 5.25/5.57 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.25/5.57 & ( X3
% 5.25/5.57 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_zero_iff
% 5.25/5.57 thf(fact_8365_mono__SucI1,axiom,
% 5.25/5.57 ! [X8: nat > real] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.25/5.57 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % mono_SucI1
% 5.25/5.57 thf(fact_8366_mono__SucI1,axiom,
% 5.25/5.57 ! [X8: nat > set_int] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.25/5.57 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % mono_SucI1
% 5.25/5.57 thf(fact_8367_mono__SucI1,axiom,
% 5.25/5.57 ! [X8: nat > rat] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.25/5.57 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % mono_SucI1
% 5.25/5.57 thf(fact_8368_mono__SucI1,axiom,
% 5.25/5.57 ! [X8: nat > num] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.25/5.57 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % mono_SucI1
% 5.25/5.57 thf(fact_8369_mono__SucI1,axiom,
% 5.25/5.57 ! [X8: nat > nat] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.25/5.57 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % mono_SucI1
% 5.25/5.57 thf(fact_8370_mono__SucI1,axiom,
% 5.25/5.57 ! [X8: nat > int] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.25/5.57 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % mono_SucI1
% 5.25/5.57 thf(fact_8371_mono__SucI2,axiom,
% 5.25/5.57 ! [X8: nat > real] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.25/5.57 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % mono_SucI2
% 5.25/5.57 thf(fact_8372_mono__SucI2,axiom,
% 5.25/5.57 ! [X8: nat > set_int] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.25/5.57 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % mono_SucI2
% 5.25/5.57 thf(fact_8373_mono__SucI2,axiom,
% 5.25/5.57 ! [X8: nat > rat] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.25/5.57 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % mono_SucI2
% 5.25/5.57 thf(fact_8374_mono__SucI2,axiom,
% 5.25/5.57 ! [X8: nat > num] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.25/5.57 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % mono_SucI2
% 5.25/5.57 thf(fact_8375_mono__SucI2,axiom,
% 5.25/5.57 ! [X8: nat > nat] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.25/5.57 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % mono_SucI2
% 5.25/5.57 thf(fact_8376_mono__SucI2,axiom,
% 5.25/5.57 ! [X8: nat > int] :
% 5.25/5.57 ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.25/5.57 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % mono_SucI2
% 5.25/5.57 thf(fact_8377_monoseq__Suc,axiom,
% 5.25/5.57 ( topolo6980174941875973593q_real
% 5.25/5.57 = ( ^ [X4: nat > real] :
% 5.25/5.57 ( ! [N2: nat] : ( ord_less_eq_real @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 5.25/5.57 | ! [N2: nat] : ( ord_less_eq_real @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoseq_Suc
% 5.25/5.57 thf(fact_8378_monoseq__Suc,axiom,
% 5.25/5.57 ( topolo3100542954746470799et_int
% 5.25/5.57 = ( ^ [X4: nat > set_int] :
% 5.25/5.57 ( ! [N2: nat] : ( ord_less_eq_set_int @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 5.25/5.57 | ! [N2: nat] : ( ord_less_eq_set_int @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoseq_Suc
% 5.25/5.57 thf(fact_8379_monoseq__Suc,axiom,
% 5.25/5.57 ( topolo4267028734544971653eq_rat
% 5.25/5.57 = ( ^ [X4: nat > rat] :
% 5.25/5.57 ( ! [N2: nat] : ( ord_less_eq_rat @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 5.25/5.57 | ! [N2: nat] : ( ord_less_eq_rat @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoseq_Suc
% 5.25/5.57 thf(fact_8380_monoseq__Suc,axiom,
% 5.25/5.57 ( topolo1459490580787246023eq_num
% 5.25/5.57 = ( ^ [X4: nat > num] :
% 5.25/5.57 ( ! [N2: nat] : ( ord_less_eq_num @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 5.25/5.57 | ! [N2: nat] : ( ord_less_eq_num @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoseq_Suc
% 5.25/5.57 thf(fact_8381_monoseq__Suc,axiom,
% 5.25/5.57 ( topolo4902158794631467389eq_nat
% 5.25/5.57 = ( ^ [X4: nat > nat] :
% 5.25/5.57 ( ! [N2: nat] : ( ord_less_eq_nat @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 5.25/5.57 | ! [N2: nat] : ( ord_less_eq_nat @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoseq_Suc
% 5.25/5.57 thf(fact_8382_monoseq__Suc,axiom,
% 5.25/5.57 ( topolo4899668324122417113eq_int
% 5.25/5.57 = ( ^ [X4: nat > int] :
% 5.25/5.57 ( ! [N2: nat] : ( ord_less_eq_int @ ( X4 @ N2 ) @ ( X4 @ ( suc @ N2 ) ) )
% 5.25/5.57 | ! [N2: nat] : ( ord_less_eq_int @ ( X4 @ ( suc @ N2 ) ) @ ( X4 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoseq_Suc
% 5.25/5.57 thf(fact_8383_monoI1,axiom,
% 5.25/5.57 ! [X8: nat > real] :
% 5.25/5.57 ( ! [M5: nat,N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.25/5.57 => ( ord_less_eq_real @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.25/5.57 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoI1
% 5.25/5.57 thf(fact_8384_monoI1,axiom,
% 5.25/5.57 ! [X8: nat > set_int] :
% 5.25/5.57 ( ! [M5: nat,N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.25/5.57 => ( ord_less_eq_set_int @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.25/5.57 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoI1
% 5.25/5.57 thf(fact_8385_monoI1,axiom,
% 5.25/5.57 ! [X8: nat > rat] :
% 5.25/5.57 ( ! [M5: nat,N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.25/5.57 => ( ord_less_eq_rat @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.25/5.57 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoI1
% 5.25/5.57 thf(fact_8386_monoI1,axiom,
% 5.25/5.57 ! [X8: nat > num] :
% 5.25/5.57 ( ! [M5: nat,N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.25/5.57 => ( ord_less_eq_num @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.25/5.57 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoI1
% 5.25/5.57 thf(fact_8387_monoI1,axiom,
% 5.25/5.57 ! [X8: nat > nat] :
% 5.25/5.57 ( ! [M5: nat,N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.25/5.57 => ( ord_less_eq_nat @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.25/5.57 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoI1
% 5.25/5.57 thf(fact_8388_monoI1,axiom,
% 5.25/5.57 ! [X8: nat > int] :
% 5.25/5.57 ( ! [M5: nat,N3: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.25/5.57 => ( ord_less_eq_int @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.25/5.57 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.25/5.57
% 5.25/5.57 % monoI1
% 5.25/5.57 thf(fact_8389_Maclaurin__minus__cos__expansion,axiom,
% 5.25/5.57 ! [N: nat,X3: real] :
% 5.25/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ zero_zero_real )
% 5.25/5.57 => ? [T3: real] :
% 5.25/5.57 ( ( ord_less_real @ X3 @ T3 )
% 5.25/5.57 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.25/5.57 & ( ( cos_real @ X3 )
% 5.25/5.57 = ( plus_plus_real
% 5.25/5.57 @ ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.57 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_minus_cos_expansion
% 5.25/5.57 thf(fact_8390_Maclaurin__cos__expansion2,axiom,
% 5.25/5.57 ! [X3: real,N: nat] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.57 => ? [T3: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.25/5.57 & ( ord_less_real @ T3 @ X3 )
% 5.25/5.57 & ( ( cos_real @ X3 )
% 5.25/5.57 = ( plus_plus_real
% 5.25/5.57 @ ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.57 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_cos_expansion2
% 5.25/5.57 thf(fact_8391_Maclaurin__cos__expansion,axiom,
% 5.25/5.57 ! [X3: real,N: nat] :
% 5.25/5.57 ? [T3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 5.25/5.57 & ( ( cos_real @ X3 )
% 5.25/5.57 = ( plus_plus_real
% 5.25/5.57 @ ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.57 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_cos_expansion
% 5.25/5.57 thf(fact_8392_sin__paired,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( sums_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.25/5.57 @ ( sin_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_paired
% 5.25/5.57 thf(fact_8393_tan__double,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( ( cos_complex @ X3 )
% 5.25/5.57 != zero_zero_complex )
% 5.25/5.57 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) )
% 5.25/5.57 != zero_zero_complex )
% 5.25/5.57 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X3 ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_double
% 5.25/5.57 thf(fact_8394_tan__double,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( cos_real @ X3 )
% 5.25/5.57 != zero_zero_real )
% 5.25/5.57 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) )
% 5.25/5.57 != zero_zero_real )
% 5.25/5.57 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) )
% 5.25/5.57 = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X3 ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_double
% 5.25/5.57 thf(fact_8395_tan__periodic__pi,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( tan_real @ ( plus_plus_real @ X3 @ pi ) )
% 5.25/5.57 = ( tan_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_periodic_pi
% 5.25/5.57 thf(fact_8396_fact__0,axiom,
% 5.25/5.57 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.25/5.57 = one_one_complex ) ).
% 5.25/5.57
% 5.25/5.57 % fact_0
% 5.25/5.57 thf(fact_8397_fact__0,axiom,
% 5.25/5.57 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 5.25/5.57 = one_one_rat ) ).
% 5.25/5.57
% 5.25/5.57 % fact_0
% 5.25/5.57 thf(fact_8398_fact__0,axiom,
% 5.25/5.57 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.25/5.57 = one_one_int ) ).
% 5.25/5.57
% 5.25/5.57 % fact_0
% 5.25/5.57 thf(fact_8399_fact__0,axiom,
% 5.25/5.57 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % fact_0
% 5.25/5.57 thf(fact_8400_fact__0,axiom,
% 5.25/5.57 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.25/5.57 = one_one_nat ) ).
% 5.25/5.57
% 5.25/5.57 % fact_0
% 5.25/5.57 thf(fact_8401_fact__1,axiom,
% 5.25/5.57 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 5.25/5.57 = one_one_complex ) ).
% 5.25/5.57
% 5.25/5.57 % fact_1
% 5.25/5.57 thf(fact_8402_fact__1,axiom,
% 5.25/5.57 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 5.25/5.57 = one_one_rat ) ).
% 5.25/5.57
% 5.25/5.57 % fact_1
% 5.25/5.57 thf(fact_8403_fact__1,axiom,
% 5.25/5.57 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 5.25/5.57 = one_one_int ) ).
% 5.25/5.57
% 5.25/5.57 % fact_1
% 5.25/5.57 thf(fact_8404_fact__1,axiom,
% 5.25/5.57 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % fact_1
% 5.25/5.57 thf(fact_8405_fact__1,axiom,
% 5.25/5.57 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 5.25/5.57 = one_one_nat ) ).
% 5.25/5.57
% 5.25/5.57 % fact_1
% 5.25/5.57 thf(fact_8406_fact__Suc__0,axiom,
% 5.25/5.57 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.25/5.57 = one_one_complex ) ).
% 5.25/5.57
% 5.25/5.57 % fact_Suc_0
% 5.25/5.57 thf(fact_8407_fact__Suc__0,axiom,
% 5.25/5.57 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 5.25/5.57 = one_one_rat ) ).
% 5.25/5.57
% 5.25/5.57 % fact_Suc_0
% 5.25/5.57 thf(fact_8408_fact__Suc__0,axiom,
% 5.25/5.57 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.25/5.57 = one_one_int ) ).
% 5.25/5.57
% 5.25/5.57 % fact_Suc_0
% 5.25/5.57 thf(fact_8409_fact__Suc__0,axiom,
% 5.25/5.57 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % fact_Suc_0
% 5.25/5.57 thf(fact_8410_fact__Suc__0,axiom,
% 5.25/5.57 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.25/5.57 = one_one_nat ) ).
% 5.25/5.57
% 5.25/5.57 % fact_Suc_0
% 5.25/5.57 thf(fact_8411_fact__Suc,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 5.25/5.57 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_Suc
% 5.25/5.57 thf(fact_8412_fact__Suc,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 5.25/5.57 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_Suc
% 5.25/5.57 thf(fact_8413_fact__Suc,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 5.25/5.57 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_Suc
% 5.25/5.57 thf(fact_8414_fact__Suc,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 5.25/5.57 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_Suc
% 5.25/5.57 thf(fact_8415_tan__npi,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.25/5.57 = zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % tan_npi
% 5.25/5.57 thf(fact_8416_tan__periodic__n,axiom,
% 5.25/5.57 ! [X3: real,N: num] :
% 5.25/5.57 ( ( tan_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 5.25/5.57 = ( tan_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_periodic_n
% 5.25/5.57 thf(fact_8417_tan__periodic__nat,axiom,
% 5.25/5.57 ! [X3: real,N: nat] :
% 5.25/5.57 ( ( tan_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 5.25/5.57 = ( tan_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_periodic_nat
% 5.25/5.57 thf(fact_8418_tan__periodic__int,axiom,
% 5.25/5.57 ! [X3: real,I2: int] :
% 5.25/5.57 ( ( tan_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) )
% 5.25/5.57 = ( tan_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_periodic_int
% 5.25/5.57 thf(fact_8419_fact__2,axiom,
% 5.25/5.57 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.57 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_2
% 5.25/5.57 thf(fact_8420_fact__2,axiom,
% 5.25/5.57 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.57 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_2
% 5.25/5.57 thf(fact_8421_fact__2,axiom,
% 5.25/5.57 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.57 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_2
% 5.25/5.57 thf(fact_8422_fact__2,axiom,
% 5.25/5.57 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.57 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_2
% 5.25/5.57 thf(fact_8423_fact__2,axiom,
% 5.25/5.57 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.57 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_2
% 5.25/5.57 thf(fact_8424_tan__periodic,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( tan_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.25/5.57 = ( tan_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_periodic
% 5.25/5.57 thf(fact_8425_fact__ge__zero,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_ge_zero
% 5.25/5.57 thf(fact_8426_fact__ge__zero,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_ge_zero
% 5.25/5.57 thf(fact_8427_fact__ge__zero,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_ge_zero
% 5.25/5.57 thf(fact_8428_fact__ge__zero,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_ge_zero
% 5.25/5.57 thf(fact_8429_fact__gt__zero,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_gt_zero
% 5.25/5.57 thf(fact_8430_fact__gt__zero,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_gt_zero
% 5.25/5.57 thf(fact_8431_fact__gt__zero,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_gt_zero
% 5.25/5.57 thf(fact_8432_fact__gt__zero,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_gt_zero
% 5.25/5.57 thf(fact_8433_fact__not__neg,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 5.25/5.57
% 5.25/5.57 % fact_not_neg
% 5.25/5.57 thf(fact_8434_fact__not__neg,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 5.25/5.57
% 5.25/5.57 % fact_not_neg
% 5.25/5.57 thf(fact_8435_fact__not__neg,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % fact_not_neg
% 5.25/5.57 thf(fact_8436_fact__not__neg,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 5.25/5.57
% 5.25/5.57 % fact_not_neg
% 5.25/5.57 thf(fact_8437_fact__ge__1,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_ge_1
% 5.25/5.57 thf(fact_8438_fact__ge__1,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_ge_1
% 5.25/5.57 thf(fact_8439_fact__ge__1,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_ge_1
% 5.25/5.57 thf(fact_8440_fact__ge__1,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_ge_1
% 5.25/5.57 thf(fact_8441_fact__mono,axiom,
% 5.25/5.57 ! [M: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.57 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_mono
% 5.25/5.57 thf(fact_8442_fact__mono,axiom,
% 5.25/5.57 ! [M: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.57 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_mono
% 5.25/5.57 thf(fact_8443_fact__mono,axiom,
% 5.25/5.57 ! [M: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.57 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_mono
% 5.25/5.57 thf(fact_8444_fact__mono,axiom,
% 5.25/5.57 ! [M: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.57 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_mono
% 5.25/5.57 thf(fact_8445_fact__dvd,axiom,
% 5.25/5.57 ! [N: nat,M: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.57 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_dvd
% 5.25/5.57 thf(fact_8446_fact__dvd,axiom,
% 5.25/5.57 ! [N: nat,M: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.57 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_dvd
% 5.25/5.57 thf(fact_8447_fact__dvd,axiom,
% 5.25/5.57 ! [N: nat,M: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.57 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_dvd
% 5.25/5.57 thf(fact_8448_fact__dvd,axiom,
% 5.25/5.57 ! [N: nat,M: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.57 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_dvd
% 5.25/5.57 thf(fact_8449_pochhammer__fact,axiom,
% 5.25/5.57 ( semiri5044797733671781792omplex
% 5.25/5.57 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 5.25/5.57
% 5.25/5.57 % pochhammer_fact
% 5.25/5.57 thf(fact_8450_pochhammer__fact,axiom,
% 5.25/5.57 ( semiri773545260158071498ct_rat
% 5.25/5.57 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 5.25/5.57
% 5.25/5.57 % pochhammer_fact
% 5.25/5.57 thf(fact_8451_pochhammer__fact,axiom,
% 5.25/5.57 ( semiri1406184849735516958ct_int
% 5.25/5.57 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 5.25/5.57
% 5.25/5.57 % pochhammer_fact
% 5.25/5.57 thf(fact_8452_pochhammer__fact,axiom,
% 5.25/5.57 ( semiri2265585572941072030t_real
% 5.25/5.57 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % pochhammer_fact
% 5.25/5.57 thf(fact_8453_pochhammer__fact,axiom,
% 5.25/5.57 ( semiri1408675320244567234ct_nat
% 5.25/5.57 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 5.25/5.57
% 5.25/5.57 % pochhammer_fact
% 5.25/5.57 thf(fact_8454_fact__less__mono,axiom,
% 5.25/5.57 ! [M: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.57 => ( ( ord_less_nat @ M @ N )
% 5.25/5.57 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_less_mono
% 5.25/5.57 thf(fact_8455_fact__less__mono,axiom,
% 5.25/5.57 ! [M: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.57 => ( ( ord_less_nat @ M @ N )
% 5.25/5.57 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_less_mono
% 5.25/5.57 thf(fact_8456_fact__less__mono,axiom,
% 5.25/5.57 ! [M: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.57 => ( ( ord_less_nat @ M @ N )
% 5.25/5.57 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_less_mono
% 5.25/5.57 thf(fact_8457_fact__less__mono,axiom,
% 5.25/5.57 ! [M: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.57 => ( ( ord_less_nat @ M @ N )
% 5.25/5.57 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_less_mono
% 5.25/5.57 thf(fact_8458_fact__fact__dvd__fact,axiom,
% 5.25/5.57 ! [K: nat,N: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_fact_dvd_fact
% 5.25/5.57 thf(fact_8459_fact__fact__dvd__fact,axiom,
% 5.25/5.57 ! [K: nat,N: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_fact_dvd_fact
% 5.25/5.57 thf(fact_8460_fact__fact__dvd__fact,axiom,
% 5.25/5.57 ! [K: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_fact_dvd_fact
% 5.25/5.57 thf(fact_8461_fact__fact__dvd__fact,axiom,
% 5.25/5.57 ! [K: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_fact_dvd_fact
% 5.25/5.57 thf(fact_8462_fact__fact__dvd__fact,axiom,
% 5.25/5.57 ! [K: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_fact_dvd_fact
% 5.25/5.57 thf(fact_8463_fact__mod,axiom,
% 5.25/5.57 ! [M: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.57 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.25/5.57 = zero_zero_int ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_mod
% 5.25/5.57 thf(fact_8464_fact__mod,axiom,
% 5.25/5.57 ! [M: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.57 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) )
% 5.25/5.57 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_mod
% 5.25/5.57 thf(fact_8465_fact__mod,axiom,
% 5.25/5.57 ! [M: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.57 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.25/5.57 = zero_zero_nat ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_mod
% 5.25/5.57 thf(fact_8466_fact__le__power,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_le_power
% 5.25/5.57 thf(fact_8467_fact__le__power,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_le_power
% 5.25/5.57 thf(fact_8468_fact__le__power,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_le_power
% 5.25/5.57 thf(fact_8469_fact__le__power,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_le_power
% 5.25/5.57 thf(fact_8470_fact__prod,axiom,
% 5.25/5.57 ( semiri1406184849735516958ct_int
% 5.25/5.57 = ( ^ [N2: nat] :
% 5.25/5.57 ( semiri1314217659103216013at_int
% 5.25/5.57 @ ( groups708209901874060359at_nat
% 5.25/5.57 @ ^ [X2: nat] : X2
% 5.25/5.57 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_prod
% 5.25/5.57 thf(fact_8471_fact__prod,axiom,
% 5.25/5.57 ( semiri773545260158071498ct_rat
% 5.25/5.57 = ( ^ [N2: nat] :
% 5.25/5.57 ( semiri681578069525770553at_rat
% 5.25/5.57 @ ( groups708209901874060359at_nat
% 5.25/5.57 @ ^ [X2: nat] : X2
% 5.25/5.57 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_prod
% 5.25/5.57 thf(fact_8472_fact__prod,axiom,
% 5.25/5.57 ( semiri2265585572941072030t_real
% 5.25/5.57 = ( ^ [N2: nat] :
% 5.25/5.57 ( semiri5074537144036343181t_real
% 5.25/5.57 @ ( groups708209901874060359at_nat
% 5.25/5.57 @ ^ [X2: nat] : X2
% 5.25/5.57 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_prod
% 5.25/5.57 thf(fact_8473_fact__prod,axiom,
% 5.25/5.57 ( semiri1408675320244567234ct_nat
% 5.25/5.57 = ( ^ [N2: nat] :
% 5.25/5.57 ( semiri1316708129612266289at_nat
% 5.25/5.57 @ ( groups708209901874060359at_nat
% 5.25/5.57 @ ^ [X2: nat] : X2
% 5.25/5.57 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_prod
% 5.25/5.57 thf(fact_8474_tan__def,axiom,
% 5.25/5.57 ( tan_complex
% 5.25/5.57 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X2 ) @ ( cos_complex @ X2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_def
% 5.25/5.57 thf(fact_8475_tan__def,axiom,
% 5.25/5.57 ( tan_real
% 5.25/5.57 = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ X2 ) @ ( cos_real @ X2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_def
% 5.25/5.57 thf(fact_8476_choose__dvd,axiom,
% 5.25/5.57 ! [K: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.57 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % choose_dvd
% 5.25/5.57 thf(fact_8477_choose__dvd,axiom,
% 5.25/5.57 ! [K: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.57 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % choose_dvd
% 5.25/5.57 thf(fact_8478_choose__dvd,axiom,
% 5.25/5.57 ! [K: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.57 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % choose_dvd
% 5.25/5.57 thf(fact_8479_choose__dvd,axiom,
% 5.25/5.57 ! [K: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.57 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % choose_dvd
% 5.25/5.57 thf(fact_8480_choose__dvd,axiom,
% 5.25/5.57 ! [K: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.57 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % choose_dvd
% 5.25/5.57 thf(fact_8481_fact__numeral,axiom,
% 5.25/5.57 ! [K: num] :
% 5.25/5.57 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 5.25/5.57 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_numeral
% 5.25/5.57 thf(fact_8482_fact__numeral,axiom,
% 5.25/5.57 ! [K: num] :
% 5.25/5.57 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 5.25/5.57 = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_numeral
% 5.25/5.57 thf(fact_8483_fact__numeral,axiom,
% 5.25/5.57 ! [K: num] :
% 5.25/5.57 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.25/5.57 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_numeral
% 5.25/5.57 thf(fact_8484_fact__numeral,axiom,
% 5.25/5.57 ! [K: num] :
% 5.25/5.57 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 5.25/5.57 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_numeral
% 5.25/5.57 thf(fact_8485_fact__numeral,axiom,
% 5.25/5.57 ! [K: num] :
% 5.25/5.57 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.25/5.57 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_numeral
% 5.25/5.57 thf(fact_8486_square__fact__le__2__fact,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % square_fact_le_2_fact
% 5.25/5.57 thf(fact_8487_tan__45,axiom,
% 5.25/5.57 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % tan_45
% 5.25/5.57 thf(fact_8488_fact__num__eq__if,axiom,
% 5.25/5.57 ( semiri5044797733671781792omplex
% 5.25/5.57 = ( ^ [M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M6 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_num_eq_if
% 5.25/5.57 thf(fact_8489_fact__num__eq__if,axiom,
% 5.25/5.57 ( semiri1406184849735516958ct_int
% 5.25/5.57 = ( ^ [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 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_num_eq_if
% 5.25/5.57 thf(fact_8490_fact__num__eq__if,axiom,
% 5.25/5.57 ( semiri773545260158071498ct_rat
% 5.25/5.57 = ( ^ [M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M6 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_num_eq_if
% 5.25/5.57 thf(fact_8491_fact__num__eq__if,axiom,
% 5.25/5.57 ( semiri2265585572941072030t_real
% 5.25/5.57 = ( ^ [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 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_num_eq_if
% 5.25/5.57 thf(fact_8492_fact__num__eq__if,axiom,
% 5.25/5.57 ( semiri1408675320244567234ct_nat
% 5.25/5.57 = ( ^ [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 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_num_eq_if
% 5.25/5.57 thf(fact_8493_fact__code,axiom,
% 5.25/5.57 ( semiri1406184849735516958ct_int
% 5.25/5.57 = ( ^ [N2: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_code
% 5.25/5.57 thf(fact_8494_fact__code,axiom,
% 5.25/5.57 ( semiri773545260158071498ct_rat
% 5.25/5.57 = ( ^ [N2: nat] : ( semiri681578069525770553at_rat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_code
% 5.25/5.57 thf(fact_8495_fact__code,axiom,
% 5.25/5.57 ( semiri2265585572941072030t_real
% 5.25/5.57 = ( ^ [N2: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_code
% 5.25/5.57 thf(fact_8496_fact__code,axiom,
% 5.25/5.57 ( semiri1408675320244567234ct_nat
% 5.25/5.57 = ( ^ [N2: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_code
% 5.25/5.57 thf(fact_8497_fact__reduce,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.57 => ( ( semiri1406184849735516958ct_int @ N )
% 5.25/5.57 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_reduce
% 5.25/5.57 thf(fact_8498_fact__reduce,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.57 => ( ( semiri773545260158071498ct_rat @ N )
% 5.25/5.57 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_reduce
% 5.25/5.57 thf(fact_8499_fact__reduce,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.57 => ( ( semiri2265585572941072030t_real @ N )
% 5.25/5.57 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_reduce
% 5.25/5.57 thf(fact_8500_fact__reduce,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.57 => ( ( semiri1408675320244567234ct_nat @ N )
% 5.25/5.57 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_reduce
% 5.25/5.57 thf(fact_8501_pochhammer__same,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 5.25/5.57 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % pochhammer_same
% 5.25/5.57 thf(fact_8502_pochhammer__same,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 5.25/5.57 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % pochhammer_same
% 5.25/5.57 thf(fact_8503_pochhammer__same,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 5.25/5.57 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % pochhammer_same
% 5.25/5.57 thf(fact_8504_pochhammer__same,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 5.25/5.57 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % pochhammer_same
% 5.25/5.57 thf(fact_8505_pochhammer__same,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 5.25/5.57 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % pochhammer_same
% 5.25/5.57 thf(fact_8506_binomial__fact,axiom,
% 5.25/5.57 ! [K: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.57 => ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % binomial_fact
% 5.25/5.57 thf(fact_8507_binomial__fact,axiom,
% 5.25/5.57 ! [K: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.57 => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 5.25/5.57 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % binomial_fact
% 5.25/5.57 thf(fact_8508_binomial__fact,axiom,
% 5.25/5.57 ! [K: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.57 => ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 5.25/5.57 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % binomial_fact
% 5.25/5.57 thf(fact_8509_fact__binomial,axiom,
% 5.25/5.57 ! [K: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.57 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_binomial
% 5.25/5.57 thf(fact_8510_fact__binomial,axiom,
% 5.25/5.57 ! [K: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.57 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) )
% 5.25/5.57 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_binomial
% 5.25/5.57 thf(fact_8511_fact__binomial,axiom,
% 5.25/5.57 ! [K: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.57 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) )
% 5.25/5.57 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_binomial
% 5.25/5.57 thf(fact_8512_tan__gt__zero,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_gt_zero
% 5.25/5.57 thf(fact_8513_lemma__tan__total,axiom,
% 5.25/5.57 ! [Y: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.57 => ? [X5: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ X5 )
% 5.25/5.57 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 & ( ord_less_real @ Y @ ( tan_real @ X5 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % lemma_tan_total
% 5.25/5.57 thf(fact_8514_tan__total,axiom,
% 5.25/5.57 ! [Y: real] :
% 5.25/5.57 ? [X5: real] :
% 5.25/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.25/5.57 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 & ( ( tan_real @ X5 )
% 5.25/5.57 = Y )
% 5.25/5.57 & ! [Y4: real] :
% 5.25/5.57 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.25/5.57 & ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 & ( ( tan_real @ Y4 )
% 5.25/5.57 = Y ) )
% 5.25/5.57 => ( Y4 = X5 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_total
% 5.25/5.57 thf(fact_8515_tan__monotone,axiom,
% 5.25/5.57 ! [Y: real,X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.25/5.57 => ( ( ord_less_real @ Y @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X3 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_monotone
% 5.25/5.57 thf(fact_8516_tan__monotone_H,axiom,
% 5.25/5.57 ! [Y: real,X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.25/5.57 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( ord_less_real @ Y @ X3 )
% 5.25/5.57 = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X3 ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_monotone'
% 5.25/5.57 thf(fact_8517_tan__mono__lt__eq,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.25/5.57 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( ord_less_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) )
% 5.25/5.57 = ( ord_less_real @ X3 @ Y ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_mono_lt_eq
% 5.25/5.57 thf(fact_8518_lemma__tan__total1,axiom,
% 5.25/5.57 ! [Y: real] :
% 5.25/5.57 ? [X5: real] :
% 5.25/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.25/5.57 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 & ( ( tan_real @ X5 )
% 5.25/5.57 = Y ) ) ).
% 5.25/5.57
% 5.25/5.57 % lemma_tan_total1
% 5.25/5.57 thf(fact_8519_tan__minus__45,axiom,
% 5.25/5.57 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.57 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_minus_45
% 5.25/5.57 thf(fact_8520_tan__inverse,axiom,
% 5.25/5.57 ! [Y: real] :
% 5.25/5.57 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y ) )
% 5.25/5.57 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_inverse
% 5.25/5.57 thf(fact_8521_add__tan__eq,axiom,
% 5.25/5.57 ! [X3: complex,Y: complex] :
% 5.25/5.57 ( ( ( cos_complex @ X3 )
% 5.25/5.57 != zero_zero_complex )
% 5.25/5.57 => ( ( ( cos_complex @ Y )
% 5.25/5.57 != zero_zero_complex )
% 5.25/5.57 => ( ( plus_plus_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X3 @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X3 ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % add_tan_eq
% 5.25/5.57 thf(fact_8522_add__tan__eq,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ( cos_real @ X3 )
% 5.25/5.57 != zero_zero_real )
% 5.25/5.57 => ( ( ( cos_real @ Y )
% 5.25/5.57 != zero_zero_real )
% 5.25/5.57 => ( ( plus_plus_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) )
% 5.25/5.57 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X3 @ Y ) ) @ ( times_times_real @ ( cos_real @ X3 ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % add_tan_eq
% 5.25/5.57 thf(fact_8523_gbinomial__pochhammer,axiom,
% 5.25/5.57 ( gbinomial_complex
% 5.25/5.57 = ( ^ [A3: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A3 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % gbinomial_pochhammer
% 5.25/5.57 thf(fact_8524_gbinomial__pochhammer,axiom,
% 5.25/5.57 ( gbinomial_rat
% 5.25/5.57 = ( ^ [A3: rat,K3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A3 ) @ K3 ) ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % gbinomial_pochhammer
% 5.25/5.57 thf(fact_8525_gbinomial__pochhammer,axiom,
% 5.25/5.57 ( gbinomial_real
% 5.25/5.57 = ( ^ [A3: 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 @ A3 ) @ K3 ) ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % gbinomial_pochhammer
% 5.25/5.57 thf(fact_8526_gbinomial__pochhammer_H,axiom,
% 5.25/5.57 ( gbinomial_complex
% 5.25/5.57 = ( ^ [A3: complex,K3: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ K3 ) ) @ one_one_complex ) @ K3 ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % gbinomial_pochhammer'
% 5.25/5.57 thf(fact_8527_gbinomial__pochhammer_H,axiom,
% 5.25/5.57 ( gbinomial_rat
% 5.25/5.57 = ( ^ [A3: rat,K3: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ K3 ) ) @ one_one_rat ) @ K3 ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % gbinomial_pochhammer'
% 5.25/5.57 thf(fact_8528_gbinomial__pochhammer_H,axiom,
% 5.25/5.57 ( gbinomial_real
% 5.25/5.57 = ( ^ [A3: real,K3: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ K3 ) ) @ one_one_real ) @ K3 ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % gbinomial_pochhammer'
% 5.25/5.57 thf(fact_8529_tan__total__pos,axiom,
% 5.25/5.57 ! [Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.57 => ? [X5: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.25/5.57 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 & ( ( tan_real @ X5 )
% 5.25/5.57 = Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_total_pos
% 5.25/5.57 thf(fact_8530_tan__pos__pi2__le,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_pos_pi2_le
% 5.25/5.57 thf(fact_8531_tan__less__zero,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ zero_zero_real )
% 5.25/5.57 => ( ord_less_real @ ( tan_real @ X3 ) @ zero_zero_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_less_zero
% 5.25/5.57 thf(fact_8532_tan__mono__le,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.57 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ord_less_eq_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_mono_le
% 5.25/5.57 thf(fact_8533_tan__mono__le__eq,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.25/5.57 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( ord_less_eq_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) )
% 5.25/5.57 = ( ord_less_eq_real @ X3 @ Y ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_mono_le_eq
% 5.25/5.57 thf(fact_8534_tan__bound__pi2,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.25/5.57 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X3 ) ) @ one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_bound_pi2
% 5.25/5.57 thf(fact_8535_arctan,axiom,
% 5.25/5.57 ! [Y: real] :
% 5.25/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.25/5.57 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 & ( ( tan_real @ ( arctan @ Y ) )
% 5.25/5.57 = Y ) ) ).
% 5.25/5.57
% 5.25/5.57 % arctan
% 5.25/5.57 thf(fact_8536_arctan__tan,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( arctan @ ( tan_real @ X3 ) )
% 5.25/5.57 = X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % arctan_tan
% 5.25/5.57 thf(fact_8537_arctan__unique,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.57 => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( ( tan_real @ X3 )
% 5.25/5.57 = Y )
% 5.25/5.57 => ( ( arctan @ Y )
% 5.25/5.57 = X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % arctan_unique
% 5.25/5.57 thf(fact_8538_Maclaurin__zero,axiom,
% 5.25/5.57 ! [X3: real,N: nat,Diff: nat > complex > real] :
% 5.25/5.57 ( ( X3 = zero_zero_real )
% 5.25/5.57 => ( ( N != zero_zero_nat )
% 5.25/5.57 => ( ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.57 = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_zero
% 5.25/5.57 thf(fact_8539_Maclaurin__zero,axiom,
% 5.25/5.57 ! [X3: real,N: nat,Diff: nat > real > real] :
% 5.25/5.57 ( ( X3 = zero_zero_real )
% 5.25/5.57 => ( ( N != zero_zero_nat )
% 5.25/5.57 => ( ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.57 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_zero
% 5.25/5.57 thf(fact_8540_Maclaurin__zero,axiom,
% 5.25/5.57 ! [X3: real,N: nat,Diff: nat > rat > real] :
% 5.25/5.57 ( ( X3 = zero_zero_real )
% 5.25/5.57 => ( ( N != zero_zero_nat )
% 5.25/5.57 => ( ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.57 = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_zero
% 5.25/5.57 thf(fact_8541_Maclaurin__zero,axiom,
% 5.25/5.57 ! [X3: real,N: nat,Diff: nat > nat > real] :
% 5.25/5.57 ( ( X3 = zero_zero_real )
% 5.25/5.57 => ( ( N != zero_zero_nat )
% 5.25/5.57 => ( ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.57 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_zero
% 5.25/5.57 thf(fact_8542_Maclaurin__zero,axiom,
% 5.25/5.57 ! [X3: real,N: nat,Diff: nat > int > real] :
% 5.25/5.57 ( ( X3 = zero_zero_real )
% 5.25/5.57 => ( ( N != zero_zero_nat )
% 5.25/5.57 => ( ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.57 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_zero
% 5.25/5.57 thf(fact_8543_Maclaurin__lemma,axiom,
% 5.25/5.57 ! [H2: real,F: real > real,J2: nat > real,N: nat] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.25/5.57 => ? [B8: real] :
% 5.25/5.57 ( ( F @ H2 )
% 5.25/5.57 = ( plus_plus_real
% 5.25/5.57 @ ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J2 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.57 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_lemma
% 5.25/5.57 thf(fact_8544_tan__add,axiom,
% 5.25/5.57 ! [X3: complex,Y: complex] :
% 5.25/5.57 ( ( ( cos_complex @ X3 )
% 5.25/5.57 != zero_zero_complex )
% 5.25/5.57 => ( ( ( cos_complex @ Y )
% 5.25/5.57 != zero_zero_complex )
% 5.25/5.57 => ( ( ( cos_complex @ ( plus_plus_complex @ X3 @ Y ) )
% 5.25/5.57 != zero_zero_complex )
% 5.25/5.57 => ( ( tan_complex @ ( plus_plus_complex @ X3 @ Y ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_add
% 5.25/5.57 thf(fact_8545_tan__add,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ( cos_real @ X3 )
% 5.25/5.57 != zero_zero_real )
% 5.25/5.57 => ( ( ( cos_real @ Y )
% 5.25/5.57 != zero_zero_real )
% 5.25/5.57 => ( ( ( cos_real @ ( plus_plus_real @ X3 @ Y ) )
% 5.25/5.57 != zero_zero_real )
% 5.25/5.57 => ( ( tan_real @ ( plus_plus_real @ X3 @ Y ) )
% 5.25/5.57 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_add
% 5.25/5.57 thf(fact_8546_tan__diff,axiom,
% 5.25/5.57 ! [X3: complex,Y: complex] :
% 5.25/5.57 ( ( ( cos_complex @ X3 )
% 5.25/5.57 != zero_zero_complex )
% 5.25/5.57 => ( ( ( cos_complex @ Y )
% 5.25/5.57 != zero_zero_complex )
% 5.25/5.57 => ( ( ( cos_complex @ ( minus_minus_complex @ X3 @ Y ) )
% 5.25/5.57 != zero_zero_complex )
% 5.25/5.57 => ( ( tan_complex @ ( minus_minus_complex @ X3 @ Y ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_diff
% 5.25/5.57 thf(fact_8547_tan__diff,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ( cos_real @ X3 )
% 5.25/5.57 != zero_zero_real )
% 5.25/5.57 => ( ( ( cos_real @ Y )
% 5.25/5.57 != zero_zero_real )
% 5.25/5.57 => ( ( ( cos_real @ ( minus_minus_real @ X3 @ Y ) )
% 5.25/5.57 != zero_zero_real )
% 5.25/5.57 => ( ( tan_real @ ( minus_minus_real @ X3 @ Y ) )
% 5.25/5.57 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_diff
% 5.25/5.57 thf(fact_8548_lemma__tan__add1,axiom,
% 5.25/5.57 ! [X3: complex,Y: complex] :
% 5.25/5.57 ( ( ( cos_complex @ X3 )
% 5.25/5.57 != zero_zero_complex )
% 5.25/5.57 => ( ( ( cos_complex @ Y )
% 5.25/5.57 != zero_zero_complex )
% 5.25/5.57 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X3 ) @ ( tan_complex @ Y ) ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X3 @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X3 ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % lemma_tan_add1
% 5.25/5.57 thf(fact_8549_lemma__tan__add1,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ( cos_real @ X3 )
% 5.25/5.57 != zero_zero_real )
% 5.25/5.57 => ( ( ( cos_real @ Y )
% 5.25/5.57 != zero_zero_real )
% 5.25/5.57 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X3 ) @ ( tan_real @ Y ) ) )
% 5.25/5.57 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X3 @ Y ) ) @ ( times_times_real @ ( cos_real @ X3 ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % lemma_tan_add1
% 5.25/5.57 thf(fact_8550_tan__total__pi4,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.57 => ? [Z2: real] :
% 5.25/5.57 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z2 )
% 5.25/5.57 & ( ord_less_real @ Z2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.25/5.57 & ( ( tan_real @ Z2 )
% 5.25/5.57 = X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_total_pi4
% 5.25/5.57 thf(fact_8551_gbinomial__Suc,axiom,
% 5.25/5.57 ! [A: complex,K: nat] :
% 5.25/5.57 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.25/5.57 = ( divide1717551699836669952omplex
% 5.25/5.57 @ ( groups6464643781859351333omplex
% 5.25/5.57 @ ^ [I3: nat] : ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ I3 ) )
% 5.25/5.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.25/5.57 @ ( semiri5044797733671781792omplex @ ( suc @ K ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % gbinomial_Suc
% 5.25/5.57 thf(fact_8552_gbinomial__Suc,axiom,
% 5.25/5.57 ! [A: rat,K: nat] :
% 5.25/5.57 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.25/5.57 = ( divide_divide_rat
% 5.25/5.57 @ ( groups73079841787564623at_rat
% 5.25/5.57 @ ^ [I3: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 5.25/5.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.25/5.57 @ ( semiri773545260158071498ct_rat @ ( suc @ K ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % gbinomial_Suc
% 5.25/5.57 thf(fact_8553_gbinomial__Suc,axiom,
% 5.25/5.57 ! [A: real,K: nat] :
% 5.25/5.57 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.25/5.57 = ( divide_divide_real
% 5.25/5.57 @ ( groups129246275422532515t_real
% 5.25/5.57 @ ^ [I3: nat] : ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ I3 ) )
% 5.25/5.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.25/5.57 @ ( semiri2265585572941072030t_real @ ( suc @ K ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % gbinomial_Suc
% 5.25/5.57 thf(fact_8554_gbinomial__Suc,axiom,
% 5.25/5.57 ! [A: int,K: nat] :
% 5.25/5.57 ( ( gbinomial_int @ A @ ( suc @ K ) )
% 5.25/5.57 = ( divide_divide_int
% 5.25/5.57 @ ( groups705719431365010083at_int
% 5.25/5.57 @ ^ [I3: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I3 ) )
% 5.25/5.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.25/5.57 @ ( semiri1406184849735516958ct_int @ ( suc @ K ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % gbinomial_Suc
% 5.25/5.57 thf(fact_8555_gbinomial__Suc,axiom,
% 5.25/5.57 ! [A: nat,K: nat] :
% 5.25/5.57 ( ( gbinomial_nat @ A @ ( suc @ K ) )
% 5.25/5.57 = ( divide_divide_nat
% 5.25/5.57 @ ( groups708209901874060359at_nat
% 5.25/5.57 @ ^ [I3: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I3 ) )
% 5.25/5.57 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.25/5.57 @ ( semiri1408675320244567234ct_nat @ ( suc @ K ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % gbinomial_Suc
% 5.25/5.57 thf(fact_8556_fact__double,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.57 = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_double
% 5.25/5.57 thf(fact_8557_fact__double,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.57 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_double
% 5.25/5.57 thf(fact_8558_fact__double,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.57 = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_double
% 5.25/5.57 thf(fact_8559_tan__half,axiom,
% 5.25/5.57 ( tan_complex
% 5.25/5.57 = ( ^ [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 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_half
% 5.25/5.57 thf(fact_8560_tan__half,axiom,
% 5.25/5.57 ( tan_real
% 5.25/5.57 = ( ^ [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 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % tan_half
% 5.25/5.57 thf(fact_8561_cos__coeff__def,axiom,
% 5.25/5.57 ( cos_coeff
% 5.25/5.57 = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ zero_zero_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_coeff_def
% 5.25/5.57 thf(fact_8562_gbinomial__code,axiom,
% 5.25/5.57 ( gbinomial_complex
% 5.25/5.57 = ( ^ [A3: complex,K3: nat] :
% 5.25/5.57 ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 5.25/5.57 @ ( divide1717551699836669952omplex
% 5.25/5.57 @ ( set_fo1517530859248394432omplex
% 5.25/5.57 @ ^ [L: nat] : ( times_times_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ L ) ) )
% 5.25/5.57 @ zero_zero_nat
% 5.25/5.57 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.25/5.57 @ one_one_complex )
% 5.25/5.57 @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % gbinomial_code
% 5.25/5.57 thf(fact_8563_gbinomial__code,axiom,
% 5.25/5.57 ( gbinomial_rat
% 5.25/5.57 = ( ^ [A3: rat,K3: nat] :
% 5.25/5.57 ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 5.25/5.57 @ ( divide_divide_rat
% 5.25/5.57 @ ( set_fo1949268297981939178at_rat
% 5.25/5.57 @ ^ [L: nat] : ( times_times_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ L ) ) )
% 5.25/5.57 @ zero_zero_nat
% 5.25/5.57 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.25/5.57 @ one_one_rat )
% 5.25/5.57 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % gbinomial_code
% 5.25/5.57 thf(fact_8564_gbinomial__code,axiom,
% 5.25/5.57 ( gbinomial_real
% 5.25/5.57 = ( ^ [A3: real,K3: nat] :
% 5.25/5.57 ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 5.25/5.57 @ ( divide_divide_real
% 5.25/5.57 @ ( set_fo3111899725591712190t_real
% 5.25/5.57 @ ^ [L: nat] : ( times_times_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ L ) ) )
% 5.25/5.57 @ zero_zero_nat
% 5.25/5.57 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.25/5.57 @ one_one_real )
% 5.25/5.57 @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % gbinomial_code
% 5.25/5.57 thf(fact_8565_cos__paired,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( sums_real
% 5.25/5.57 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_real @ X3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.25/5.57 @ ( cos_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_paired
% 5.25/5.57 thf(fact_8566_Maclaurin__sin__expansion3,axiom,
% 5.25/5.57 ! [N: nat,X3: real] :
% 5.25/5.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.57 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ? [T3: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.25/5.57 & ( ord_less_real @ T3 @ X3 )
% 5.25/5.57 & ( ( sin_real @ X3 )
% 5.25/5.57 = ( plus_plus_real
% 5.25/5.57 @ ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.57 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_sin_expansion3
% 5.25/5.57 thf(fact_8567_Maclaurin__sin__expansion4,axiom,
% 5.25/5.57 ! [X3: real,N: nat] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ? [T3: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.25/5.57 & ( ord_less_eq_real @ T3 @ X3 )
% 5.25/5.57 & ( ( sin_real @ X3 )
% 5.25/5.57 = ( plus_plus_real
% 5.25/5.57 @ ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.57 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_sin_expansion4
% 5.25/5.57 thf(fact_8568_Maclaurin__sin__expansion2,axiom,
% 5.25/5.57 ! [X3: real,N: nat] :
% 5.25/5.57 ? [T3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 5.25/5.57 & ( ( sin_real @ X3 )
% 5.25/5.57 = ( plus_plus_real
% 5.25/5.57 @ ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.57 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_sin_expansion2
% 5.25/5.57 thf(fact_8569_sin__x__sin__y,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( sums_real
% 5.25/5.57 @ ^ [P4: nat] :
% 5.25/5.57 ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [N2: nat] :
% 5.25/5.57 ( if_real
% 5.25/5.57 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 )
% 5.25/5.57 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.57 @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) ) @ ( power_power_real @ X3 @ N2 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P4 @ N2 ) ) )
% 5.25/5.57 @ zero_zero_real )
% 5.25/5.57 @ ( set_ord_atMost_nat @ P4 ) )
% 5.25/5.57 @ ( times_times_real @ ( sin_real @ X3 ) @ ( sin_real @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_x_sin_y
% 5.25/5.57 thf(fact_8570_sin__x__sin__y,axiom,
% 5.25/5.57 ! [X3: complex,Y: complex] :
% 5.25/5.57 ( sums_complex
% 5.25/5.57 @ ^ [P4: nat] :
% 5.25/5.57 ( groups2073611262835488442omplex
% 5.25/5.57 @ ^ [N2: nat] :
% 5.25/5.57 ( if_complex
% 5.25/5.57 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 )
% 5.25/5.57 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.57 @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( uminus_uminus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) ) @ ( power_power_complex @ X3 @ N2 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P4 @ N2 ) ) )
% 5.25/5.57 @ zero_zero_complex )
% 5.25/5.57 @ ( set_ord_atMost_nat @ P4 ) )
% 5.25/5.57 @ ( times_times_complex @ ( sin_complex @ X3 ) @ ( sin_complex @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_x_sin_y
% 5.25/5.57 thf(fact_8571_sums__cos__x__plus__y,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( sums_real
% 5.25/5.57 @ ^ [P4: nat] :
% 5.25/5.57 ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 ) @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ X3 @ N2 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P4 @ N2 ) ) ) @ zero_zero_real )
% 5.25/5.57 @ ( set_ord_atMost_nat @ P4 ) )
% 5.25/5.57 @ ( cos_real @ ( plus_plus_real @ X3 @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sums_cos_x_plus_y
% 5.25/5.57 thf(fact_8572_sums__cos__x__plus__y,axiom,
% 5.25/5.57 ! [X3: complex,Y: complex] :
% 5.25/5.57 ( sums_complex
% 5.25/5.57 @ ^ [P4: nat] :
% 5.25/5.57 ( groups2073611262835488442omplex
% 5.25/5.57 @ ^ [N2: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 ) @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_complex @ X3 @ N2 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P4 @ N2 ) ) ) @ zero_zero_complex )
% 5.25/5.57 @ ( set_ord_atMost_nat @ P4 ) )
% 5.25/5.57 @ ( cos_complex @ ( plus_plus_complex @ X3 @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sums_cos_x_plus_y
% 5.25/5.57 thf(fact_8573_mult__scaleR__right,axiom,
% 5.25/5.57 ! [X3: real,A: real,Y: real] :
% 5.25/5.57 ( ( times_times_real @ X3 @ ( real_V1485227260804924795R_real @ A @ Y ) )
% 5.25/5.57 = ( real_V1485227260804924795R_real @ A @ ( times_times_real @ X3 @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_scaleR_right
% 5.25/5.57 thf(fact_8574_mult__scaleR__right,axiom,
% 5.25/5.57 ! [X3: complex,A: real,Y: complex] :
% 5.25/5.57 ( ( times_times_complex @ X3 @ ( real_V2046097035970521341omplex @ A @ Y ) )
% 5.25/5.57 = ( real_V2046097035970521341omplex @ A @ ( times_times_complex @ X3 @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_scaleR_right
% 5.25/5.57 thf(fact_8575_mult__scaleR__left,axiom,
% 5.25/5.57 ! [A: real,X3: real,Y: real] :
% 5.25/5.57 ( ( times_times_real @ ( real_V1485227260804924795R_real @ A @ X3 ) @ Y )
% 5.25/5.57 = ( real_V1485227260804924795R_real @ A @ ( times_times_real @ X3 @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_scaleR_left
% 5.25/5.57 thf(fact_8576_mult__scaleR__left,axiom,
% 5.25/5.57 ! [A: real,X3: complex,Y: complex] :
% 5.25/5.57 ( ( times_times_complex @ ( real_V2046097035970521341omplex @ A @ X3 ) @ Y )
% 5.25/5.57 = ( real_V2046097035970521341omplex @ A @ ( times_times_complex @ X3 @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_scaleR_left
% 5.25/5.57 thf(fact_8577_scaleR__one,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( real_V1485227260804924795R_real @ one_one_real @ X3 )
% 5.25/5.57 = X3 ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_one
% 5.25/5.57 thf(fact_8578_scaleR__one,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( real_V2046097035970521341omplex @ one_one_real @ X3 )
% 5.25/5.57 = X3 ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_one
% 5.25/5.57 thf(fact_8579_scaleR__scaleR,axiom,
% 5.25/5.57 ! [A: real,B: real,X3: real] :
% 5.25/5.57 ( ( real_V1485227260804924795R_real @ A @ ( real_V1485227260804924795R_real @ B @ X3 ) )
% 5.25/5.57 = ( real_V1485227260804924795R_real @ ( times_times_real @ A @ B ) @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_scaleR
% 5.25/5.57 thf(fact_8580_scaleR__scaleR,axiom,
% 5.25/5.57 ! [A: real,B: real,X3: complex] :
% 5.25/5.57 ( ( real_V2046097035970521341omplex @ A @ ( real_V2046097035970521341omplex @ B @ X3 ) )
% 5.25/5.57 = ( real_V2046097035970521341omplex @ ( times_times_real @ A @ B ) @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_scaleR
% 5.25/5.57 thf(fact_8581_scaleR__eq__iff,axiom,
% 5.25/5.57 ! [B: real,U: real,A: real] :
% 5.25/5.57 ( ( ( plus_plus_real @ B @ ( real_V1485227260804924795R_real @ U @ A ) )
% 5.25/5.57 = ( plus_plus_real @ A @ ( real_V1485227260804924795R_real @ U @ B ) ) )
% 5.25/5.57 = ( ( A = B )
% 5.25/5.57 | ( U = one_one_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_eq_iff
% 5.25/5.57 thf(fact_8582_scaleR__eq__iff,axiom,
% 5.25/5.57 ! [B: complex,U: real,A: complex] :
% 5.25/5.57 ( ( ( plus_plus_complex @ B @ ( real_V2046097035970521341omplex @ U @ A ) )
% 5.25/5.57 = ( plus_plus_complex @ A @ ( real_V2046097035970521341omplex @ U @ B ) ) )
% 5.25/5.57 = ( ( A = B )
% 5.25/5.57 | ( U = one_one_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_eq_iff
% 5.25/5.57 thf(fact_8583_scaleR__power,axiom,
% 5.25/5.57 ! [X3: real,Y: real,N: nat] :
% 5.25/5.57 ( ( power_power_real @ ( real_V1485227260804924795R_real @ X3 @ Y ) @ N )
% 5.25/5.57 = ( real_V1485227260804924795R_real @ ( power_power_real @ X3 @ N ) @ ( power_power_real @ Y @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_power
% 5.25/5.57 thf(fact_8584_scaleR__power,axiom,
% 5.25/5.57 ! [X3: real,Y: complex,N: nat] :
% 5.25/5.57 ( ( power_power_complex @ ( real_V2046097035970521341omplex @ X3 @ Y ) @ N )
% 5.25/5.57 = ( real_V2046097035970521341omplex @ ( power_power_real @ X3 @ N ) @ ( power_power_complex @ Y @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_power
% 5.25/5.57 thf(fact_8585_scaleR__minus1__left,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( real_V1485227260804924795R_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.57 = ( uminus_uminus_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_minus1_left
% 5.25/5.57 thf(fact_8586_scaleR__minus1__left,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( real_V2046097035970521341omplex @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.57 = ( uminus1482373934393186551omplex @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_minus1_left
% 5.25/5.57 thf(fact_8587_scaleR__collapse,axiom,
% 5.25/5.57 ! [U: real,A: real] :
% 5.25/5.57 ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V1485227260804924795R_real @ U @ A ) )
% 5.25/5.57 = A ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_collapse
% 5.25/5.57 thf(fact_8588_scaleR__collapse,axiom,
% 5.25/5.57 ! [U: real,A: complex] :
% 5.25/5.57 ( ( plus_plus_complex @ ( real_V2046097035970521341omplex @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V2046097035970521341omplex @ U @ A ) )
% 5.25/5.57 = A ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_collapse
% 5.25/5.57 thf(fact_8589_norm__scaleR,axiom,
% 5.25/5.57 ! [A: real,X3: real] :
% 5.25/5.57 ( ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ A @ X3 ) )
% 5.25/5.57 = ( times_times_real @ ( abs_abs_real @ A ) @ ( real_V7735802525324610683m_real @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % norm_scaleR
% 5.25/5.57 thf(fact_8590_norm__scaleR,axiom,
% 5.25/5.57 ! [A: real,X3: complex] :
% 5.25/5.57 ( ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ A @ X3 ) )
% 5.25/5.57 = ( times_times_real @ ( abs_abs_real @ A ) @ ( real_V1022390504157884413omplex @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % norm_scaleR
% 5.25/5.57 thf(fact_8591_scaleR__times,axiom,
% 5.25/5.57 ! [U: num,W: num,A: real] :
% 5.25/5.57 ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ U ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.25/5.57 = ( real_V1485227260804924795R_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_times
% 5.25/5.57 thf(fact_8592_scaleR__times,axiom,
% 5.25/5.57 ! [U: num,W: num,A: complex] :
% 5.25/5.57 ( ( real_V2046097035970521341omplex @ ( numeral_numeral_real @ U ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.25/5.57 = ( real_V2046097035970521341omplex @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_times
% 5.25/5.57 thf(fact_8593_inverse__scaleR__times,axiom,
% 5.25/5.57 ! [V: num,W: num,A: real] :
% 5.25/5.57 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.25/5.57 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ W ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_scaleR_times
% 5.25/5.57 thf(fact_8594_inverse__scaleR__times,axiom,
% 5.25/5.57 ! [V: num,W: num,A: complex] :
% 5.25/5.57 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.25/5.57 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ W ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_scaleR_times
% 5.25/5.57 thf(fact_8595_fraction__scaleR__times,axiom,
% 5.25/5.57 ! [U: num,V: num,W: num,A: real] :
% 5.25/5.57 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.25/5.57 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % fraction_scaleR_times
% 5.25/5.57 thf(fact_8596_fraction__scaleR__times,axiom,
% 5.25/5.57 ! [U: num,V: num,W: num,A: complex] :
% 5.25/5.57 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.25/5.57 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % fraction_scaleR_times
% 5.25/5.57 thf(fact_8597_scaleR__half__double,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ A @ A ) )
% 5.25/5.57 = A ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_half_double
% 5.25/5.57 thf(fact_8598_scaleR__half__double,axiom,
% 5.25/5.57 ! [A: complex] :
% 5.25/5.57 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_complex @ A @ A ) )
% 5.25/5.57 = A ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_half_double
% 5.25/5.57 thf(fact_8599_fact__ge__self,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_ge_self
% 5.25/5.57 thf(fact_8600_fact__mono__nat,axiom,
% 5.25/5.57 ! [M: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.57 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_mono_nat
% 5.25/5.57 thf(fact_8601_real__scaleR__def,axiom,
% 5.25/5.57 real_V1485227260804924795R_real = times_times_real ).
% 5.25/5.57
% 5.25/5.57 % real_scaleR_def
% 5.25/5.57 thf(fact_8602_scaleR__right__distrib,axiom,
% 5.25/5.57 ! [A: real,X3: real,Y: real] :
% 5.25/5.57 ( ( real_V1485227260804924795R_real @ A @ ( plus_plus_real @ X3 @ Y ) )
% 5.25/5.57 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X3 ) @ ( real_V1485227260804924795R_real @ A @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_right_distrib
% 5.25/5.57 thf(fact_8603_scaleR__right__distrib,axiom,
% 5.25/5.57 ! [A: real,X3: complex,Y: complex] :
% 5.25/5.57 ( ( real_V2046097035970521341omplex @ A @ ( plus_plus_complex @ X3 @ Y ) )
% 5.25/5.57 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ A @ X3 ) @ ( real_V2046097035970521341omplex @ A @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_right_distrib
% 5.25/5.57 thf(fact_8604_fact__less__mono__nat,axiom,
% 5.25/5.57 ! [M: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.57 => ( ( ord_less_nat @ M @ N )
% 5.25/5.57 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_less_mono_nat
% 5.25/5.57 thf(fact_8605_sin__converges,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( sums_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( sin_coeff @ N2 ) @ ( power_power_real @ X3 @ N2 ) )
% 5.25/5.57 @ ( sin_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_converges
% 5.25/5.57 thf(fact_8606_sin__converges,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( sums_complex
% 5.25/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( sin_coeff @ N2 ) @ ( power_power_complex @ X3 @ N2 ) )
% 5.25/5.57 @ ( sin_complex @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_converges
% 5.25/5.57 thf(fact_8607_sin__def,axiom,
% 5.25/5.57 ( sin_real
% 5.25/5.57 = ( ^ [X2: real] :
% 5.25/5.57 ( suminf_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( sin_coeff @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_def
% 5.25/5.57 thf(fact_8608_sin__def,axiom,
% 5.25/5.57 ( sin_complex
% 5.25/5.57 = ( ^ [X2: complex] :
% 5.25/5.57 ( suminf_complex
% 5.25/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( sin_coeff @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_def
% 5.25/5.57 thf(fact_8609_scaleR__left_Oadd,axiom,
% 5.25/5.57 ! [X3: real,Y: real,Xa2: real] :
% 5.25/5.57 ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ X3 @ Y ) @ Xa2 )
% 5.25/5.57 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ X3 @ Xa2 ) @ ( real_V1485227260804924795R_real @ Y @ Xa2 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_left.add
% 5.25/5.57 thf(fact_8610_scaleR__left_Oadd,axiom,
% 5.25/5.57 ! [X3: real,Y: real,Xa2: complex] :
% 5.25/5.57 ( ( real_V2046097035970521341omplex @ ( plus_plus_real @ X3 @ Y ) @ Xa2 )
% 5.25/5.57 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ X3 @ Xa2 ) @ ( real_V2046097035970521341omplex @ Y @ Xa2 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_left.add
% 5.25/5.57 thf(fact_8611_scaleR__left__distrib,axiom,
% 5.25/5.57 ! [A: real,B: real,X3: real] :
% 5.25/5.57 ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ A @ B ) @ X3 )
% 5.25/5.57 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X3 ) @ ( real_V1485227260804924795R_real @ B @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_left_distrib
% 5.25/5.57 thf(fact_8612_scaleR__left__distrib,axiom,
% 5.25/5.57 ! [A: real,B: real,X3: complex] :
% 5.25/5.57 ( ( real_V2046097035970521341omplex @ ( plus_plus_real @ A @ B ) @ X3 )
% 5.25/5.57 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ A @ X3 ) @ ( real_V2046097035970521341omplex @ B @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_left_distrib
% 5.25/5.57 thf(fact_8613_summable__norm__sin,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( sin_coeff @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_norm_sin
% 5.25/5.57 thf(fact_8614_summable__norm__sin,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( sin_coeff @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_norm_sin
% 5.25/5.57 thf(fact_8615_sin__minus__converges,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( sums_real
% 5.25/5.57 @ ^ [N2: nat] : ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( sin_coeff @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ X3 ) @ N2 ) ) )
% 5.25/5.57 @ ( sin_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_minus_converges
% 5.25/5.57 thf(fact_8616_sin__minus__converges,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( sums_complex
% 5.25/5.57 @ ^ [N2: nat] : ( uminus1482373934393186551omplex @ ( real_V2046097035970521341omplex @ ( sin_coeff @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X3 ) @ N2 ) ) )
% 5.25/5.57 @ ( sin_complex @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_minus_converges
% 5.25/5.57 thf(fact_8617_fact__ge__Suc__0__nat,axiom,
% 5.25/5.57 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_ge_Suc_0_nat
% 5.25/5.57 thf(fact_8618_scaleR__right__mono__neg,axiom,
% 5.25/5.57 ! [B: real,A: real,C: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ B @ A )
% 5.25/5.57 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ C ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_right_mono_neg
% 5.25/5.57 thf(fact_8619_scaleR__right__mono,axiom,
% 5.25/5.57 ! [A: real,B: real,X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X3 ) @ ( real_V1485227260804924795R_real @ B @ X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_right_mono
% 5.25/5.57 thf(fact_8620_scaleR__le__cancel__left,axiom,
% 5.25/5.57 ! [C: real,A: real,B: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.25/5.57 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.57 => ( ord_less_eq_real @ A @ B ) )
% 5.25/5.57 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.57 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_le_cancel_left
% 5.25/5.57 thf(fact_8621_scaleR__le__cancel__left__neg,axiom,
% 5.25/5.57 ! [C: real,A: real,B: real] :
% 5.25/5.57 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.57 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.25/5.57 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_le_cancel_left_neg
% 5.25/5.57 thf(fact_8622_scaleR__le__cancel__left__pos,axiom,
% 5.25/5.57 ! [C: real,A: real,B: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.57 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.25/5.57 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_le_cancel_left_pos
% 5.25/5.57 thf(fact_8623_scaleR__left__mono__neg,axiom,
% 5.25/5.57 ! [B: real,A: real,C: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ B @ A )
% 5.25/5.57 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_left_mono_neg
% 5.25/5.57 thf(fact_8624_scaleR__left__mono,axiom,
% 5.25/5.57 ! [X3: real,Y: real,A: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X3 ) @ ( real_V1485227260804924795R_real @ A @ Y ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_left_mono
% 5.25/5.57 thf(fact_8625_dvd__fact,axiom,
% 5.25/5.57 ! [M: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.25/5.57 => ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.57 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % dvd_fact
% 5.25/5.57 thf(fact_8626_Real__Vector__Spaces_Ole__add__iff1,axiom,
% 5.25/5.57 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E ) @ D ) )
% 5.25/5.57 = ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.25/5.57
% 5.25/5.57 % Real_Vector_Spaces.le_add_iff1
% 5.25/5.57 thf(fact_8627_Real__Vector__Spaces_Ole__add__iff2,axiom,
% 5.25/5.57 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E ) @ D ) )
% 5.25/5.57 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Real_Vector_Spaces.le_add_iff2
% 5.25/5.57 thf(fact_8628_fact__diff__Suc,axiom,
% 5.25/5.57 ! [N: nat,M: nat] :
% 5.25/5.57 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.25/5.57 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 5.25/5.57 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_diff_Suc
% 5.25/5.57 thf(fact_8629_scaleR__le__0__iff,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ B ) @ zero_zero_real )
% 5.25/5.57 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.57 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.25/5.57 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.57 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.25/5.57 | ( A = zero_zero_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_le_0_iff
% 5.25/5.57 thf(fact_8630_zero__le__scaleR__iff,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) )
% 5.25/5.57 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.57 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.25/5.57 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.57 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.25/5.57 | ( A = zero_zero_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % zero_le_scaleR_iff
% 5.25/5.57 thf(fact_8631_scaleR__mono,axiom,
% 5.25/5.57 ! [A: real,B: real,X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X3 ) @ ( real_V1485227260804924795R_real @ B @ Y ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_mono
% 5.25/5.57 thf(fact_8632_scaleR__mono_H,axiom,
% 5.25/5.57 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.57 => ( ( ord_less_eq_real @ C @ D )
% 5.25/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ D ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_mono'
% 5.25/5.57 thf(fact_8633_split__scaleR__neg__le,axiom,
% 5.25/5.57 ! [A: real,X3: real] :
% 5.25/5.57 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.57 & ( ord_less_eq_real @ X3 @ zero_zero_real ) )
% 5.25/5.57 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.57 & ( ord_less_eq_real @ zero_zero_real @ X3 ) ) )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X3 ) @ zero_zero_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % split_scaleR_neg_le
% 5.25/5.57 thf(fact_8634_split__scaleR__pos__le,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.57 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.25/5.57 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.57 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.25/5.57 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % split_scaleR_pos_le
% 5.25/5.57 thf(fact_8635_scaleR__nonneg__nonneg,axiom,
% 5.25/5.57 ! [A: real,X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_nonneg_nonneg
% 5.25/5.57 thf(fact_8636_scaleR__nonneg__nonpos,axiom,
% 5.25/5.57 ! [A: real,X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.57 => ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X3 ) @ zero_zero_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_nonneg_nonpos
% 5.25/5.57 thf(fact_8637_scaleR__nonpos__nonneg,axiom,
% 5.25/5.57 ! [A: real,X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.57 => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X3 ) @ zero_zero_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_nonpos_nonneg
% 5.25/5.57 thf(fact_8638_scaleR__nonpos__nonpos,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.57 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.25/5.57 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_nonpos_nonpos
% 5.25/5.57 thf(fact_8639_scaleR__left__le__one__le,axiom,
% 5.25/5.57 ! [X3: real,A: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X3 ) @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_left_le_one_le
% 5.25/5.57 thf(fact_8640_fact__div__fact__le__pow,axiom,
% 5.25/5.57 ! [R2: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ R2 @ N )
% 5.25/5.57 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R2 ) ) ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_div_fact_le_pow
% 5.25/5.57 thf(fact_8641_scaleR__2,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 )
% 5.25/5.57 = ( plus_plus_real @ X3 @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_2
% 5.25/5.57 thf(fact_8642_scaleR__2,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( real_V2046097035970521341omplex @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 )
% 5.25/5.57 = ( plus_plus_complex @ X3 @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % scaleR_2
% 5.25/5.57 thf(fact_8643_binomial__fact__lemma,axiom,
% 5.25/5.57 ! [K: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.57 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 5.25/5.57 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % binomial_fact_lemma
% 5.25/5.57 thf(fact_8644_fact__eq__fact__times,axiom,
% 5.25/5.57 ! [N: nat,M: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.57 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.25/5.57 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 5.25/5.57 @ ( groups708209901874060359at_nat
% 5.25/5.57 @ ^ [X2: nat] : X2
% 5.25/5.57 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_eq_fact_times
% 5.25/5.57 thf(fact_8645_cos__converges,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( sums_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N2 ) @ ( power_power_real @ X3 @ N2 ) )
% 5.25/5.57 @ ( cos_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_converges
% 5.25/5.57 thf(fact_8646_cos__converges,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( sums_complex
% 5.25/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N2 ) @ ( power_power_complex @ X3 @ N2 ) )
% 5.25/5.57 @ ( cos_complex @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_converges
% 5.25/5.57 thf(fact_8647_cos__def,axiom,
% 5.25/5.57 ( cos_real
% 5.25/5.57 = ( ^ [X2: real] :
% 5.25/5.57 ( suminf_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_def
% 5.25/5.57 thf(fact_8648_cos__def,axiom,
% 5.25/5.57 ( cos_complex
% 5.25/5.57 = ( ^ [X2: complex] :
% 5.25/5.57 ( suminf_complex
% 5.25/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_def
% 5.25/5.57 thf(fact_8649_summable__norm__cos,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( cos_coeff @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_norm_cos
% 5.25/5.57 thf(fact_8650_summable__norm__cos,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( summable_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( cos_coeff @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % summable_norm_cos
% 5.25/5.57 thf(fact_8651_binomial__altdef__nat,axiom,
% 5.25/5.57 ! [K: nat,N: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ K @ N )
% 5.25/5.57 => ( ( binomial @ N @ K )
% 5.25/5.57 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % binomial_altdef_nat
% 5.25/5.57 thf(fact_8652_fact__div__fact,axiom,
% 5.25/5.57 ! [N: nat,M: nat] :
% 5.25/5.57 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.57 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.25/5.57 = ( groups708209901874060359at_nat
% 5.25/5.57 @ ^ [X2: nat] : X2
% 5.25/5.57 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % fact_div_fact
% 5.25/5.57 thf(fact_8653_cos__minus__converges,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( sums_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ X3 ) @ N2 ) )
% 5.25/5.57 @ ( cos_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_minus_converges
% 5.25/5.57 thf(fact_8654_cos__minus__converges,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( sums_complex
% 5.25/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X3 ) @ N2 ) )
% 5.25/5.57 @ ( cos_complex @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_minus_converges
% 5.25/5.57 thf(fact_8655_sin__coeff__Suc,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( sin_coeff @ ( suc @ N ) )
% 5.25/5.57 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_coeff_Suc
% 5.25/5.57 thf(fact_8656_cos__coeff__Suc,axiom,
% 5.25/5.57 ! [N: nat] :
% 5.25/5.57 ( ( cos_coeff @ ( suc @ N ) )
% 5.25/5.57 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_coeff_Suc
% 5.25/5.57 thf(fact_8657_binomial__code,axiom,
% 5.25/5.57 ( binomial
% 5.25/5.57 = ( ^ [N2: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N2 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N2 @ K3 ) @ one_one_nat ) @ N2 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % binomial_code
% 5.25/5.57 thf(fact_8658_sin__coeff__def,axiom,
% 5.25/5.57 ( sin_coeff
% 5.25/5.57 = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_coeff_def
% 5.25/5.57 thf(fact_8659_cos__x__cos__y,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( sums_real
% 5.25/5.57 @ ^ [P4: nat] :
% 5.25/5.57 ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [N2: nat] :
% 5.25/5.57 ( if_real
% 5.25/5.57 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 )
% 5.25/5.57 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.57 @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ X3 @ N2 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P4 @ N2 ) ) )
% 5.25/5.57 @ zero_zero_real )
% 5.25/5.57 @ ( set_ord_atMost_nat @ P4 ) )
% 5.25/5.57 @ ( times_times_real @ ( cos_real @ X3 ) @ ( cos_real @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_x_cos_y
% 5.25/5.57 thf(fact_8660_cos__x__cos__y,axiom,
% 5.25/5.57 ! [X3: complex,Y: complex] :
% 5.25/5.57 ( sums_complex
% 5.25/5.57 @ ^ [P4: nat] :
% 5.25/5.57 ( groups2073611262835488442omplex
% 5.25/5.57 @ ^ [N2: nat] :
% 5.25/5.57 ( if_complex
% 5.25/5.57 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 )
% 5.25/5.57 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.57 @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_complex @ X3 @ N2 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P4 @ N2 ) ) )
% 5.25/5.57 @ zero_zero_complex )
% 5.25/5.57 @ ( set_ord_atMost_nat @ P4 ) )
% 5.25/5.57 @ ( times_times_complex @ ( cos_complex @ X3 ) @ ( cos_complex @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_x_cos_y
% 5.25/5.57 thf(fact_8661_Maclaurin__sin__expansion,axiom,
% 5.25/5.57 ! [X3: real,N: nat] :
% 5.25/5.57 ? [T3: real] :
% 5.25/5.57 ( ( sin_real @ X3 )
% 5.25/5.57 = ( plus_plus_real
% 5.25/5.57 @ ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.57 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_sin_expansion
% 5.25/5.57 thf(fact_8662_sin__tan,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( sin_real @ X3 )
% 5.25/5.57 = ( divide_divide_real @ ( tan_real @ X3 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sin_tan
% 5.25/5.57 thf(fact_8663_cos__tan,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.57 => ( ( cos_real @ X3 )
% 5.25/5.57 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % cos_tan
% 5.25/5.57 thf(fact_8664_complex__unimodular__polar,axiom,
% 5.25/5.57 ! [Z: complex] :
% 5.25/5.57 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.25/5.57 = one_one_real )
% 5.25/5.57 => ~ ! [T3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.25/5.57 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.25/5.57 => ( Z
% 5.25/5.57 != ( complex2 @ ( cos_real @ T3 ) @ ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % complex_unimodular_polar
% 5.25/5.57 thf(fact_8665_Maclaurin__exp__lt,axiom,
% 5.25/5.57 ! [X3: real,N: nat] :
% 5.25/5.57 ( ( X3 != zero_zero_real )
% 5.25/5.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.57 => ? [T3: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.25/5.57 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 5.25/5.57 & ( ( exp_real @ X3 )
% 5.25/5.57 = ( plus_plus_real
% 5.25/5.57 @ ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X3 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.57 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_exp_lt
% 5.25/5.57 thf(fact_8666_Maclaurin__sin__bound,axiom,
% 5.25/5.57 ! [X3: real,N: nat] :
% 5.25/5.57 ( ord_less_eq_real
% 5.25/5.57 @ ( abs_abs_real
% 5.25/5.57 @ ( minus_minus_real @ ( sin_real @ X3 )
% 5.25/5.57 @ ( groups6591440286371151544t_real
% 5.25/5.57 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.57 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.25/5.57 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X3 ) @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Maclaurin_sin_bound
% 5.25/5.57 thf(fact_8667_inverse__eq__iff__eq,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ( inverse_inverse_real @ A )
% 5.25/5.57 = ( inverse_inverse_real @ B ) )
% 5.25/5.57 = ( A = B ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_iff_eq
% 5.25/5.57 thf(fact_8668_inverse__eq__iff__eq,axiom,
% 5.25/5.57 ! [A: complex,B: complex] :
% 5.25/5.57 ( ( ( invers8013647133539491842omplex @ A )
% 5.25/5.57 = ( invers8013647133539491842omplex @ B ) )
% 5.25/5.57 = ( A = B ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_iff_eq
% 5.25/5.57 thf(fact_8669_inverse__eq__iff__eq,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( ( inverse_inverse_rat @ A )
% 5.25/5.57 = ( inverse_inverse_rat @ B ) )
% 5.25/5.57 = ( A = B ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_iff_eq
% 5.25/5.57 thf(fact_8670_inverse__inverse__eq,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 5.25/5.57 = A ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_inverse_eq
% 5.25/5.57 thf(fact_8671_inverse__inverse__eq,axiom,
% 5.25/5.57 ! [A: complex] :
% 5.25/5.57 ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.25/5.57 = A ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_inverse_eq
% 5.25/5.57 thf(fact_8672_inverse__inverse__eq,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 5.25/5.57 = A ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_inverse_eq
% 5.25/5.57 thf(fact_8673_real__sqrt__eq__iff,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ( sqrt @ X3 )
% 5.25/5.57 = ( sqrt @ Y ) )
% 5.25/5.57 = ( X3 = Y ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_eq_iff
% 5.25/5.57 thf(fact_8674_inverse__zero,axiom,
% 5.25/5.57 ( ( inverse_inverse_real @ zero_zero_real )
% 5.25/5.57 = zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_zero
% 5.25/5.57 thf(fact_8675_inverse__zero,axiom,
% 5.25/5.57 ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 5.25/5.57 = zero_zero_complex ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_zero
% 5.25/5.57 thf(fact_8676_inverse__zero,axiom,
% 5.25/5.57 ( ( inverse_inverse_rat @ zero_zero_rat )
% 5.25/5.57 = zero_zero_rat ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_zero
% 5.25/5.57 thf(fact_8677_inverse__nonzero__iff__nonzero,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( ( inverse_inverse_real @ A )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 = ( A = zero_zero_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_nonzero_iff_nonzero
% 5.25/5.57 thf(fact_8678_inverse__nonzero__iff__nonzero,axiom,
% 5.25/5.57 ! [A: complex] :
% 5.25/5.57 ( ( ( invers8013647133539491842omplex @ A )
% 5.25/5.57 = zero_zero_complex )
% 5.25/5.57 = ( A = zero_zero_complex ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_nonzero_iff_nonzero
% 5.25/5.57 thf(fact_8679_inverse__nonzero__iff__nonzero,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( ( inverse_inverse_rat @ A )
% 5.25/5.57 = zero_zero_rat )
% 5.25/5.57 = ( A = zero_zero_rat ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_nonzero_iff_nonzero
% 5.25/5.57 thf(fact_8680_inverse__mult__distrib,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.25/5.57 = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_mult_distrib
% 5.25/5.57 thf(fact_8681_inverse__mult__distrib,axiom,
% 5.25/5.57 ! [A: complex,B: complex] :
% 5.25/5.57 ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.25/5.57 = ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_mult_distrib
% 5.25/5.57 thf(fact_8682_inverse__mult__distrib,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.57 = ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_mult_distrib
% 5.25/5.57 thf(fact_8683_inverse__1,axiom,
% 5.25/5.57 ( ( inverse_inverse_real @ one_one_real )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_1
% 5.25/5.57 thf(fact_8684_inverse__1,axiom,
% 5.25/5.57 ( ( invers8013647133539491842omplex @ one_one_complex )
% 5.25/5.57 = one_one_complex ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_1
% 5.25/5.57 thf(fact_8685_inverse__1,axiom,
% 5.25/5.57 ( ( inverse_inverse_rat @ one_one_rat )
% 5.25/5.57 = one_one_rat ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_1
% 5.25/5.57 thf(fact_8686_inverse__eq__1__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( inverse_inverse_real @ X3 )
% 5.25/5.57 = one_one_real )
% 5.25/5.57 = ( X3 = one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_1_iff
% 5.25/5.57 thf(fact_8687_inverse__eq__1__iff,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( ( ( invers8013647133539491842omplex @ X3 )
% 5.25/5.57 = one_one_complex )
% 5.25/5.57 = ( X3 = one_one_complex ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_1_iff
% 5.25/5.57 thf(fact_8688_inverse__eq__1__iff,axiom,
% 5.25/5.57 ! [X3: rat] :
% 5.25/5.57 ( ( ( inverse_inverse_rat @ X3 )
% 5.25/5.57 = one_one_rat )
% 5.25/5.57 = ( X3 = one_one_rat ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_1_iff
% 5.25/5.57 thf(fact_8689_inverse__divide,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 5.25/5.57 = ( divide_divide_real @ B @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_divide
% 5.25/5.57 thf(fact_8690_inverse__divide,axiom,
% 5.25/5.57 ! [A: complex,B: complex] :
% 5.25/5.57 ( ( invers8013647133539491842omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ B @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_divide
% 5.25/5.57 thf(fact_8691_inverse__divide,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( inverse_inverse_rat @ ( divide_divide_rat @ A @ B ) )
% 5.25/5.57 = ( divide_divide_rat @ B @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_divide
% 5.25/5.57 thf(fact_8692_inverse__minus__eq,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 5.25/5.57 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_minus_eq
% 5.25/5.57 thf(fact_8693_inverse__minus__eq,axiom,
% 5.25/5.57 ! [A: complex] :
% 5.25/5.57 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.25/5.57 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_minus_eq
% 5.25/5.57 thf(fact_8694_inverse__minus__eq,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 5.25/5.57 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_minus_eq
% 5.25/5.57 thf(fact_8695_abs__inverse,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 5.25/5.57 = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % abs_inverse
% 5.25/5.57 thf(fact_8696_abs__inverse,axiom,
% 5.25/5.57 ! [A: complex] :
% 5.25/5.57 ( ( abs_abs_complex @ ( invers8013647133539491842omplex @ A ) )
% 5.25/5.57 = ( invers8013647133539491842omplex @ ( abs_abs_complex @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % abs_inverse
% 5.25/5.57 thf(fact_8697_abs__inverse,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 5.25/5.57 = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % abs_inverse
% 5.25/5.57 thf(fact_8698_real__sqrt__eq__zero__cancel__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( sqrt @ X3 )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 = ( X3 = zero_zero_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_eq_zero_cancel_iff
% 5.25/5.57 thf(fact_8699_real__sqrt__zero,axiom,
% 5.25/5.57 ( ( sqrt @ zero_zero_real )
% 5.25/5.57 = zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_zero
% 5.25/5.57 thf(fact_8700_real__sqrt__less__iff,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_real @ ( sqrt @ X3 ) @ ( sqrt @ Y ) )
% 5.25/5.57 = ( ord_less_real @ X3 @ Y ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_less_iff
% 5.25/5.57 thf(fact_8701_real__sqrt__le__iff,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( sqrt @ X3 ) @ ( sqrt @ Y ) )
% 5.25/5.57 = ( ord_less_eq_real @ X3 @ Y ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_le_iff
% 5.25/5.57 thf(fact_8702_real__sqrt__eq__1__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( sqrt @ X3 )
% 5.25/5.57 = one_one_real )
% 5.25/5.57 = ( X3 = one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_eq_1_iff
% 5.25/5.57 thf(fact_8703_real__sqrt__one,axiom,
% 5.25/5.57 ( ( sqrt @ one_one_real )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_one
% 5.25/5.57 thf(fact_8704_exp__le__cancel__iff,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( exp_real @ X3 ) @ ( exp_real @ Y ) )
% 5.25/5.57 = ( ord_less_eq_real @ X3 @ Y ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_le_cancel_iff
% 5.25/5.57 thf(fact_8705_inverse__nonnegative__iff__nonnegative,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.25/5.57 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_nonnegative_iff_nonnegative
% 5.25/5.57 thf(fact_8706_inverse__nonnegative__iff__nonnegative,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( ord_less_eq_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.25/5.57 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_nonnegative_iff_nonnegative
% 5.25/5.57 thf(fact_8707_inverse__nonpositive__iff__nonpositive,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.25/5.57 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_nonpositive_iff_nonpositive
% 5.25/5.57 thf(fact_8708_inverse__nonpositive__iff__nonpositive,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.25/5.57 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_nonpositive_iff_nonpositive
% 5.25/5.57 thf(fact_8709_inverse__less__iff__less,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.57 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.57 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.25/5.57 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_less_iff_less
% 5.25/5.57 thf(fact_8710_inverse__less__iff__less,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.57 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.25/5.57 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.25/5.57 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_less_iff_less
% 5.25/5.57 thf(fact_8711_inverse__less__iff__less__neg,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.57 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.25/5.57 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.25/5.57 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_less_iff_less_neg
% 5.25/5.57 thf(fact_8712_inverse__less__iff__less__neg,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.57 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.25/5.57 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.25/5.57 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_less_iff_less_neg
% 5.25/5.57 thf(fact_8713_inverse__negative__iff__negative,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.25/5.57 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_negative_iff_negative
% 5.25/5.57 thf(fact_8714_inverse__negative__iff__negative,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.25/5.57 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_negative_iff_negative
% 5.25/5.57 thf(fact_8715_inverse__positive__iff__positive,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.25/5.57 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_positive_iff_positive
% 5.25/5.57 thf(fact_8716_inverse__positive__iff__positive,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.25/5.57 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_positive_iff_positive
% 5.25/5.57 thf(fact_8717_exp__zero,axiom,
% 5.25/5.57 ( ( exp_complex @ zero_zero_complex )
% 5.25/5.57 = one_one_complex ) ).
% 5.25/5.57
% 5.25/5.57 % exp_zero
% 5.25/5.57 thf(fact_8718_exp__zero,axiom,
% 5.25/5.57 ( ( exp_real @ zero_zero_real )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % exp_zero
% 5.25/5.57 thf(fact_8719_real__sqrt__lt__0__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( sqrt @ X3 ) @ zero_zero_real )
% 5.25/5.57 = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_lt_0_iff
% 5.25/5.57 thf(fact_8720_real__sqrt__gt__0__iff,axiom,
% 5.25/5.57 ! [Y: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 5.25/5.57 = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_gt_0_iff
% 5.25/5.57 thf(fact_8721_real__sqrt__le__0__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( sqrt @ X3 ) @ zero_zero_real )
% 5.25/5.57 = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_le_0_iff
% 5.25/5.57 thf(fact_8722_real__sqrt__ge__0__iff,axiom,
% 5.25/5.57 ! [Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 5.25/5.57 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_ge_0_iff
% 5.25/5.57 thf(fact_8723_real__sqrt__lt__1__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( sqrt @ X3 ) @ one_one_real )
% 5.25/5.57 = ( ord_less_real @ X3 @ one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_lt_1_iff
% 5.25/5.57 thf(fact_8724_real__sqrt__gt__1__iff,axiom,
% 5.25/5.57 ! [Y: real] :
% 5.25/5.57 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 5.25/5.57 = ( ord_less_real @ one_one_real @ Y ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_gt_1_iff
% 5.25/5.57 thf(fact_8725_real__sqrt__le__1__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( sqrt @ X3 ) @ one_one_real )
% 5.25/5.57 = ( ord_less_eq_real @ X3 @ one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_le_1_iff
% 5.25/5.57 thf(fact_8726_real__sqrt__ge__1__iff,axiom,
% 5.25/5.57 ! [Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 5.25/5.57 = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_ge_1_iff
% 5.25/5.57 thf(fact_8727_exp__eq__one__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( exp_real @ X3 )
% 5.25/5.57 = one_one_real )
% 5.25/5.57 = ( X3 = zero_zero_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_eq_one_iff
% 5.25/5.57 thf(fact_8728_real__sqrt__abs2,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( sqrt @ ( times_times_real @ X3 @ X3 ) )
% 5.25/5.57 = ( abs_abs_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_abs2
% 5.25/5.57 thf(fact_8729_real__sqrt__mult__self,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.25/5.57 = ( abs_abs_real @ A ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_mult_self
% 5.25/5.57 thf(fact_8730_inverse__le__iff__le__neg,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.57 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.25/5.57 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.25/5.57 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_le_iff_le_neg
% 5.25/5.57 thf(fact_8731_inverse__le__iff__le__neg,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.57 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.25/5.57 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.25/5.57 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_le_iff_le_neg
% 5.25/5.57 thf(fact_8732_inverse__le__iff__le,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.57 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.57 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.25/5.57 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_le_iff_le
% 5.25/5.57 thf(fact_8733_inverse__le__iff__le,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.57 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.25/5.57 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.25/5.57 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_le_iff_le
% 5.25/5.57 thf(fact_8734_right__inverse,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( A != zero_zero_real )
% 5.25/5.57 => ( ( times_times_real @ A @ ( inverse_inverse_real @ A ) )
% 5.25/5.57 = one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % right_inverse
% 5.25/5.57 thf(fact_8735_right__inverse,axiom,
% 5.25/5.57 ! [A: complex] :
% 5.25/5.57 ( ( A != zero_zero_complex )
% 5.25/5.57 => ( ( times_times_complex @ A @ ( invers8013647133539491842omplex @ A ) )
% 5.25/5.57 = one_one_complex ) ) ).
% 5.25/5.57
% 5.25/5.57 % right_inverse
% 5.25/5.57 thf(fact_8736_right__inverse,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( A != zero_zero_rat )
% 5.25/5.57 => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 5.25/5.57 = one_one_rat ) ) ).
% 5.25/5.57
% 5.25/5.57 % right_inverse
% 5.25/5.57 thf(fact_8737_left__inverse,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( A != zero_zero_real )
% 5.25/5.57 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.25/5.57 = one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % left_inverse
% 5.25/5.57 thf(fact_8738_left__inverse,axiom,
% 5.25/5.57 ! [A: complex] :
% 5.25/5.57 ( ( A != zero_zero_complex )
% 5.25/5.57 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.25/5.57 = one_one_complex ) ) ).
% 5.25/5.57
% 5.25/5.57 % left_inverse
% 5.25/5.57 thf(fact_8739_left__inverse,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( A != zero_zero_rat )
% 5.25/5.57 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.25/5.57 = one_one_rat ) ) ).
% 5.25/5.57
% 5.25/5.57 % left_inverse
% 5.25/5.57 thf(fact_8740_inverse__eq__divide__numeral,axiom,
% 5.25/5.57 ! [W: num] :
% 5.25/5.57 ( ( inverse_inverse_real @ ( numeral_numeral_real @ W ) )
% 5.25/5.57 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_divide_numeral
% 5.25/5.57 thf(fact_8741_inverse__eq__divide__numeral,axiom,
% 5.25/5.57 ! [W: num] :
% 5.25/5.57 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_divide_numeral
% 5.25/5.57 thf(fact_8742_inverse__eq__divide__numeral,axiom,
% 5.25/5.57 ! [W: num] :
% 5.25/5.57 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W ) )
% 5.25/5.57 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_divide_numeral
% 5.25/5.57 thf(fact_8743_real__sqrt__four,axiom,
% 5.25/5.57 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.25/5.57 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_four
% 5.25/5.57 thf(fact_8744_exp__less__one__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ ( exp_real @ X3 ) @ one_one_real )
% 5.25/5.57 = ( ord_less_real @ X3 @ zero_zero_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_less_one_iff
% 5.25/5.57 thf(fact_8745_one__less__exp__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ one_one_real @ ( exp_real @ X3 ) )
% 5.25/5.57 = ( ord_less_real @ zero_zero_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % one_less_exp_iff
% 5.25/5.57 thf(fact_8746_one__le__exp__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X3 ) )
% 5.25/5.57 = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % one_le_exp_iff
% 5.25/5.57 thf(fact_8747_exp__le__one__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ ( exp_real @ X3 ) @ one_one_real )
% 5.25/5.57 = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_le_one_iff
% 5.25/5.57 thf(fact_8748_inverse__eq__divide__neg__numeral,axiom,
% 5.25/5.57 ! [W: num] :
% 5.25/5.57 ( ( inverse_inverse_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.57 = ( divide_divide_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_divide_neg_numeral
% 5.25/5.57 thf(fact_8749_inverse__eq__divide__neg__numeral,axiom,
% 5.25/5.57 ! [W: num] :
% 5.25/5.57 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_divide_neg_numeral
% 5.25/5.57 thf(fact_8750_inverse__eq__divide__neg__numeral,axiom,
% 5.25/5.57 ! [W: num] :
% 5.25/5.57 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.25/5.57 = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_divide_neg_numeral
% 5.25/5.57 thf(fact_8751_norm__cos__sin,axiom,
% 5.25/5.57 ! [T: real] :
% 5.25/5.57 ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 5.25/5.57 = one_one_real ) ).
% 5.25/5.57
% 5.25/5.57 % norm_cos_sin
% 5.25/5.57 thf(fact_8752_real__sqrt__abs,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( sqrt @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.57 = ( abs_abs_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_abs
% 5.25/5.57 thf(fact_8753_real__sqrt__pow2__iff,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ( power_power_real @ ( sqrt @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.57 = X3 )
% 5.25/5.57 = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_pow2_iff
% 5.25/5.57 thf(fact_8754_real__sqrt__pow2,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( power_power_real @ ( sqrt @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.57 = X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_pow2
% 5.25/5.57 thf(fact_8755_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.25/5.57 ! [X3: real,Y: real,Xa2: real,Ya: real] :
% 5.25/5.57 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( 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 ) ) )
% 5.25/5.57 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( 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 ) ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_sum_squares_mult_squared_eq
% 5.25/5.57 thf(fact_8756_complex__scaleR,axiom,
% 5.25/5.57 ! [R2: real,A: real,B: real] :
% 5.25/5.57 ( ( real_V2046097035970521341omplex @ R2 @ ( complex2 @ A @ B ) )
% 5.25/5.57 = ( complex2 @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ B ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % complex_scaleR
% 5.25/5.57 thf(fact_8757_real__sqrt__power,axiom,
% 5.25/5.57 ! [X3: real,K: nat] :
% 5.25/5.57 ( ( sqrt @ ( power_power_real @ X3 @ K ) )
% 5.25/5.57 = ( power_power_real @ ( sqrt @ X3 ) @ K ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_power
% 5.25/5.57 thf(fact_8758_power__inverse,axiom,
% 5.25/5.57 ! [A: real,N: nat] :
% 5.25/5.57 ( ( power_power_real @ ( inverse_inverse_real @ A ) @ N )
% 5.25/5.57 = ( inverse_inverse_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % power_inverse
% 5.25/5.57 thf(fact_8759_power__inverse,axiom,
% 5.25/5.57 ! [A: complex,N: nat] :
% 5.25/5.57 ( ( power_power_complex @ ( invers8013647133539491842omplex @ A ) @ N )
% 5.25/5.57 = ( invers8013647133539491842omplex @ ( power_power_complex @ A @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % power_inverse
% 5.25/5.57 thf(fact_8760_power__inverse,axiom,
% 5.25/5.57 ! [A: rat,N: nat] :
% 5.25/5.57 ( ( power_power_rat @ ( inverse_inverse_rat @ A ) @ N )
% 5.25/5.57 = ( inverse_inverse_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % power_inverse
% 5.25/5.57 thf(fact_8761_field__class_Ofield__inverse__zero,axiom,
% 5.25/5.57 ( ( inverse_inverse_real @ zero_zero_real )
% 5.25/5.57 = zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % field_class.field_inverse_zero
% 5.25/5.57 thf(fact_8762_field__class_Ofield__inverse__zero,axiom,
% 5.25/5.57 ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 5.25/5.57 = zero_zero_complex ) ).
% 5.25/5.57
% 5.25/5.57 % field_class.field_inverse_zero
% 5.25/5.57 thf(fact_8763_field__class_Ofield__inverse__zero,axiom,
% 5.25/5.57 ( ( inverse_inverse_rat @ zero_zero_rat )
% 5.25/5.57 = zero_zero_rat ) ).
% 5.25/5.57
% 5.25/5.57 % field_class.field_inverse_zero
% 5.25/5.57 thf(fact_8764_inverse__zero__imp__zero,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( ( inverse_inverse_real @ A )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 => ( A = zero_zero_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_zero_imp_zero
% 5.25/5.57 thf(fact_8765_inverse__zero__imp__zero,axiom,
% 5.25/5.57 ! [A: complex] :
% 5.25/5.57 ( ( ( invers8013647133539491842omplex @ A )
% 5.25/5.57 = zero_zero_complex )
% 5.25/5.57 => ( A = zero_zero_complex ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_zero_imp_zero
% 5.25/5.57 thf(fact_8766_inverse__zero__imp__zero,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( ( inverse_inverse_rat @ A )
% 5.25/5.57 = zero_zero_rat )
% 5.25/5.57 => ( A = zero_zero_rat ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_zero_imp_zero
% 5.25/5.57 thf(fact_8767_nonzero__inverse__eq__imp__eq,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ( inverse_inverse_real @ A )
% 5.25/5.57 = ( inverse_inverse_real @ B ) )
% 5.25/5.57 => ( ( A != zero_zero_real )
% 5.25/5.57 => ( ( B != zero_zero_real )
% 5.25/5.57 => ( A = B ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_inverse_eq_imp_eq
% 5.25/5.57 thf(fact_8768_nonzero__inverse__eq__imp__eq,axiom,
% 5.25/5.57 ! [A: complex,B: complex] :
% 5.25/5.57 ( ( ( invers8013647133539491842omplex @ A )
% 5.25/5.57 = ( invers8013647133539491842omplex @ B ) )
% 5.25/5.57 => ( ( A != zero_zero_complex )
% 5.25/5.57 => ( ( B != zero_zero_complex )
% 5.25/5.57 => ( A = B ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_inverse_eq_imp_eq
% 5.25/5.57 thf(fact_8769_nonzero__inverse__eq__imp__eq,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( ( inverse_inverse_rat @ A )
% 5.25/5.57 = ( inverse_inverse_rat @ B ) )
% 5.25/5.57 => ( ( A != zero_zero_rat )
% 5.25/5.57 => ( ( B != zero_zero_rat )
% 5.25/5.57 => ( A = B ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_inverse_eq_imp_eq
% 5.25/5.57 thf(fact_8770_nonzero__inverse__inverse__eq,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( A != zero_zero_real )
% 5.25/5.57 => ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 5.25/5.57 = A ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_inverse_inverse_eq
% 5.25/5.57 thf(fact_8771_nonzero__inverse__inverse__eq,axiom,
% 5.25/5.57 ! [A: complex] :
% 5.25/5.57 ( ( A != zero_zero_complex )
% 5.25/5.57 => ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.25/5.57 = A ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_inverse_inverse_eq
% 5.25/5.57 thf(fact_8772_nonzero__inverse__inverse__eq,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( A != zero_zero_rat )
% 5.25/5.57 => ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 5.25/5.57 = A ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_inverse_inverse_eq
% 5.25/5.57 thf(fact_8773_nonzero__imp__inverse__nonzero,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( A != zero_zero_real )
% 5.25/5.57 => ( ( inverse_inverse_real @ A )
% 5.25/5.57 != zero_zero_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_imp_inverse_nonzero
% 5.25/5.57 thf(fact_8774_nonzero__imp__inverse__nonzero,axiom,
% 5.25/5.57 ! [A: complex] :
% 5.25/5.57 ( ( A != zero_zero_complex )
% 5.25/5.57 => ( ( invers8013647133539491842omplex @ A )
% 5.25/5.57 != zero_zero_complex ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_imp_inverse_nonzero
% 5.25/5.57 thf(fact_8775_nonzero__imp__inverse__nonzero,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( A != zero_zero_rat )
% 5.25/5.57 => ( ( inverse_inverse_rat @ A )
% 5.25/5.57 != zero_zero_rat ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_imp_inverse_nonzero
% 5.25/5.57 thf(fact_8776_norm__exp,axiom,
% 5.25/5.57 ! [X3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X3 ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % norm_exp
% 5.25/5.57 thf(fact_8777_norm__exp,axiom,
% 5.25/5.57 ! [X3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X3 ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % norm_exp
% 5.25/5.57 thf(fact_8778_mult__commute__imp__mult__inverse__commute,axiom,
% 5.25/5.57 ! [Y: real,X3: real] :
% 5.25/5.57 ( ( ( times_times_real @ Y @ X3 )
% 5.25/5.57 = ( times_times_real @ X3 @ Y ) )
% 5.25/5.57 => ( ( times_times_real @ ( inverse_inverse_real @ Y ) @ X3 )
% 5.25/5.57 = ( times_times_real @ X3 @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_commute_imp_mult_inverse_commute
% 5.25/5.57 thf(fact_8779_mult__commute__imp__mult__inverse__commute,axiom,
% 5.25/5.57 ! [Y: complex,X3: complex] :
% 5.25/5.57 ( ( ( times_times_complex @ Y @ X3 )
% 5.25/5.57 = ( times_times_complex @ X3 @ Y ) )
% 5.25/5.57 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ Y ) @ X3 )
% 5.25/5.57 = ( times_times_complex @ X3 @ ( invers8013647133539491842omplex @ Y ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_commute_imp_mult_inverse_commute
% 5.25/5.57 thf(fact_8780_mult__commute__imp__mult__inverse__commute,axiom,
% 5.25/5.57 ! [Y: rat,X3: rat] :
% 5.25/5.57 ( ( ( times_times_rat @ Y @ X3 )
% 5.25/5.57 = ( times_times_rat @ X3 @ Y ) )
% 5.25/5.57 => ( ( times_times_rat @ ( inverse_inverse_rat @ Y ) @ X3 )
% 5.25/5.57 = ( times_times_rat @ X3 @ ( inverse_inverse_rat @ Y ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_commute_imp_mult_inverse_commute
% 5.25/5.57 thf(fact_8781_real__sqrt__less__mono,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.57 => ( ord_less_real @ ( sqrt @ X3 ) @ ( sqrt @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_less_mono
% 5.25/5.57 thf(fact_8782_inverse__eq__imp__eq,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ( inverse_inverse_real @ A )
% 5.25/5.57 = ( inverse_inverse_real @ B ) )
% 5.25/5.57 => ( A = B ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_imp_eq
% 5.25/5.57 thf(fact_8783_inverse__eq__imp__eq,axiom,
% 5.25/5.57 ! [A: complex,B: complex] :
% 5.25/5.57 ( ( ( invers8013647133539491842omplex @ A )
% 5.25/5.57 = ( invers8013647133539491842omplex @ B ) )
% 5.25/5.57 => ( A = B ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_imp_eq
% 5.25/5.57 thf(fact_8784_inverse__eq__imp__eq,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( ( inverse_inverse_rat @ A )
% 5.25/5.57 = ( inverse_inverse_rat @ B ) )
% 5.25/5.57 => ( A = B ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_imp_eq
% 5.25/5.57 thf(fact_8785_real__sqrt__inverse,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( sqrt @ ( inverse_inverse_real @ X3 ) )
% 5.25/5.57 = ( inverse_inverse_real @ ( sqrt @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_inverse
% 5.25/5.57 thf(fact_8786_real__sqrt__mult,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( sqrt @ ( times_times_real @ X3 @ Y ) )
% 5.25/5.57 = ( times_times_real @ ( sqrt @ X3 ) @ ( sqrt @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_mult
% 5.25/5.57 thf(fact_8787_real__sqrt__divide,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( sqrt @ ( divide_divide_real @ X3 @ Y ) )
% 5.25/5.57 = ( divide_divide_real @ ( sqrt @ X3 ) @ ( sqrt @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_divide
% 5.25/5.57 thf(fact_8788_real__sqrt__le__mono,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.57 => ( ord_less_eq_real @ ( sqrt @ X3 ) @ ( sqrt @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_le_mono
% 5.25/5.57 thf(fact_8789_exp__times__arg__commute,axiom,
% 5.25/5.57 ! [A2: complex] :
% 5.25/5.57 ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 5.25/5.57 = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_times_arg_commute
% 5.25/5.57 thf(fact_8790_exp__times__arg__commute,axiom,
% 5.25/5.57 ! [A2: real] :
% 5.25/5.57 ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 5.25/5.57 = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_times_arg_commute
% 5.25/5.57 thf(fact_8791_real__sqrt__minus,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( sqrt @ ( uminus_uminus_real @ X3 ) )
% 5.25/5.57 = ( uminus_uminus_real @ ( sqrt @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_minus
% 5.25/5.57 thf(fact_8792_sqrt__divide__self__eq,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( divide_divide_real @ ( sqrt @ X3 ) @ X3 )
% 5.25/5.57 = ( inverse_inverse_real @ ( sqrt @ X3 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % sqrt_divide_self_eq
% 5.25/5.57 thf(fact_8793_norm__inverse__le__norm,axiom,
% 5.25/5.57 ! [R2: real,X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ R2 @ ( real_V7735802525324610683m_real @ X3 ) )
% 5.25/5.57 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ X3 ) ) @ ( inverse_inverse_real @ R2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % norm_inverse_le_norm
% 5.25/5.57 thf(fact_8794_norm__inverse__le__norm,axiom,
% 5.25/5.57 ! [R2: real,X3: complex] :
% 5.25/5.57 ( ( ord_less_eq_real @ R2 @ ( real_V1022390504157884413omplex @ X3 ) )
% 5.25/5.57 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.25/5.57 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ X3 ) ) @ ( inverse_inverse_real @ R2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % norm_inverse_le_norm
% 5.25/5.57 thf(fact_8795_inverse__less__imp__less,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.25/5.57 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.57 => ( ord_less_real @ B @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_less_imp_less
% 5.25/5.57 thf(fact_8796_inverse__less__imp__less,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.25/5.57 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.57 => ( ord_less_rat @ B @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_less_imp_less
% 5.25/5.57 thf(fact_8797_less__imp__inverse__less,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ord_less_real @ A @ B )
% 5.25/5.57 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.57 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % less_imp_inverse_less
% 5.25/5.57 thf(fact_8798_less__imp__inverse__less,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( ord_less_rat @ A @ B )
% 5.25/5.57 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.57 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % less_imp_inverse_less
% 5.25/5.57 thf(fact_8799_inverse__less__imp__less__neg,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.25/5.57 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.25/5.57 => ( ord_less_real @ B @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_less_imp_less_neg
% 5.25/5.57 thf(fact_8800_inverse__less__imp__less__neg,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.25/5.57 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.25/5.57 => ( ord_less_rat @ B @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_less_imp_less_neg
% 5.25/5.57 thf(fact_8801_less__imp__inverse__less__neg,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ord_less_real @ A @ B )
% 5.25/5.57 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.25/5.57 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % less_imp_inverse_less_neg
% 5.25/5.57 thf(fact_8802_less__imp__inverse__less__neg,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( ord_less_rat @ A @ B )
% 5.25/5.57 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.25/5.57 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % less_imp_inverse_less_neg
% 5.25/5.57 thf(fact_8803_inverse__negative__imp__negative,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.25/5.57 => ( ( A != zero_zero_real )
% 5.25/5.57 => ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_negative_imp_negative
% 5.25/5.57 thf(fact_8804_inverse__negative__imp__negative,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.25/5.57 => ( ( A != zero_zero_rat )
% 5.25/5.57 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_negative_imp_negative
% 5.25/5.57 thf(fact_8805_inverse__positive__imp__positive,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.25/5.57 => ( ( A != zero_zero_real )
% 5.25/5.57 => ( ord_less_real @ zero_zero_real @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_positive_imp_positive
% 5.25/5.57 thf(fact_8806_inverse__positive__imp__positive,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.25/5.57 => ( ( A != zero_zero_rat )
% 5.25/5.57 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_positive_imp_positive
% 5.25/5.57 thf(fact_8807_negative__imp__inverse__negative,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.57 => ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % negative_imp_inverse_negative
% 5.25/5.57 thf(fact_8808_negative__imp__inverse__negative,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.57 => ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat ) ) ).
% 5.25/5.57
% 5.25/5.57 % negative_imp_inverse_negative
% 5.25/5.57 thf(fact_8809_positive__imp__inverse__positive,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.57 => ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % positive_imp_inverse_positive
% 5.25/5.57 thf(fact_8810_positive__imp__inverse__positive,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.57 => ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % positive_imp_inverse_positive
% 5.25/5.57 thf(fact_8811_nonzero__inverse__mult__distrib,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( A != zero_zero_real )
% 5.25/5.57 => ( ( B != zero_zero_real )
% 5.25/5.57 => ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.25/5.57 = ( times_times_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_inverse_mult_distrib
% 5.25/5.57 thf(fact_8812_nonzero__inverse__mult__distrib,axiom,
% 5.25/5.57 ! [A: complex,B: complex] :
% 5.25/5.57 ( ( A != zero_zero_complex )
% 5.25/5.57 => ( ( B != zero_zero_complex )
% 5.25/5.57 => ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.25/5.57 = ( times_times_complex @ ( invers8013647133539491842omplex @ B ) @ ( invers8013647133539491842omplex @ A ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_inverse_mult_distrib
% 5.25/5.57 thf(fact_8813_nonzero__inverse__mult__distrib,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( A != zero_zero_rat )
% 5.25/5.57 => ( ( B != zero_zero_rat )
% 5.25/5.57 => ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.57 = ( times_times_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_inverse_mult_distrib
% 5.25/5.57 thf(fact_8814_nonzero__inverse__minus__eq,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( A != zero_zero_real )
% 5.25/5.57 => ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 5.25/5.57 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_inverse_minus_eq
% 5.25/5.57 thf(fact_8815_nonzero__inverse__minus__eq,axiom,
% 5.25/5.57 ! [A: complex] :
% 5.25/5.57 ( ( A != zero_zero_complex )
% 5.25/5.57 => ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.25/5.57 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_inverse_minus_eq
% 5.25/5.57 thf(fact_8816_nonzero__inverse__minus__eq,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( A != zero_zero_rat )
% 5.25/5.57 => ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 5.25/5.57 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_inverse_minus_eq
% 5.25/5.57 thf(fact_8817_inverse__numeral__1,axiom,
% 5.25/5.57 ( ( inverse_inverse_real @ ( numeral_numeral_real @ one ) )
% 5.25/5.57 = ( numeral_numeral_real @ one ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_numeral_1
% 5.25/5.57 thf(fact_8818_inverse__numeral__1,axiom,
% 5.25/5.57 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.25/5.57 = ( numera6690914467698888265omplex @ one ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_numeral_1
% 5.25/5.57 thf(fact_8819_inverse__numeral__1,axiom,
% 5.25/5.57 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ one ) )
% 5.25/5.57 = ( numeral_numeral_rat @ one ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_numeral_1
% 5.25/5.57 thf(fact_8820_inverse__unique,axiom,
% 5.25/5.57 ! [A: real,B: real] :
% 5.25/5.57 ( ( ( times_times_real @ A @ B )
% 5.25/5.57 = one_one_real )
% 5.25/5.57 => ( ( inverse_inverse_real @ A )
% 5.25/5.57 = B ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_unique
% 5.25/5.57 thf(fact_8821_inverse__unique,axiom,
% 5.25/5.57 ! [A: complex,B: complex] :
% 5.25/5.57 ( ( ( times_times_complex @ A @ B )
% 5.25/5.57 = one_one_complex )
% 5.25/5.57 => ( ( invers8013647133539491842omplex @ A )
% 5.25/5.57 = B ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_unique
% 5.25/5.57 thf(fact_8822_inverse__unique,axiom,
% 5.25/5.57 ! [A: rat,B: rat] :
% 5.25/5.57 ( ( ( times_times_rat @ A @ B )
% 5.25/5.57 = one_one_rat )
% 5.25/5.57 => ( ( inverse_inverse_rat @ A )
% 5.25/5.57 = B ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_unique
% 5.25/5.57 thf(fact_8823_field__class_Ofield__divide__inverse,axiom,
% 5.25/5.57 ( divide_divide_real
% 5.25/5.57 = ( ^ [A3: real,B2: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % field_class.field_divide_inverse
% 5.25/5.57 thf(fact_8824_field__class_Ofield__divide__inverse,axiom,
% 5.25/5.57 ( divide1717551699836669952omplex
% 5.25/5.57 = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ A3 @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % field_class.field_divide_inverse
% 5.25/5.57 thf(fact_8825_field__class_Ofield__divide__inverse,axiom,
% 5.25/5.57 ( divide_divide_rat
% 5.25/5.57 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ A3 @ ( inverse_inverse_rat @ B2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % field_class.field_divide_inverse
% 5.25/5.57 thf(fact_8826_divide__inverse,axiom,
% 5.25/5.57 ( divide_divide_real
% 5.25/5.57 = ( ^ [A3: real,B2: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % divide_inverse
% 5.25/5.57 thf(fact_8827_divide__inverse,axiom,
% 5.25/5.57 ( divide1717551699836669952omplex
% 5.25/5.57 = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ A3 @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % divide_inverse
% 5.25/5.57 thf(fact_8828_divide__inverse,axiom,
% 5.25/5.57 ( divide_divide_rat
% 5.25/5.57 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ A3 @ ( inverse_inverse_rat @ B2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % divide_inverse
% 5.25/5.57 thf(fact_8829_divide__inverse__commute,axiom,
% 5.25/5.57 ( divide_divide_real
% 5.25/5.57 = ( ^ [A3: real,B2: real] : ( times_times_real @ ( inverse_inverse_real @ B2 ) @ A3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % divide_inverse_commute
% 5.25/5.57 thf(fact_8830_divide__inverse__commute,axiom,
% 5.25/5.57 ( divide1717551699836669952omplex
% 5.25/5.57 = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ ( invers8013647133539491842omplex @ B2 ) @ A3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % divide_inverse_commute
% 5.25/5.57 thf(fact_8831_divide__inverse__commute,axiom,
% 5.25/5.57 ( divide_divide_rat
% 5.25/5.57 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ ( inverse_inverse_rat @ B2 ) @ A3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % divide_inverse_commute
% 5.25/5.57 thf(fact_8832_real__sqrt__gt__zero,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_gt_zero
% 5.25/5.57 thf(fact_8833_inverse__eq__divide,axiom,
% 5.25/5.57 ( inverse_inverse_real
% 5.25/5.57 = ( divide_divide_real @ one_one_real ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_divide
% 5.25/5.57 thf(fact_8834_inverse__eq__divide,axiom,
% 5.25/5.57 ( invers8013647133539491842omplex
% 5.25/5.57 = ( divide1717551699836669952omplex @ one_one_complex ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_divide
% 5.25/5.57 thf(fact_8835_inverse__eq__divide,axiom,
% 5.25/5.57 ( inverse_inverse_rat
% 5.25/5.57 = ( divide_divide_rat @ one_one_rat ) ) ).
% 5.25/5.57
% 5.25/5.57 % inverse_eq_divide
% 5.25/5.57 thf(fact_8836_power__mult__inverse__distrib,axiom,
% 5.25/5.57 ! [X3: real,M: nat] :
% 5.25/5.57 ( ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( inverse_inverse_real @ X3 ) )
% 5.25/5.57 = ( times_times_real @ ( inverse_inverse_real @ X3 ) @ ( power_power_real @ X3 @ M ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % power_mult_inverse_distrib
% 5.25/5.57 thf(fact_8837_power__mult__inverse__distrib,axiom,
% 5.25/5.57 ! [X3: complex,M: nat] :
% 5.25/5.57 ( ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( invers8013647133539491842omplex @ X3 ) )
% 5.25/5.57 = ( times_times_complex @ ( invers8013647133539491842omplex @ X3 ) @ ( power_power_complex @ X3 @ M ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % power_mult_inverse_distrib
% 5.25/5.57 thf(fact_8838_power__mult__inverse__distrib,axiom,
% 5.25/5.57 ! [X3: rat,M: nat] :
% 5.25/5.57 ( ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( inverse_inverse_rat @ X3 ) )
% 5.25/5.57 = ( times_times_rat @ ( inverse_inverse_rat @ X3 ) @ ( power_power_rat @ X3 @ M ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % power_mult_inverse_distrib
% 5.25/5.57 thf(fact_8839_power__mult__power__inverse__commute,axiom,
% 5.25/5.57 ! [X3: real,M: nat,N: nat] :
% 5.25/5.57 ( ( times_times_real @ ( power_power_real @ X3 @ M ) @ ( power_power_real @ ( inverse_inverse_real @ X3 ) @ N ) )
% 5.25/5.57 = ( times_times_real @ ( power_power_real @ ( inverse_inverse_real @ X3 ) @ N ) @ ( power_power_real @ X3 @ M ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % power_mult_power_inverse_commute
% 5.25/5.57 thf(fact_8840_power__mult__power__inverse__commute,axiom,
% 5.25/5.57 ! [X3: complex,M: nat,N: nat] :
% 5.25/5.57 ( ( times_times_complex @ ( power_power_complex @ X3 @ M ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X3 ) @ N ) )
% 5.25/5.57 = ( times_times_complex @ ( power_power_complex @ ( invers8013647133539491842omplex @ X3 ) @ N ) @ ( power_power_complex @ X3 @ M ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % power_mult_power_inverse_commute
% 5.25/5.57 thf(fact_8841_power__mult__power__inverse__commute,axiom,
% 5.25/5.57 ! [X3: rat,M: nat,N: nat] :
% 5.25/5.57 ( ( times_times_rat @ ( power_power_rat @ X3 @ M ) @ ( power_power_rat @ ( inverse_inverse_rat @ X3 ) @ N ) )
% 5.25/5.57 = ( times_times_rat @ ( power_power_rat @ ( inverse_inverse_rat @ X3 ) @ N ) @ ( power_power_rat @ X3 @ M ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % power_mult_power_inverse_commute
% 5.25/5.57 thf(fact_8842_real__sqrt__eq__zero__cancel,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ( ( sqrt @ X3 )
% 5.25/5.57 = zero_zero_real )
% 5.25/5.57 => ( X3 = zero_zero_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_eq_zero_cancel
% 5.25/5.57 thf(fact_8843_real__sqrt__ge__zero,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.57 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_ge_zero
% 5.25/5.57 thf(fact_8844_not__exp__le__zero,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ~ ( ord_less_eq_real @ ( exp_real @ X3 ) @ zero_zero_real ) ).
% 5.25/5.57
% 5.25/5.57 % not_exp_le_zero
% 5.25/5.57 thf(fact_8845_exp__ge__zero,axiom,
% 5.25/5.57 ! [X3: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_ge_zero
% 5.25/5.57 thf(fact_8846_mult__inverse__of__nat__commute,axiom,
% 5.25/5.57 ! [Xa2: nat,X3: real] :
% 5.25/5.57 ( ( times_times_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa2 ) ) @ X3 )
% 5.25/5.57 = ( times_times_real @ X3 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_inverse_of_nat_commute
% 5.25/5.57 thf(fact_8847_mult__inverse__of__nat__commute,axiom,
% 5.25/5.57 ! [Xa2: nat,X3: complex] :
% 5.25/5.57 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa2 ) ) @ X3 )
% 5.25/5.57 = ( times_times_complex @ X3 @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_inverse_of_nat_commute
% 5.25/5.57 thf(fact_8848_mult__inverse__of__nat__commute,axiom,
% 5.25/5.57 ! [Xa2: nat,X3: rat] :
% 5.25/5.57 ( ( times_times_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ Xa2 ) ) @ X3 )
% 5.25/5.57 = ( times_times_rat @ X3 @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ Xa2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_inverse_of_nat_commute
% 5.25/5.57 thf(fact_8849_nonzero__abs__inverse,axiom,
% 5.25/5.57 ! [A: real] :
% 5.25/5.57 ( ( A != zero_zero_real )
% 5.25/5.57 => ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 5.25/5.57 = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_abs_inverse
% 5.25/5.57 thf(fact_8850_nonzero__abs__inverse,axiom,
% 5.25/5.57 ! [A: rat] :
% 5.25/5.57 ( ( A != zero_zero_rat )
% 5.25/5.57 => ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 5.25/5.57 = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % nonzero_abs_inverse
% 5.25/5.57 thf(fact_8851_real__sqrt__ge__one,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( ( ord_less_eq_real @ one_one_real @ X3 )
% 5.25/5.57 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X3 ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % real_sqrt_ge_one
% 5.25/5.57 thf(fact_8852_mult__inverse__of__int__commute,axiom,
% 5.25/5.57 ! [Xa2: int,X3: real] :
% 5.25/5.57 ( ( times_times_real @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa2 ) ) @ X3 )
% 5.25/5.57 = ( times_times_real @ X3 @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_inverse_of_int_commute
% 5.25/5.57 thf(fact_8853_mult__inverse__of__int__commute,axiom,
% 5.25/5.57 ! [Xa2: int,X3: complex] :
% 5.25/5.57 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa2 ) ) @ X3 )
% 5.25/5.57 = ( times_times_complex @ X3 @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_inverse_of_int_commute
% 5.25/5.57 thf(fact_8854_mult__inverse__of__int__commute,axiom,
% 5.25/5.57 ! [Xa2: int,X3: rat] :
% 5.25/5.57 ( ( times_times_rat @ ( inverse_inverse_rat @ ( ring_1_of_int_rat @ Xa2 ) ) @ X3 )
% 5.25/5.57 = ( times_times_rat @ X3 @ ( inverse_inverse_rat @ ( ring_1_of_int_rat @ Xa2 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_inverse_of_int_commute
% 5.25/5.57 thf(fact_8855_mult__exp__exp,axiom,
% 5.25/5.57 ! [X3: complex,Y: complex] :
% 5.25/5.57 ( ( times_times_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ Y ) )
% 5.25/5.57 = ( exp_complex @ ( plus_plus_complex @ X3 @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_exp_exp
% 5.25/5.57 thf(fact_8856_mult__exp__exp,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( times_times_real @ ( exp_real @ X3 ) @ ( exp_real @ Y ) )
% 5.25/5.57 = ( exp_real @ ( plus_plus_real @ X3 @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % mult_exp_exp
% 5.25/5.57 thf(fact_8857_exp__add__commuting,axiom,
% 5.25/5.57 ! [X3: complex,Y: complex] :
% 5.25/5.57 ( ( ( times_times_complex @ X3 @ Y )
% 5.25/5.57 = ( times_times_complex @ Y @ X3 ) )
% 5.25/5.57 => ( ( exp_complex @ ( plus_plus_complex @ X3 @ Y ) )
% 5.25/5.57 = ( times_times_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ Y ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_add_commuting
% 5.25/5.57 thf(fact_8858_exp__add__commuting,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( ( times_times_real @ X3 @ Y )
% 5.25/5.57 = ( times_times_real @ Y @ X3 ) )
% 5.25/5.57 => ( ( exp_real @ ( plus_plus_real @ X3 @ Y ) )
% 5.25/5.57 = ( times_times_real @ ( exp_real @ X3 ) @ ( exp_real @ Y ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_add_commuting
% 5.25/5.57 thf(fact_8859_exp__diff,axiom,
% 5.25/5.57 ! [X3: complex,Y: complex] :
% 5.25/5.57 ( ( exp_complex @ ( minus_minus_complex @ X3 @ Y ) )
% 5.25/5.57 = ( divide1717551699836669952omplex @ ( exp_complex @ X3 ) @ ( exp_complex @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_diff
% 5.25/5.57 thf(fact_8860_exp__diff,axiom,
% 5.25/5.57 ! [X3: real,Y: real] :
% 5.25/5.57 ( ( exp_real @ ( minus_minus_real @ X3 @ Y ) )
% 5.25/5.57 = ( divide_divide_real @ ( exp_real @ X3 ) @ ( exp_real @ Y ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_diff
% 5.25/5.57 thf(fact_8861_Complex__eq__numeral,axiom,
% 5.25/5.57 ! [A: real,B: real,W: num] :
% 5.25/5.57 ( ( ( complex2 @ A @ B )
% 5.25/5.57 = ( numera6690914467698888265omplex @ W ) )
% 5.25/5.57 = ( ( A
% 5.25/5.57 = ( numeral_numeral_real @ W ) )
% 5.25/5.57 & ( B = zero_zero_real ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % Complex_eq_numeral
% 5.25/5.57 thf(fact_8862_divide__real__def,axiom,
% 5.25/5.57 ( divide_divide_real
% 5.25/5.57 = ( ^ [X2: real,Y6: real] : ( times_times_real @ X2 @ ( inverse_inverse_real @ Y6 ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % divide_real_def
% 5.25/5.57 thf(fact_8863_exp__converges,axiom,
% 5.25/5.57 ! [X3: real] :
% 5.25/5.57 ( sums_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X3 @ N2 ) )
% 5.25/5.57 @ ( exp_real @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_converges
% 5.25/5.57 thf(fact_8864_exp__converges,axiom,
% 5.25/5.57 ! [X3: complex] :
% 5.25/5.57 ( sums_complex
% 5.25/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_complex @ X3 @ N2 ) )
% 5.25/5.57 @ ( exp_complex @ X3 ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_converges
% 5.25/5.57 thf(fact_8865_exp__def,axiom,
% 5.25/5.57 ( exp_real
% 5.25/5.57 = ( ^ [X2: real] :
% 5.25/5.57 ( suminf_real
% 5.25/5.57 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_def
% 5.25/5.57 thf(fact_8866_exp__def,axiom,
% 5.25/5.57 ( exp_complex
% 5.25/5.57 = ( ^ [X2: complex] :
% 5.25/5.57 ( suminf_complex
% 5.25/5.57 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ) ).
% 5.25/5.57
% 5.25/5.57 % exp_def
% 5.25/5.57 thf(fact_8867_exp__plus__inverse__exp,axiom,
% 5.25/5.57 ! [X3: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X3 ) @ ( inverse_inverse_real @ ( exp_real @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_plus_inverse_exp
% 5.25/5.58 thf(fact_8868_complex__add,axiom,
% 5.25/5.58 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.58 ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.25/5.58 = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_add
% 5.25/5.58 thf(fact_8869_real__inv__sqrt__pow2,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.58 = ( inverse_inverse_real @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_inv_sqrt_pow2
% 5.25/5.58 thf(fact_8870_le__imp__inverse__le__neg,axiom,
% 5.25/5.58 ! [A: real,B: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.58 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.25/5.58 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % le_imp_inverse_le_neg
% 5.25/5.58 thf(fact_8871_le__imp__inverse__le__neg,axiom,
% 5.25/5.58 ! [A: rat,B: rat] :
% 5.25/5.58 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.58 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.25/5.58 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % le_imp_inverse_le_neg
% 5.25/5.58 thf(fact_8872_inverse__le__imp__le__neg,axiom,
% 5.25/5.58 ! [A: real,B: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.25/5.58 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.25/5.58 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % inverse_le_imp_le_neg
% 5.25/5.58 thf(fact_8873_inverse__le__imp__le__neg,axiom,
% 5.25/5.58 ! [A: rat,B: rat] :
% 5.25/5.58 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.25/5.58 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.25/5.58 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % inverse_le_imp_le_neg
% 5.25/5.58 thf(fact_8874_le__imp__inverse__le,axiom,
% 5.25/5.58 ! [A: real,B: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % le_imp_inverse_le
% 5.25/5.58 thf(fact_8875_le__imp__inverse__le,axiom,
% 5.25/5.58 ! [A: rat,B: rat] :
% 5.25/5.58 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.58 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.58 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % le_imp_inverse_le
% 5.25/5.58 thf(fact_8876_inverse__le__imp__le,axiom,
% 5.25/5.58 ! [A: real,B: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % inverse_le_imp_le
% 5.25/5.58 thf(fact_8877_inverse__le__imp__le,axiom,
% 5.25/5.58 ! [A: rat,B: rat] :
% 5.25/5.58 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.25/5.58 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.58 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % inverse_le_imp_le
% 5.25/5.58 thf(fact_8878_inverse__le__1__iff,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( inverse_inverse_real @ X3 ) @ one_one_real )
% 5.25/5.58 = ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.58 | ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % inverse_le_1_iff
% 5.25/5.58 thf(fact_8879_inverse__le__1__iff,axiom,
% 5.25/5.58 ! [X3: rat] :
% 5.25/5.58 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ X3 ) @ one_one_rat )
% 5.25/5.58 = ( ( ord_less_eq_rat @ X3 @ zero_zero_rat )
% 5.25/5.58 | ( ord_less_eq_rat @ one_one_rat @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % inverse_le_1_iff
% 5.25/5.58 thf(fact_8880_one__less__inverse__iff,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ X3 ) )
% 5.25/5.58 = ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 & ( ord_less_real @ X3 @ one_one_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % one_less_inverse_iff
% 5.25/5.58 thf(fact_8881_one__less__inverse__iff,axiom,
% 5.25/5.58 ! [X3: rat] :
% 5.25/5.58 ( ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ X3 ) )
% 5.25/5.58 = ( ( ord_less_rat @ zero_zero_rat @ X3 )
% 5.25/5.58 & ( ord_less_rat @ X3 @ one_one_rat ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % one_less_inverse_iff
% 5.25/5.58 thf(fact_8882_one__less__inverse,axiom,
% 5.25/5.58 ! [A: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( ord_less_real @ A @ one_one_real )
% 5.25/5.58 => ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % one_less_inverse
% 5.25/5.58 thf(fact_8883_one__less__inverse,axiom,
% 5.25/5.58 ! [A: rat] :
% 5.25/5.58 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.58 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.25/5.58 => ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % one_less_inverse
% 5.25/5.58 thf(fact_8884_field__class_Ofield__inverse,axiom,
% 5.25/5.58 ! [A: real] :
% 5.25/5.58 ( ( A != zero_zero_real )
% 5.25/5.58 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.25/5.58 = one_one_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % field_class.field_inverse
% 5.25/5.58 thf(fact_8885_field__class_Ofield__inverse,axiom,
% 5.25/5.58 ! [A: complex] :
% 5.25/5.58 ( ( A != zero_zero_complex )
% 5.25/5.58 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.25/5.58 = one_one_complex ) ) ).
% 5.25/5.58
% 5.25/5.58 % field_class.field_inverse
% 5.25/5.58 thf(fact_8886_field__class_Ofield__inverse,axiom,
% 5.25/5.58 ! [A: rat] :
% 5.25/5.58 ( ( A != zero_zero_rat )
% 5.25/5.58 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.25/5.58 = one_one_rat ) ) ).
% 5.25/5.58
% 5.25/5.58 % field_class.field_inverse
% 5.25/5.58 thf(fact_8887_inverse__add,axiom,
% 5.25/5.58 ! [A: real,B: real] :
% 5.25/5.58 ( ( A != zero_zero_real )
% 5.25/5.58 => ( ( B != zero_zero_real )
% 5.25/5.58 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.25/5.58 = ( times_times_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( inverse_inverse_real @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % inverse_add
% 5.25/5.58 thf(fact_8888_inverse__add,axiom,
% 5.25/5.58 ! [A: complex,B: complex] :
% 5.25/5.58 ( ( A != zero_zero_complex )
% 5.25/5.58 => ( ( B != zero_zero_complex )
% 5.25/5.58 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.25/5.58 = ( times_times_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( invers8013647133539491842omplex @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % inverse_add
% 5.25/5.58 thf(fact_8889_inverse__add,axiom,
% 5.25/5.58 ! [A: rat,B: rat] :
% 5.25/5.58 ( ( A != zero_zero_rat )
% 5.25/5.58 => ( ( B != zero_zero_rat )
% 5.25/5.58 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.25/5.58 = ( times_times_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( inverse_inverse_rat @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % inverse_add
% 5.25/5.58 thf(fact_8890_division__ring__inverse__add,axiom,
% 5.25/5.58 ! [A: real,B: real] :
% 5.25/5.58 ( ( A != zero_zero_real )
% 5.25/5.58 => ( ( B != zero_zero_real )
% 5.25/5.58 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.25/5.58 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( plus_plus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % division_ring_inverse_add
% 5.25/5.58 thf(fact_8891_division__ring__inverse__add,axiom,
% 5.25/5.58 ! [A: complex,B: complex] :
% 5.25/5.58 ( ( A != zero_zero_complex )
% 5.25/5.58 => ( ( B != zero_zero_complex )
% 5.25/5.58 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.25/5.58 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( plus_plus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % division_ring_inverse_add
% 5.25/5.58 thf(fact_8892_division__ring__inverse__add,axiom,
% 5.25/5.58 ! [A: rat,B: rat] :
% 5.25/5.58 ( ( A != zero_zero_rat )
% 5.25/5.58 => ( ( B != zero_zero_rat )
% 5.25/5.58 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.25/5.58 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( plus_plus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % division_ring_inverse_add
% 5.25/5.58 thf(fact_8893_division__ring__inverse__diff,axiom,
% 5.25/5.58 ! [A: real,B: real] :
% 5.25/5.58 ( ( A != zero_zero_real )
% 5.25/5.58 => ( ( B != zero_zero_real )
% 5.25/5.58 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.25/5.58 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ B @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % division_ring_inverse_diff
% 5.25/5.58 thf(fact_8894_division__ring__inverse__diff,axiom,
% 5.25/5.58 ! [A: complex,B: complex] :
% 5.25/5.58 ( ( A != zero_zero_complex )
% 5.25/5.58 => ( ( B != zero_zero_complex )
% 5.25/5.58 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.25/5.58 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ B @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % division_ring_inverse_diff
% 5.25/5.58 thf(fact_8895_division__ring__inverse__diff,axiom,
% 5.25/5.58 ! [A: rat,B: rat] :
% 5.25/5.58 ( ( A != zero_zero_rat )
% 5.25/5.58 => ( ( B != zero_zero_rat )
% 5.25/5.58 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.25/5.58 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ B @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % division_ring_inverse_diff
% 5.25/5.58 thf(fact_8896_nonzero__inverse__eq__divide,axiom,
% 5.25/5.58 ! [A: real] :
% 5.25/5.58 ( ( A != zero_zero_real )
% 5.25/5.58 => ( ( inverse_inverse_real @ A )
% 5.25/5.58 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nonzero_inverse_eq_divide
% 5.25/5.58 thf(fact_8897_nonzero__inverse__eq__divide,axiom,
% 5.25/5.58 ! [A: complex] :
% 5.25/5.58 ( ( A != zero_zero_complex )
% 5.25/5.58 => ( ( invers8013647133539491842omplex @ A )
% 5.25/5.58 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nonzero_inverse_eq_divide
% 5.25/5.58 thf(fact_8898_nonzero__inverse__eq__divide,axiom,
% 5.25/5.58 ! [A: rat] :
% 5.25/5.58 ( ( A != zero_zero_rat )
% 5.25/5.58 => ( ( inverse_inverse_rat @ A )
% 5.25/5.58 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nonzero_inverse_eq_divide
% 5.25/5.58 thf(fact_8899_complex__norm,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( real_V1022390504157884413omplex @ ( complex2 @ X3 @ Y ) )
% 5.25/5.58 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_norm
% 5.25/5.58 thf(fact_8900_exp__gt__one,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ord_less_real @ one_one_real @ ( exp_real @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_gt_one
% 5.25/5.58 thf(fact_8901_real__div__sqrt,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( divide_divide_real @ X3 @ ( sqrt @ X3 ) )
% 5.25/5.58 = ( sqrt @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_div_sqrt
% 5.25/5.58 thf(fact_8902_sqrt__add__le__add__sqrt,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X3 @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X3 ) @ ( sqrt @ Y ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sqrt_add_le_add_sqrt
% 5.25/5.58 thf(fact_8903_exp__ge__add__one__self,axiom,
% 5.25/5.58 ! [X3: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( exp_real @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_ge_add_one_self
% 5.25/5.58 thf(fact_8904_le__real__sqrt__sumsq,axiom,
% 5.25/5.58 ! [X3: real,Y: real] : ( ord_less_eq_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X3 @ X3 ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % le_real_sqrt_sumsq
% 5.25/5.58 thf(fact_8905_exp__minus__inverse,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( times_times_real @ ( exp_real @ X3 ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) )
% 5.25/5.58 = one_one_real ) ).
% 5.25/5.58
% 5.25/5.58 % exp_minus_inverse
% 5.25/5.58 thf(fact_8906_exp__minus__inverse,axiom,
% 5.25/5.58 ! [X3: complex] :
% 5.25/5.58 ( ( times_times_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X3 ) ) )
% 5.25/5.58 = one_one_complex ) ).
% 5.25/5.58
% 5.25/5.58 % exp_minus_inverse
% 5.25/5.58 thf(fact_8907_exp__of__nat2__mult,axiom,
% 5.25/5.58 ! [X3: complex,N: nat] :
% 5.25/5.58 ( ( exp_complex @ ( times_times_complex @ X3 @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.25/5.58 = ( power_power_complex @ ( exp_complex @ X3 ) @ N ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_of_nat2_mult
% 5.25/5.58 thf(fact_8908_exp__of__nat2__mult,axiom,
% 5.25/5.58 ! [X3: real,N: nat] :
% 5.25/5.58 ( ( exp_real @ ( times_times_real @ X3 @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.25/5.58 = ( power_power_real @ ( exp_real @ X3 ) @ N ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_of_nat2_mult
% 5.25/5.58 thf(fact_8909_exp__of__nat__mult,axiom,
% 5.25/5.58 ! [N: nat,X3: complex] :
% 5.25/5.58 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X3 ) )
% 5.25/5.58 = ( power_power_complex @ ( exp_complex @ X3 ) @ N ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_of_nat_mult
% 5.25/5.58 thf(fact_8910_exp__of__nat__mult,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X3 ) )
% 5.25/5.58 = ( power_power_real @ ( exp_real @ X3 ) @ N ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_of_nat_mult
% 5.25/5.58 thf(fact_8911_Complex__eq__neg__numeral,axiom,
% 5.25/5.58 ! [A: real,B: real,W: num] :
% 5.25/5.58 ( ( ( complex2 @ A @ B )
% 5.25/5.58 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.25/5.58 = ( ( A
% 5.25/5.58 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.58 & ( B = zero_zero_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Complex_eq_neg_numeral
% 5.25/5.58 thf(fact_8912_complex__mult,axiom,
% 5.25/5.58 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.58 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.25/5.58 = ( 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 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_mult
% 5.25/5.58 thf(fact_8913_one__complex_Ocode,axiom,
% 5.25/5.58 ( one_one_complex
% 5.25/5.58 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % one_complex.code
% 5.25/5.58 thf(fact_8914_Complex__eq__1,axiom,
% 5.25/5.58 ! [A: real,B: real] :
% 5.25/5.58 ( ( ( complex2 @ A @ B )
% 5.25/5.58 = one_one_complex )
% 5.25/5.58 = ( ( A = one_one_real )
% 5.25/5.58 & ( B = zero_zero_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Complex_eq_1
% 5.25/5.58 thf(fact_8915_real__le__x__sinh,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ord_less_eq_real @ X3 @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X3 ) @ ( inverse_inverse_real @ ( exp_real @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_le_x_sinh
% 5.25/5.58 thf(fact_8916_real__le__abs__sinh,axiom,
% 5.25/5.58 ! [X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X3 ) @ ( inverse_inverse_real @ ( exp_real @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_le_abs_sinh
% 5.25/5.58 thf(fact_8917_exp__first__term,axiom,
% 5.25/5.58 ( exp_real
% 5.25/5.58 = ( ^ [X2: real] :
% 5.25/5.58 ( plus_plus_real @ one_one_real
% 5.25/5.58 @ ( suminf_real
% 5.25/5.58 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X2 @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_first_term
% 5.25/5.58 thf(fact_8918_exp__first__term,axiom,
% 5.25/5.58 ( exp_complex
% 5.25/5.58 = ( ^ [X2: complex] :
% 5.25/5.58 ( plus_plus_complex @ one_one_complex
% 5.25/5.58 @ ( suminf_complex
% 5.25/5.58 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( suc @ N2 ) ) ) @ ( power_power_complex @ X2 @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_first_term
% 5.25/5.58 thf(fact_8919_inverse__less__iff,axiom,
% 5.25/5.58 ! [A: rat,B: rat] :
% 5.25/5.58 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.25/5.58 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.58 => ( ord_less_rat @ B @ A ) )
% 5.25/5.58 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.25/5.58 => ( ord_less_rat @ A @ B ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % inverse_less_iff
% 5.25/5.58 thf(fact_8920_sqrt2__less__2,axiom,
% 5.25/5.58 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.25/5.58
% 5.25/5.58 % sqrt2_less_2
% 5.25/5.58 thf(fact_8921_exp__ge__add__one__self__aux,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( exp_real @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_ge_add_one_self_aux
% 5.25/5.58 thf(fact_8922_lemma__exp__total,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ one_one_real @ Y )
% 5.25/5.58 => ? [X5: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.25/5.58 & ( ord_less_eq_real @ X5 @ ( minus_minus_real @ Y @ one_one_real ) )
% 5.25/5.58 & ( ( exp_real @ X5 )
% 5.25/5.58 = Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % lemma_exp_total
% 5.25/5.58 thf(fact_8923_ln__ge__iff,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X3 ) )
% 5.25/5.58 = ( ord_less_eq_real @ ( exp_real @ Y ) @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ln_ge_iff
% 5.25/5.58 thf(fact_8924_ln__x__over__x__mono,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.58 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X3 ) @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ln_x_over_x_mono
% 5.25/5.58 thf(fact_8925_forall__pos__mono__1,axiom,
% 5.25/5.58 ! [P: real > $o,E: real] :
% 5.25/5.58 ( ! [D3: real,E2: real] :
% 5.25/5.58 ( ( ord_less_real @ D3 @ E2 )
% 5.25/5.58 => ( ( P @ D3 )
% 5.25/5.58 => ( P @ E2 ) ) )
% 5.25/5.58 => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.25/5.58 => ( P @ E ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % forall_pos_mono_1
% 5.25/5.58 thf(fact_8926_real__arch__inverse,axiom,
% 5.25/5.58 ! [E: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ E )
% 5.25/5.58 = ( ? [N2: nat] :
% 5.25/5.58 ( ( N2 != zero_zero_nat )
% 5.25/5.58 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.25/5.58 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ E ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_arch_inverse
% 5.25/5.58 thf(fact_8927_forall__pos__mono,axiom,
% 5.25/5.58 ! [P: real > $o,E: real] :
% 5.25/5.58 ( ! [D3: real,E2: real] :
% 5.25/5.58 ( ( ord_less_real @ D3 @ E2 )
% 5.25/5.58 => ( ( P @ D3 )
% 5.25/5.58 => ( P @ E2 ) ) )
% 5.25/5.58 => ( ! [N3: nat] :
% 5.25/5.58 ( ( N3 != zero_zero_nat )
% 5.25/5.58 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.25/5.58 => ( P @ E ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % forall_pos_mono
% 5.25/5.58 thf(fact_8928_Complex__eq__neg__1,axiom,
% 5.25/5.58 ! [A: real,B: real] :
% 5.25/5.58 ( ( ( complex2 @ A @ B )
% 5.25/5.58 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.25/5.58 = ( ( A
% 5.25/5.58 = ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.58 & ( B = zero_zero_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Complex_eq_neg_1
% 5.25/5.58 thf(fact_8929_real__less__rsqrt,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.25/5.58 => ( ord_less_real @ X3 @ ( sqrt @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_less_rsqrt
% 5.25/5.58 thf(fact_8930_real__le__rsqrt,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.25/5.58 => ( ord_less_eq_real @ X3 @ ( sqrt @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_le_rsqrt
% 5.25/5.58 thf(fact_8931_sqrt__le__D,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( sqrt @ X3 ) @ Y )
% 5.25/5.58 => ( ord_less_eq_real @ X3 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sqrt_le_D
% 5.25/5.58 thf(fact_8932_exp__le,axiom,
% 5.25/5.58 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_le
% 5.25/5.58 thf(fact_8933_real__sqrt__unique,axiom,
% 5.25/5.58 ! [Y: real,X3: real] :
% 5.25/5.58 ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.58 = X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ( sqrt @ X3 )
% 5.25/5.58 = Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_sqrt_unique
% 5.25/5.58 thf(fact_8934_real__le__lsqrt,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.58 => ( ord_less_eq_real @ ( sqrt @ X3 ) @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_le_lsqrt
% 5.25/5.58 thf(fact_8935_lemma__real__divide__sqrt__less,axiom,
% 5.25/5.58 ! [U: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ U )
% 5.25/5.58 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.25/5.58
% 5.25/5.58 % lemma_real_divide_sqrt_less
% 5.25/5.58 thf(fact_8936_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.58 = Y )
% 5.25/5.58 => ( X3 = zero_zero_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_sqrt_sum_squares_eq_cancel2
% 5.25/5.58 thf(fact_8937_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.58 = X3 )
% 5.25/5.58 => ( Y = zero_zero_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_sqrt_sum_squares_eq_cancel
% 5.25/5.58 thf(fact_8938_exp__half__le2,axiom,
% 5.25/5.58 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_half_le2
% 5.25/5.58 thf(fact_8939_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.25/5.58 ! [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 ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_sqrt_sum_squares_triangle_ineq
% 5.25/5.58 thf(fact_8940_real__sqrt__sum__squares__ge2,axiom,
% 5.25/5.58 ! [Y: real,X3: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_sqrt_sum_squares_ge2
% 5.25/5.58 thf(fact_8941_real__sqrt__sum__squares__ge1,axiom,
% 5.25/5.58 ! [X3: real,Y: real] : ( ord_less_eq_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_sqrt_sum_squares_ge1
% 5.25/5.58 thf(fact_8942_sqrt__ge__absD,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( sqrt @ Y ) )
% 5.25/5.58 => ( ord_less_eq_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 5.25/5.58
% 5.25/5.58 % sqrt_ge_absD
% 5.25/5.58 thf(fact_8943_cos__45,axiom,
% 5.25/5.58 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.25/5.58 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cos_45
% 5.25/5.58 thf(fact_8944_sin__45,axiom,
% 5.25/5.58 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.25/5.58 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sin_45
% 5.25/5.58 thf(fact_8945_tan__60,axiom,
% 5.25/5.58 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.25/5.58 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % tan_60
% 5.25/5.58 thf(fact_8946_real__less__lsqrt,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.58 => ( ord_less_real @ ( sqrt @ X3 ) @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_less_lsqrt
% 5.25/5.58 thf(fact_8947_sqrt__sum__squares__le__sum,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sqrt_sum_squares_le_sum
% 5.25/5.58 thf(fact_8948_sqrt__even__pow2,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.58 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.58 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sqrt_even_pow2
% 5.25/5.58 thf(fact_8949_real__sqrt__ge__abs1,axiom,
% 5.25/5.58 ! [X3: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_sqrt_ge_abs1
% 5.25/5.58 thf(fact_8950_real__sqrt__ge__abs2,axiom,
% 5.25/5.58 ! [Y: real,X3: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_sqrt_ge_abs2
% 5.25/5.58 thf(fact_8951_sqrt__sum__squares__le__sum__abs,axiom,
% 5.25/5.58 ! [X3: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X3 ) @ ( abs_abs_real @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sqrt_sum_squares_le_sum_abs
% 5.25/5.58 thf(fact_8952_ln__sqrt,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ln_ln_real @ ( sqrt @ X3 ) )
% 5.25/5.58 = ( divide_divide_real @ ( ln_ln_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ln_sqrt
% 5.25/5.58 thf(fact_8953_cos__30,axiom,
% 5.25/5.58 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.25/5.58 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cos_30
% 5.25/5.58 thf(fact_8954_sin__60,axiom,
% 5.25/5.58 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.25/5.58 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sin_60
% 5.25/5.58 thf(fact_8955_plus__inverse__ge__2,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % plus_inverse_ge_2
% 5.25/5.58 thf(fact_8956_tan__cot,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) )
% 5.25/5.58 = ( inverse_inverse_real @ ( tan_real @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % tan_cot
% 5.25/5.58 thf(fact_8957_arsinh__real__aux,axiom,
% 5.25/5.58 ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arsinh_real_aux
% 5.25/5.58 thf(fact_8958_exp__bound,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 5.25/5.58 => ( ord_less_eq_real @ ( exp_real @ X3 ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_bound
% 5.25/5.58 thf(fact_8959_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.25/5.58 ! [X3: real,Y: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( 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 ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_sqrt_sum_squares_mult_ge_zero
% 5.25/5.58 thf(fact_8960_real__sqrt__power__even,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( power_power_real @ ( sqrt @ X3 ) @ N )
% 5.25/5.58 = ( power_power_real @ X3 @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_sqrt_power_even
% 5.25/5.58 thf(fact_8961_arith__geo__mean__sqrt,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X3 @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X3 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arith_geo_mean_sqrt
% 5.25/5.58 thf(fact_8962_tan__30,axiom,
% 5.25/5.58 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.25/5.58 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % tan_30
% 5.25/5.58 thf(fact_8963_real__exp__bound__lemma,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.58 => ( ord_less_eq_real @ ( exp_real @ X3 ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_exp_bound_lemma
% 5.25/5.58 thf(fact_8964_cos__x__y__le__one,axiom,
% 5.25/5.58 ! [X3: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.25/5.58
% 5.25/5.58 % cos_x_y_le_one
% 5.25/5.58 thf(fact_8965_real__sqrt__sum__squares__less,axiom,
% 5.25/5.58 ! [X3: real,U: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.25/5.58 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.25/5.58 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_sqrt_sum_squares_less
% 5.25/5.58 thf(fact_8966_arcosh__real__def,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ one_one_real @ X3 )
% 5.25/5.58 => ( ( arcosh_real @ X3 )
% 5.25/5.58 = ( ln_ln_real @ ( plus_plus_real @ X3 @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcosh_real_def
% 5.25/5.58 thf(fact_8967_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X3 )
% 5.25/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X3 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_ge_one_plus_x_over_n_power_n
% 5.25/5.58 thf(fact_8968_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.25/5.58 ! [X3: real,N: nat] :
% 5.25/5.58 ( ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ N ) )
% 5.25/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X3 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_ge_one_minus_x_over_n_power_n
% 5.25/5.58 thf(fact_8969_cos__arctan,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( cos_real @ ( arctan @ X3 ) )
% 5.25/5.58 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cos_arctan
% 5.25/5.58 thf(fact_8970_sin__arctan,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( sin_real @ ( arctan @ X3 ) )
% 5.25/5.58 = ( divide_divide_real @ X3 @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sin_arctan
% 5.25/5.58 thf(fact_8971_Maclaurin__exp__le,axiom,
% 5.25/5.58 ! [X3: real,N: nat] :
% 5.25/5.58 ? [T3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 5.25/5.58 & ( ( exp_real @ X3 )
% 5.25/5.58 = ( plus_plus_real
% 5.25/5.58 @ ( groups6591440286371151544t_real
% 5.25/5.58 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X3 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.25/5.58 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.58 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Maclaurin_exp_le
% 5.25/5.58 thf(fact_8972_sqrt__sum__squares__half__less,axiom,
% 5.25/5.58 ! [X3: real,U: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ X3 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.58 => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sqrt_sum_squares_half_less
% 5.25/5.58 thf(fact_8973_exp__lower__Taylor__quadratic,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( divide_divide_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_lower_Taylor_quadratic
% 5.25/5.58 thf(fact_8974_sin__cos__sqrt,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X3 ) )
% 5.25/5.58 => ( ( sin_real @ X3 )
% 5.25/5.58 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sin_cos_sqrt
% 5.25/5.58 thf(fact_8975_arctan__half,axiom,
% 5.25/5.58 ( arctan
% 5.25/5.58 = ( ^ [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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arctan_half
% 5.25/5.58 thf(fact_8976_tanh__real__altdef,axiom,
% 5.25/5.58 ( tanh_real
% 5.25/5.58 = ( ^ [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 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % tanh_real_altdef
% 5.25/5.58 thf(fact_8977_arsinh__real__def,axiom,
% 5.25/5.58 ( arsinh_real
% 5.25/5.58 = ( ^ [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 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arsinh_real_def
% 5.25/5.58 thf(fact_8978_cos__arcsin,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 5.25/5.58 => ( ( cos_real @ ( arcsin @ X3 ) )
% 5.25/5.58 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cos_arcsin
% 5.25/5.58 thf(fact_8979_sin__arccos__abs,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.25/5.58 => ( ( sin_real @ ( arccos @ Y ) )
% 5.25/5.58 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sin_arccos_abs
% 5.25/5.58 thf(fact_8980_sinh__real__le__iff,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( sinh_real @ X3 ) @ ( sinh_real @ Y ) )
% 5.25/5.58 = ( ord_less_eq_real @ X3 @ Y ) ) ).
% 5.25/5.58
% 5.25/5.58 % sinh_real_le_iff
% 5.25/5.58 thf(fact_8981_sinh__real__nonneg__iff,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X3 ) )
% 5.25/5.58 = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % sinh_real_nonneg_iff
% 5.25/5.58 thf(fact_8982_sinh__real__nonpos__iff,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( sinh_real @ X3 ) @ zero_zero_real )
% 5.25/5.58 = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % sinh_real_nonpos_iff
% 5.25/5.58 thf(fact_8983_arccos__1,axiom,
% 5.25/5.58 ( ( arccos @ one_one_real )
% 5.25/5.58 = zero_zero_real ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_1
% 5.25/5.58 thf(fact_8984_arccos__minus__1,axiom,
% 5.25/5.58 ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.58 = pi ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_minus_1
% 5.25/5.58 thf(fact_8985_cos__arccos,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ( cos_real @ ( arccos @ Y ) )
% 5.25/5.58 = Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cos_arccos
% 5.25/5.58 thf(fact_8986_sin__arcsin,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ( sin_real @ ( arcsin @ Y ) )
% 5.25/5.58 = Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sin_arcsin
% 5.25/5.58 thf(fact_8987_arccos__0,axiom,
% 5.25/5.58 ( ( arccos @ zero_zero_real )
% 5.25/5.58 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_0
% 5.25/5.58 thf(fact_8988_arcsin__1,axiom,
% 5.25/5.58 ( ( arcsin @ one_one_real )
% 5.25/5.58 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_1
% 5.25/5.58 thf(fact_8989_arcsin__minus__1,axiom,
% 5.25/5.58 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.58 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_minus_1
% 5.25/5.58 thf(fact_8990_divide__complex__def,axiom,
% 5.25/5.58 ( divide1717551699836669952omplex
% 5.25/5.58 = ( ^ [X2: complex,Y6: complex] : ( times_times_complex @ X2 @ ( invers8013647133539491842omplex @ Y6 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % divide_complex_def
% 5.25/5.58 thf(fact_8991_sinh__le__cosh__real,axiom,
% 5.25/5.58 ! [X3: real] : ( ord_less_eq_real @ ( sinh_real @ X3 ) @ ( cosh_real @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % sinh_le_cosh_real
% 5.25/5.58 thf(fact_8992_cosh__real__nonneg,axiom,
% 5.25/5.58 ! [X3: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % cosh_real_nonneg
% 5.25/5.58 thf(fact_8993_cosh__real__nonneg__le__iff,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y ) )
% 5.25/5.58 = ( ord_less_eq_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cosh_real_nonneg_le_iff
% 5.25/5.58 thf(fact_8994_cosh__real__nonpos__le__iff,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y ) )
% 5.25/5.58 = ( ord_less_eq_real @ Y @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cosh_real_nonpos_le_iff
% 5.25/5.58 thf(fact_8995_arcosh__cosh__real,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( arcosh_real @ ( cosh_real @ X3 ) )
% 5.25/5.58 = X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcosh_cosh_real
% 5.25/5.58 thf(fact_8996_cosh__real__ge__1,axiom,
% 5.25/5.58 ! [X3: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % cosh_real_ge_1
% 5.25/5.58 thf(fact_8997_cosh__real__strict__mono,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ Y )
% 5.25/5.58 => ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cosh_real_strict_mono
% 5.25/5.58 thf(fact_8998_cosh__real__nonneg__less__iff,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y ) )
% 5.25/5.58 = ( ord_less_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cosh_real_nonneg_less_iff
% 5.25/5.58 thf(fact_8999_cosh__real__nonpos__less__iff,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.25/5.58 => ( ( ord_less_real @ ( cosh_real @ X3 ) @ ( cosh_real @ Y ) )
% 5.25/5.58 = ( ord_less_real @ Y @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cosh_real_nonpos_less_iff
% 5.25/5.58 thf(fact_9000_arccos__le__arccos,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X3 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_le_arccos
% 5.25/5.58 thf(fact_9001_arccos__le__mono,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( arccos @ X3 ) @ ( arccos @ Y ) )
% 5.25/5.58 = ( ord_less_eq_real @ Y @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_le_mono
% 5.25/5.58 thf(fact_9002_arccos__eq__iff,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.58 & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 5.25/5.58 => ( ( ( arccos @ X3 )
% 5.25/5.58 = ( arccos @ Y ) )
% 5.25/5.58 = ( X3 = Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_eq_iff
% 5.25/5.58 thf(fact_9003_arcsin__minus,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 5.25/5.58 => ( ( arcsin @ ( uminus_uminus_real @ X3 ) )
% 5.25/5.58 = ( uminus_uminus_real @ ( arcsin @ X3 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_minus
% 5.25/5.58 thf(fact_9004_arcsin__le__arcsin,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ord_less_eq_real @ ( arcsin @ X3 ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_le_arcsin
% 5.25/5.58 thf(fact_9005_arcsin__le__mono,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( arcsin @ X3 ) @ ( arcsin @ Y ) )
% 5.25/5.58 = ( ord_less_eq_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_le_mono
% 5.25/5.58 thf(fact_9006_arcsin__eq__iff,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.25/5.58 => ( ( ( arcsin @ X3 )
% 5.25/5.58 = ( arcsin @ Y ) )
% 5.25/5.58 = ( X3 = Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_eq_iff
% 5.25/5.58 thf(fact_9007_arccos__lbound,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_lbound
% 5.25/5.58 thf(fact_9008_arccos__less__arccos,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X3 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_less_arccos
% 5.25/5.58 thf(fact_9009_arccos__less__mono,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.25/5.58 => ( ( ord_less_real @ ( arccos @ X3 ) @ ( arccos @ Y ) )
% 5.25/5.58 = ( ord_less_real @ Y @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_less_mono
% 5.25/5.58 thf(fact_9010_arccos__ubound,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_ubound
% 5.25/5.58 thf(fact_9011_arccos__cos,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ pi )
% 5.25/5.58 => ( ( arccos @ ( cos_real @ X3 ) )
% 5.25/5.58 = X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_cos
% 5.25/5.58 thf(fact_9012_arcsin__less__arcsin,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ord_less_real @ ( arcsin @ X3 ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_less_arcsin
% 5.25/5.58 thf(fact_9013_arcsin__less__mono,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.25/5.58 => ( ( ord_less_real @ ( arcsin @ X3 ) @ ( arcsin @ Y ) )
% 5.25/5.58 = ( ord_less_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_less_mono
% 5.25/5.58 thf(fact_9014_cos__arccos__abs,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.25/5.58 => ( ( cos_real @ ( arccos @ Y ) )
% 5.25/5.58 = Y ) ) ).
% 5.25/5.58
% 5.25/5.58 % cos_arccos_abs
% 5.25/5.58 thf(fact_9015_arccos__cos__eq__abs,axiom,
% 5.25/5.58 ! [Theta: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 5.25/5.58 => ( ( arccos @ ( cos_real @ Theta ) )
% 5.25/5.58 = ( abs_abs_real @ Theta ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_cos_eq_abs
% 5.25/5.58 thf(fact_9016_arccos__lt__bounded,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.58 => ( ( ord_less_real @ Y @ one_one_real )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.25/5.58 & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_lt_bounded
% 5.25/5.58 thf(fact_9017_arccos__bounded,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.25/5.58 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_bounded
% 5.25/5.58 thf(fact_9018_sin__arccos__nonzero,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ one_one_real )
% 5.25/5.58 => ( ( sin_real @ ( arccos @ X3 ) )
% 5.25/5.58 != zero_zero_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sin_arccos_nonzero
% 5.25/5.58 thf(fact_9019_arccos__cos2,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X3 )
% 5.25/5.58 => ( ( arccos @ ( cos_real @ X3 ) )
% 5.25/5.58 = ( uminus_uminus_real @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_cos2
% 5.25/5.58 thf(fact_9020_arccos__minus,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 5.25/5.58 => ( ( arccos @ ( uminus_uminus_real @ X3 ) )
% 5.25/5.58 = ( minus_minus_real @ pi @ ( arccos @ X3 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_minus
% 5.25/5.58 thf(fact_9021_cos__arcsin__nonzero,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ one_one_real )
% 5.25/5.58 => ( ( cos_real @ ( arcsin @ X3 ) )
% 5.25/5.58 != zero_zero_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cos_arcsin_nonzero
% 5.25/5.58 thf(fact_9022_arccos,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.25/5.58 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 5.25/5.58 & ( ( cos_real @ ( arccos @ Y ) )
% 5.25/5.58 = Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos
% 5.25/5.58 thf(fact_9023_arccos__minus__abs,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.58 => ( ( arccos @ ( uminus_uminus_real @ X3 ) )
% 5.25/5.58 = ( minus_minus_real @ pi @ ( arccos @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_minus_abs
% 5.25/5.58 thf(fact_9024_complex__inverse,axiom,
% 5.25/5.58 ! [A: real,B: real] :
% 5.25/5.58 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.25/5.58 = ( 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 ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_inverse
% 5.25/5.58 thf(fact_9025_arccos__le__pi2,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_le_pi2
% 5.25/5.58 thf(fact_9026_cosh__ln__real,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( cosh_real @ ( ln_ln_real @ X3 ) )
% 5.25/5.58 = ( divide_divide_real @ ( plus_plus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cosh_ln_real
% 5.25/5.58 thf(fact_9027_arcsin__lt__bounded,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.58 => ( ( ord_less_real @ Y @ one_one_real )
% 5.25/5.58 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.25/5.58 & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_lt_bounded
% 5.25/5.58 thf(fact_9028_arcsin__lbound,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_lbound
% 5.25/5.58 thf(fact_9029_arcsin__ubound,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_ubound
% 5.25/5.58 thf(fact_9030_arcsin__bounded,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.25/5.58 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_bounded
% 5.25/5.58 thf(fact_9031_arcsin__sin,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.58 => ( ( arcsin @ ( sin_real @ X3 ) )
% 5.25/5.58 = X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_sin
% 5.25/5.58 thf(fact_9032_sinh__ln__real,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( sinh_real @ ( ln_ln_real @ X3 ) )
% 5.25/5.58 = ( divide_divide_real @ ( minus_minus_real @ X3 @ ( inverse_inverse_real @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sinh_ln_real
% 5.25/5.58 thf(fact_9033_arcsin,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.25/5.58 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.58 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.25/5.58 = Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin
% 5.25/5.58 thf(fact_9034_arcsin__pi,axiom,
% 5.25/5.58 ! [Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.25/5.58 & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 5.25/5.58 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.25/5.58 = Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_pi
% 5.25/5.58 thf(fact_9035_arcsin__le__iff,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( arcsin @ X3 ) @ Y )
% 5.25/5.58 = ( ord_less_eq_real @ X3 @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_le_iff
% 5.25/5.58 thf(fact_9036_le__arcsin__iff,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ ( arcsin @ X3 ) )
% 5.25/5.58 = ( ord_less_eq_real @ ( sin_real @ Y ) @ X3 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % le_arcsin_iff
% 5.25/5.58 thf(fact_9037_arccos__cos__eq__abs__2pi,axiom,
% 5.25/5.58 ! [Theta: real] :
% 5.25/5.58 ~ ! [K2: int] :
% 5.25/5.58 ( ( arccos @ ( cos_real @ Theta ) )
% 5.25/5.58 != ( 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 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_cos_eq_abs_2pi
% 5.25/5.58 thf(fact_9038_sin__arccos,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 5.25/5.58 => ( ( sin_real @ ( arccos @ X3 ) )
% 5.25/5.58 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sin_arccos
% 5.25/5.58 thf(fact_9039_cot__less__zero,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ zero_zero_real )
% 5.25/5.58 => ( ord_less_real @ ( cot_real @ X3 ) @ zero_zero_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cot_less_zero
% 5.25/5.58 thf(fact_9040_i__even__power,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.58 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 5.25/5.58
% 5.25/5.58 % i_even_power
% 5.25/5.58 thf(fact_9041_log__base__10__eq1,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.58 = ( 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 @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_base_10_eq1
% 5.25/5.58 thf(fact_9042_cot__periodic,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( cot_real @ ( plus_plus_real @ X3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.25/5.58 = ( cot_real @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % cot_periodic
% 5.25/5.58 thf(fact_9043_log__one,axiom,
% 5.25/5.58 ! [A: real] :
% 5.25/5.58 ( ( log @ A @ one_one_real )
% 5.25/5.58 = zero_zero_real ) ).
% 5.25/5.58
% 5.25/5.58 % log_one
% 5.25/5.58 thf(fact_9044_norm__ii,axiom,
% 5.25/5.58 ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 5.25/5.58 = one_one_real ) ).
% 5.25/5.58
% 5.25/5.58 % norm_ii
% 5.25/5.58 thf(fact_9045_complex__i__mult__minus,axiom,
% 5.25/5.58 ! [X3: complex] :
% 5.25/5.58 ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X3 ) )
% 5.25/5.58 = ( uminus1482373934393186551omplex @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_i_mult_minus
% 5.25/5.58 thf(fact_9046_log__eq__one,axiom,
% 5.25/5.58 ! [A: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( A != one_one_real )
% 5.25/5.58 => ( ( log @ A @ A )
% 5.25/5.58 = one_one_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_eq_one
% 5.25/5.58 thf(fact_9047_log__less__cancel__iff,axiom,
% 5.25/5.58 ! [A: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ( ord_less_real @ ( log @ A @ X3 ) @ ( log @ A @ Y ) )
% 5.25/5.58 = ( ord_less_real @ X3 @ Y ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_less_cancel_iff
% 5.25/5.58 thf(fact_9048_log__less__one__cancel__iff,axiom,
% 5.25/5.58 ! [A: real,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ ( log @ A @ X3 ) @ one_one_real )
% 5.25/5.58 = ( ord_less_real @ X3 @ A ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_less_one_cancel_iff
% 5.25/5.58 thf(fact_9049_one__less__log__cancel__iff,axiom,
% 5.25/5.58 ! [A: real,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X3 ) )
% 5.25/5.58 = ( ord_less_real @ A @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % one_less_log_cancel_iff
% 5.25/5.58 thf(fact_9050_log__less__zero__cancel__iff,axiom,
% 5.25/5.58 ! [A: real,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ ( log @ A @ X3 ) @ zero_zero_real )
% 5.25/5.58 = ( ord_less_real @ X3 @ one_one_real ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_less_zero_cancel_iff
% 5.25/5.58 thf(fact_9051_zero__less__log__cancel__iff,axiom,
% 5.25/5.58 ! [A: real,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X3 ) )
% 5.25/5.58 = ( ord_less_real @ one_one_real @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % zero_less_log_cancel_iff
% 5.25/5.58 thf(fact_9052_divide__i,axiom,
% 5.25/5.58 ! [X3: complex] :
% 5.25/5.58 ( ( divide1717551699836669952omplex @ X3 @ imaginary_unit )
% 5.25/5.58 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % divide_i
% 5.25/5.58 thf(fact_9053_i__squared,axiom,
% 5.25/5.58 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 5.25/5.58 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.25/5.58
% 5.25/5.58 % i_squared
% 5.25/5.58 thf(fact_9054_zero__le__log__cancel__iff,axiom,
% 5.25/5.58 ! [A: real,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X3 ) )
% 5.25/5.58 = ( ord_less_eq_real @ one_one_real @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % zero_le_log_cancel_iff
% 5.25/5.58 thf(fact_9055_log__le__zero__cancel__iff,axiom,
% 5.25/5.58 ! [A: real,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ zero_zero_real )
% 5.25/5.58 = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_le_zero_cancel_iff
% 5.25/5.58 thf(fact_9056_one__le__log__cancel__iff,axiom,
% 5.25/5.58 ! [A: real,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X3 ) )
% 5.25/5.58 = ( ord_less_eq_real @ A @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % one_le_log_cancel_iff
% 5.25/5.58 thf(fact_9057_log__le__one__cancel__iff,axiom,
% 5.25/5.58 ! [A: real,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ one_one_real )
% 5.25/5.58 = ( ord_less_eq_real @ X3 @ A ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_le_one_cancel_iff
% 5.25/5.58 thf(fact_9058_log__le__cancel__iff,axiom,
% 5.25/5.58 ! [A: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( log @ A @ X3 ) @ ( log @ A @ Y ) )
% 5.25/5.58 = ( ord_less_eq_real @ X3 @ Y ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_le_cancel_iff
% 5.25/5.58 thf(fact_9059_cot__npi,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.25/5.58 = zero_zero_real ) ).
% 5.25/5.58
% 5.25/5.58 % cot_npi
% 5.25/5.58 thf(fact_9060_divide__numeral__i,axiom,
% 5.25/5.58 ! [Z: complex,N: num] :
% 5.25/5.58 ( ( divide1717551699836669952omplex @ Z @ ( times_times_complex @ ( numera6690914467698888265omplex @ N ) @ imaginary_unit ) )
% 5.25/5.58 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % divide_numeral_i
% 5.25/5.58 thf(fact_9061_log__pow__cancel,axiom,
% 5.25/5.58 ! [A: real,B: nat] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( A != one_one_real )
% 5.25/5.58 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 5.25/5.58 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_pow_cancel
% 5.25/5.58 thf(fact_9062_power2__i,axiom,
% 5.25/5.58 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.58 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.25/5.58
% 5.25/5.58 % power2_i
% 5.25/5.58 thf(fact_9063_complex__i__not__one,axiom,
% 5.25/5.58 imaginary_unit != one_one_complex ).
% 5.25/5.58
% 5.25/5.58 % complex_i_not_one
% 5.25/5.58 thf(fact_9064_complex__i__not__numeral,axiom,
% 5.25/5.58 ! [W: num] :
% 5.25/5.58 ( imaginary_unit
% 5.25/5.58 != ( numera6690914467698888265omplex @ W ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_i_not_numeral
% 5.25/5.58 thf(fact_9065_i__times__eq__iff,axiom,
% 5.25/5.58 ! [W: complex,Z: complex] :
% 5.25/5.58 ( ( ( times_times_complex @ imaginary_unit @ W )
% 5.25/5.58 = Z )
% 5.25/5.58 = ( W
% 5.25/5.58 = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % i_times_eq_iff
% 5.25/5.58 thf(fact_9066_complex__i__not__neg__numeral,axiom,
% 5.25/5.58 ! [W: num] :
% 5.25/5.58 ( imaginary_unit
% 5.25/5.58 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_i_not_neg_numeral
% 5.25/5.58 thf(fact_9067_log__ln,axiom,
% 5.25/5.58 ( ln_ln_real
% 5.25/5.58 = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_ln
% 5.25/5.58 thf(fact_9068_imaginary__unit_Ocode,axiom,
% 5.25/5.58 ( imaginary_unit
% 5.25/5.58 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % imaginary_unit.code
% 5.25/5.58 thf(fact_9069_Complex__eq__i,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ( complex2 @ X3 @ Y )
% 5.25/5.58 = imaginary_unit )
% 5.25/5.58 = ( ( X3 = zero_zero_real )
% 5.25/5.58 & ( Y = one_one_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Complex_eq_i
% 5.25/5.58 thf(fact_9070_Complex__mult__i,axiom,
% 5.25/5.58 ! [A: real,B: real] :
% 5.25/5.58 ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 5.25/5.58 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.25/5.58
% 5.25/5.58 % Complex_mult_i
% 5.25/5.58 thf(fact_9071_i__mult__Complex,axiom,
% 5.25/5.58 ! [A: real,B: real] :
% 5.25/5.58 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 5.25/5.58 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.25/5.58
% 5.25/5.58 % i_mult_Complex
% 5.25/5.58 thf(fact_9072_log__base__change,axiom,
% 5.25/5.58 ! [A: real,B: real,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( A != one_one_real )
% 5.25/5.58 => ( ( log @ B @ X3 )
% 5.25/5.58 = ( divide_divide_real @ ( log @ A @ X3 ) @ ( log @ A @ B ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_base_change
% 5.25/5.58 thf(fact_9073_less__log__of__power,axiom,
% 5.25/5.58 ! [B: real,N: nat,M: real] :
% 5.25/5.58 ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 5.25/5.58 => ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % less_log_of_power
% 5.25/5.58 thf(fact_9074_log__of__power__eq,axiom,
% 5.25/5.58 ! [M: nat,B: real,N: nat] :
% 5.25/5.58 ( ( ( semiri5074537144036343181t_real @ M )
% 5.25/5.58 = ( power_power_real @ B @ N ) )
% 5.25/5.58 => ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ( semiri5074537144036343181t_real @ N )
% 5.25/5.58 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_of_power_eq
% 5.25/5.58 thf(fact_9075_log__mult,axiom,
% 5.25/5.58 ! [A: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( A != one_one_real )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ( log @ A @ ( times_times_real @ X3 @ Y ) )
% 5.25/5.58 = ( plus_plus_real @ ( log @ A @ X3 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_mult
% 5.25/5.58 thf(fact_9076_log__divide,axiom,
% 5.25/5.58 ! [A: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( A != one_one_real )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ( log @ A @ ( divide_divide_real @ X3 @ Y ) )
% 5.25/5.58 = ( minus_minus_real @ ( log @ A @ X3 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_divide
% 5.25/5.58 thf(fact_9077_le__log__of__power,axiom,
% 5.25/5.58 ! [B: real,N: nat,M: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 5.25/5.58 => ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % le_log_of_power
% 5.25/5.58 thf(fact_9078_log__base__pow,axiom,
% 5.25/5.58 ! [A: real,N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( log @ ( power_power_real @ A @ N ) @ X3 )
% 5.25/5.58 = ( divide_divide_real @ ( log @ A @ X3 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_base_pow
% 5.25/5.58 thf(fact_9079_log__nat__power,axiom,
% 5.25/5.58 ! [X3: real,B: real,N: nat] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( log @ B @ ( power_power_real @ X3 @ N ) )
% 5.25/5.58 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_nat_power
% 5.25/5.58 thf(fact_9080_log__inverse,axiom,
% 5.25/5.58 ! [A: real,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( A != one_one_real )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( log @ A @ ( inverse_inverse_real @ X3 ) )
% 5.25/5.58 = ( uminus_uminus_real @ ( log @ A @ X3 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_inverse
% 5.25/5.58 thf(fact_9081_log2__of__power__eq,axiom,
% 5.25/5.58 ! [M: nat,N: nat] :
% 5.25/5.58 ( ( M
% 5.25/5.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.58 => ( ( semiri5074537144036343181t_real @ N )
% 5.25/5.58 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log2_of_power_eq
% 5.25/5.58 thf(fact_9082_log__of__power__less,axiom,
% 5.25/5.58 ! [M: nat,B: real,N: nat] :
% 5.25/5.58 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.25/5.58 => ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.58 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_of_power_less
% 5.25/5.58 thf(fact_9083_log__eq__div__ln__mult__log,axiom,
% 5.25/5.58 ! [A: real,B: real,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( A != one_one_real )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.58 => ( ( B != one_one_real )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( log @ A @ X3 )
% 5.25/5.58 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X3 ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_eq_div_ln_mult_log
% 5.25/5.58 thf(fact_9084_log__of__power__le,axiom,
% 5.25/5.58 ! [M: nat,B: real,N: nat] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.25/5.58 => ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.58 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_of_power_le
% 5.25/5.58 thf(fact_9085_less__log2__of__power,axiom,
% 5.25/5.58 ! [N: nat,M: nat] :
% 5.25/5.58 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.25/5.58 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % less_log2_of_power
% 5.25/5.58 thf(fact_9086_le__log2__of__power,axiom,
% 5.25/5.58 ! [N: nat,M: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.25/5.58 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % le_log2_of_power
% 5.25/5.58 thf(fact_9087_log2__of__power__less,axiom,
% 5.25/5.58 ! [M: nat,N: nat] :
% 5.25/5.58 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.58 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.58 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log2_of_power_less
% 5.25/5.58 thf(fact_9088_cot__gt__zero,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.58 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cot_gt_zero
% 5.25/5.58 thf(fact_9089_log2__of__power__le,axiom,
% 5.25/5.58 ! [M: nat,N: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.58 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.58 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log2_of_power_le
% 5.25/5.58 thf(fact_9090_log__base__10__eq2,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.25/5.58 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_base_10_eq2
% 5.25/5.58 thf(fact_9091_tan__cot_H,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) )
% 5.25/5.58 = ( cot_real @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % tan_cot'
% 5.25/5.58 thf(fact_9092_Arg__minus__ii,axiom,
% 5.25/5.58 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.25/5.58 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Arg_minus_ii
% 5.25/5.58 thf(fact_9093_ceiling__log__nat__eq__powr__iff,axiom,
% 5.25/5.58 ! [B: nat,K: nat,N: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.25/5.58 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.58 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.25/5.58 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 5.25/5.58 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.25/5.58 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ceiling_log_nat_eq_powr_iff
% 5.25/5.58 thf(fact_9094_Arg__ii,axiom,
% 5.25/5.58 ( ( arg @ imaginary_unit )
% 5.25/5.58 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Arg_ii
% 5.25/5.58 thf(fact_9095_ceiling__log__nat__eq__if,axiom,
% 5.25/5.58 ! [B: nat,N: nat,K: nat] :
% 5.25/5.58 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.25/5.58 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.25/5.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.25/5.58 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.25/5.58 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ceiling_log_nat_eq_if
% 5.25/5.58 thf(fact_9096_ceiling__divide__eq__div__numeral,axiom,
% 5.25/5.58 ! [A: num,B: num] :
% 5.25/5.58 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.25/5.58 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ceiling_divide_eq_div_numeral
% 5.25/5.58 thf(fact_9097_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.25/5.58 ! [A: num,B: num] :
% 5.25/5.58 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.25/5.58 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ceiling_minus_divide_eq_div_numeral
% 5.25/5.58 thf(fact_9098_Arg__bounded,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.25/5.58 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.25/5.58
% 5.25/5.58 % Arg_bounded
% 5.25/5.58 thf(fact_9099_ceiling__log2__div2,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.58 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.25/5.58 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ceiling_log2_div2
% 5.25/5.58 thf(fact_9100_cis__minus__pi__half,axiom,
% 5.25/5.58 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.25/5.58 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.25/5.58
% 5.25/5.58 % cis_minus_pi_half
% 5.25/5.58 thf(fact_9101_ceiling__log__eq__powr__iff,axiom,
% 5.25/5.58 ! [X3: real,B: real,K: nat] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X3 ) )
% 5.25/5.58 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.25/5.58 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X3 )
% 5.25/5.58 & ( ord_less_eq_real @ X3 @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ceiling_log_eq_powr_iff
% 5.25/5.58 thf(fact_9102_floor__log__nat__eq__powr__iff,axiom,
% 5.25/5.58 ! [B: nat,K: nat,N: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.25/5.58 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.58 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.25/5.58 = ( semiri1314217659103216013at_int @ N ) )
% 5.25/5.58 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.25/5.58 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % floor_log_nat_eq_powr_iff
% 5.25/5.58 thf(fact_9103_floor__log__nat__eq__if,axiom,
% 5.25/5.58 ! [B: nat,N: nat,K: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.25/5.58 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.25/5.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.25/5.58 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.25/5.58 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % floor_log_nat_eq_if
% 5.25/5.58 thf(fact_9104_powr__nonneg__iff,axiom,
% 5.25/5.58 ! [A: real,X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( powr_real @ A @ X3 ) @ zero_zero_real )
% 5.25/5.58 = ( A = zero_zero_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_nonneg_iff
% 5.25/5.58 thf(fact_9105_powr__less__cancel__iff,axiom,
% 5.25/5.58 ! [X3: real,A: real,B: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 5.25/5.58 = ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_less_cancel_iff
% 5.25/5.58 thf(fact_9106_norm__cis,axiom,
% 5.25/5.58 ! [A: real] :
% 5.25/5.58 ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 5.25/5.58 = one_one_real ) ).
% 5.25/5.58
% 5.25/5.58 % norm_cis
% 5.25/5.58 thf(fact_9107_cis__zero,axiom,
% 5.25/5.58 ( ( cis @ zero_zero_real )
% 5.25/5.58 = one_one_complex ) ).
% 5.25/5.58
% 5.25/5.58 % cis_zero
% 5.25/5.58 thf(fact_9108_powr__eq__one__iff,axiom,
% 5.25/5.58 ! [A: real,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.58 => ( ( ( powr_real @ A @ X3 )
% 5.25/5.58 = one_one_real )
% 5.25/5.58 = ( X3 = zero_zero_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_eq_one_iff
% 5.25/5.58 thf(fact_9109_powr__one__gt__zero__iff,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ( powr_real @ X3 @ one_one_real )
% 5.25/5.58 = X3 )
% 5.25/5.58 = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_one_gt_zero_iff
% 5.25/5.58 thf(fact_9110_powr__one,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( powr_real @ X3 @ one_one_real )
% 5.25/5.58 = X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_one
% 5.25/5.58 thf(fact_9111_powr__le__cancel__iff,axiom,
% 5.25/5.58 ! [X3: real,A: real,B: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 5.25/5.58 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_le_cancel_iff
% 5.25/5.58 thf(fact_9112_numeral__powr__numeral__real,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.25/5.58 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % numeral_powr_numeral_real
% 5.25/5.58 thf(fact_9113_cis__pi,axiom,
% 5.25/5.58 ( ( cis @ pi )
% 5.25/5.58 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.25/5.58
% 5.25/5.58 % cis_pi
% 5.25/5.58 thf(fact_9114_log__powr__cancel,axiom,
% 5.25/5.58 ! [A: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( A != one_one_real )
% 5.25/5.58 => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 5.25/5.58 = Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_powr_cancel
% 5.25/5.58 thf(fact_9115_powr__log__cancel,axiom,
% 5.25/5.58 ! [A: real,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( A != one_one_real )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( powr_real @ A @ ( log @ A @ X3 ) )
% 5.25/5.58 = X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_log_cancel
% 5.25/5.58 thf(fact_9116_floor__divide__eq__div__numeral,axiom,
% 5.25/5.58 ! [A: num,B: num] :
% 5.25/5.58 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.25/5.58 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % floor_divide_eq_div_numeral
% 5.25/5.58 thf(fact_9117_powr__numeral,axiom,
% 5.25/5.58 ! [X3: real,N: num] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( powr_real @ X3 @ ( numeral_numeral_real @ N ) )
% 5.25/5.58 = ( power_power_real @ X3 @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_numeral
% 5.25/5.58 thf(fact_9118_cis__pi__half,axiom,
% 5.25/5.58 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.58 = imaginary_unit ) ).
% 5.25/5.58
% 5.25/5.58 % cis_pi_half
% 5.25/5.58 thf(fact_9119_floor__one__divide__eq__div__numeral,axiom,
% 5.25/5.58 ! [B: num] :
% 5.25/5.58 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.25/5.58 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % floor_one_divide_eq_div_numeral
% 5.25/5.58 thf(fact_9120_cis__2pi,axiom,
% 5.25/5.58 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.25/5.58 = one_one_complex ) ).
% 5.25/5.58
% 5.25/5.58 % cis_2pi
% 5.25/5.58 thf(fact_9121_floor__minus__divide__eq__div__numeral,axiom,
% 5.25/5.58 ! [A: num,B: num] :
% 5.25/5.58 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.25/5.58 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % floor_minus_divide_eq_div_numeral
% 5.25/5.58 thf(fact_9122_square__powr__half,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( powr_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.58 = ( abs_abs_real @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % square_powr_half
% 5.25/5.58 thf(fact_9123_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.25/5.58 ! [B: num] :
% 5.25/5.58 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.25/5.58 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % floor_minus_one_divide_eq_div_numeral
% 5.25/5.58 thf(fact_9124_powr__powr,axiom,
% 5.25/5.58 ! [X3: real,A: real,B: real] :
% 5.25/5.58 ( ( powr_real @ ( powr_real @ X3 @ A ) @ B )
% 5.25/5.58 = ( powr_real @ X3 @ ( times_times_real @ A @ B ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_powr
% 5.25/5.58 thf(fact_9125_powr__ge__pzero,axiom,
% 5.25/5.58 ! [X3: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X3 @ Y ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_ge_pzero
% 5.25/5.58 thf(fact_9126_powr__mono2,axiom,
% 5.25/5.58 ! [A: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.58 => ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_mono2
% 5.25/5.58 thf(fact_9127_powr__less__cancel,axiom,
% 5.25/5.58 ! [X3: real,A: real,B: real] :
% 5.25/5.58 ( ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) )
% 5.25/5.58 => ( ( ord_less_real @ one_one_real @ X3 )
% 5.25/5.58 => ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_less_cancel
% 5.25/5.58 thf(fact_9128_powr__less__mono,axiom,
% 5.25/5.58 ! [A: real,B: real,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ A @ B )
% 5.25/5.58 => ( ( ord_less_real @ one_one_real @ X3 )
% 5.25/5.58 => ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_less_mono
% 5.25/5.58 thf(fact_9129_powr__mono,axiom,
% 5.25/5.58 ! [A: real,B: real,X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.58 => ( ( ord_less_eq_real @ one_one_real @ X3 )
% 5.25/5.58 => ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ X3 @ B ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_mono
% 5.25/5.58 thf(fact_9130_cis__mult,axiom,
% 5.25/5.58 ! [A: real,B: real] :
% 5.25/5.58 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 5.25/5.58 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cis_mult
% 5.25/5.58 thf(fact_9131_powr__less__mono2,axiom,
% 5.25/5.58 ! [A: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ Y )
% 5.25/5.58 => ( ord_less_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_less_mono2
% 5.25/5.58 thf(fact_9132_powr__mono2_H,axiom,
% 5.25/5.58 ! [A: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.58 => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X3 @ A ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_mono2'
% 5.25/5.58 thf(fact_9133_powr__inj,axiom,
% 5.25/5.58 ! [A: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( A != one_one_real )
% 5.25/5.58 => ( ( ( powr_real @ A @ X3 )
% 5.25/5.58 = ( powr_real @ A @ Y ) )
% 5.25/5.58 = ( X3 = Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_inj
% 5.25/5.58 thf(fact_9134_gr__one__powr,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ord_less_real @ one_one_real @ ( powr_real @ X3 @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % gr_one_powr
% 5.25/5.58 thf(fact_9135_ge__one__powr__ge__zero,axiom,
% 5.25/5.58 ! [X3: real,A: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ one_one_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X3 @ A ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ge_one_powr_ge_zero
% 5.25/5.58 thf(fact_9136_powr__mono__both,axiom,
% 5.25/5.58 ! [A: real,B: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( ord_less_eq_real @ A @ B )
% 5.25/5.58 => ( ( ord_less_eq_real @ one_one_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.58 => ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_mono_both
% 5.25/5.58 thf(fact_9137_powr__le1,axiom,
% 5.25/5.58 ! [A: real,X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 5.25/5.58 => ( ord_less_eq_real @ ( powr_real @ X3 @ A ) @ one_one_real ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_le1
% 5.25/5.58 thf(fact_9138_powr__divide,axiom,
% 5.25/5.58 ! [X3: real,Y: real,A: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ( powr_real @ ( divide_divide_real @ X3 @ Y ) @ A )
% 5.25/5.58 = ( divide_divide_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_divide
% 5.25/5.58 thf(fact_9139_powr__mult,axiom,
% 5.25/5.58 ! [X3: real,Y: real,A: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ( powr_real @ ( times_times_real @ X3 @ Y ) @ A )
% 5.25/5.58 = ( times_times_real @ ( powr_real @ X3 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_mult
% 5.25/5.58 thf(fact_9140_inverse__powr,axiom,
% 5.25/5.58 ! [Y: real,A: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 5.25/5.58 = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % inverse_powr
% 5.25/5.58 thf(fact_9141_divide__powr__uminus,axiom,
% 5.25/5.58 ! [A: real,B: real,C: real] :
% 5.25/5.58 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 5.25/5.58 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % divide_powr_uminus
% 5.25/5.58 thf(fact_9142_ln__powr,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( X3 != zero_zero_real )
% 5.25/5.58 => ( ( ln_ln_real @ ( powr_real @ X3 @ Y ) )
% 5.25/5.58 = ( times_times_real @ Y @ ( ln_ln_real @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ln_powr
% 5.25/5.58 thf(fact_9143_log__powr,axiom,
% 5.25/5.58 ! [X3: real,B: real,Y: real] :
% 5.25/5.58 ( ( X3 != zero_zero_real )
% 5.25/5.58 => ( ( log @ B @ ( powr_real @ X3 @ Y ) )
% 5.25/5.58 = ( times_times_real @ Y @ ( log @ B @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_powr
% 5.25/5.58 thf(fact_9144_floor__log__eq__powr__iff,axiom,
% 5.25/5.58 ! [X3: real,B: real,K: int] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X3 ) )
% 5.25/5.58 = K )
% 5.25/5.58 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X3 )
% 5.25/5.58 & ( ord_less_real @ X3 @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % floor_log_eq_powr_iff
% 5.25/5.58 thf(fact_9145_powr__realpow,axiom,
% 5.25/5.58 ! [X3: real,N: nat] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( powr_real @ X3 @ ( semiri5074537144036343181t_real @ N ) )
% 5.25/5.58 = ( power_power_real @ X3 @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_realpow
% 5.25/5.58 thf(fact_9146_powr__less__iff,axiom,
% 5.25/5.58 ! [B: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X3 )
% 5.25/5.58 = ( ord_less_real @ Y @ ( log @ B @ X3 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_less_iff
% 5.25/5.58 thf(fact_9147_less__powr__iff,axiom,
% 5.25/5.58 ! [B: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ ( powr_real @ B @ Y ) )
% 5.25/5.58 = ( ord_less_real @ ( log @ B @ X3 ) @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % less_powr_iff
% 5.25/5.58 thf(fact_9148_log__less__iff,axiom,
% 5.25/5.58 ! [B: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ ( log @ B @ X3 ) @ Y )
% 5.25/5.58 = ( ord_less_real @ X3 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_less_iff
% 5.25/5.58 thf(fact_9149_less__log__iff,axiom,
% 5.25/5.58 ! [B: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ Y @ ( log @ B @ X3 ) )
% 5.25/5.58 = ( ord_less_real @ ( powr_real @ B @ Y ) @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % less_log_iff
% 5.25/5.58 thf(fact_9150_real__of__int__floor__add__one__gt,axiom,
% 5.25/5.58 ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_of_int_floor_add_one_gt
% 5.25/5.58 thf(fact_9151_floor__eq,axiom,
% 5.25/5.58 ! [N: int,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.25/5.58 => ( ( archim6058952711729229775r_real @ X3 )
% 5.25/5.58 = N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % floor_eq
% 5.25/5.58 thf(fact_9152_real__of__int__floor__add__one__ge,axiom,
% 5.25/5.58 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_of_int_floor_add_one_ge
% 5.25/5.58 thf(fact_9153_real__of__int__floor__gt__diff__one,axiom,
% 5.25/5.58 ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_of_int_floor_gt_diff_one
% 5.25/5.58 thf(fact_9154_real__of__int__floor__ge__diff__one,axiom,
% 5.25/5.58 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_of_int_floor_ge_diff_one
% 5.25/5.58 thf(fact_9155_DeMoivre,axiom,
% 5.25/5.58 ! [A: real,N: nat] :
% 5.25/5.58 ( ( power_power_complex @ ( cis @ A ) @ N )
% 5.25/5.58 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % DeMoivre
% 5.25/5.58 thf(fact_9156_powr__neg__one,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( powr_real @ X3 @ ( uminus_uminus_real @ one_one_real ) )
% 5.25/5.58 = ( divide_divide_real @ one_one_real @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_neg_one
% 5.25/5.58 thf(fact_9157_powr__mult__base,axiom,
% 5.25/5.58 ! [X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( times_times_real @ X3 @ ( powr_real @ X3 @ Y ) )
% 5.25/5.58 = ( powr_real @ X3 @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_mult_base
% 5.25/5.58 thf(fact_9158_le__log__iff,axiom,
% 5.25/5.58 ! [B: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ Y @ ( log @ B @ X3 ) )
% 5.25/5.58 = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % le_log_iff
% 5.25/5.58 thf(fact_9159_log__le__iff,axiom,
% 5.25/5.58 ! [B: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( log @ B @ X3 ) @ Y )
% 5.25/5.58 = ( ord_less_eq_real @ X3 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_le_iff
% 5.25/5.58 thf(fact_9160_le__powr__iff,axiom,
% 5.25/5.58 ! [B: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ ( powr_real @ B @ Y ) )
% 5.25/5.58 = ( ord_less_eq_real @ ( log @ B @ X3 ) @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % le_powr_iff
% 5.25/5.58 thf(fact_9161_powr__le__iff,axiom,
% 5.25/5.58 ! [B: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X3 )
% 5.25/5.58 = ( ord_less_eq_real @ Y @ ( log @ B @ X3 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_le_iff
% 5.25/5.58 thf(fact_9162_floor__eq2,axiom,
% 5.25/5.58 ! [N: int,X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.25/5.58 => ( ( archim6058952711729229775r_real @ X3 )
% 5.25/5.58 = N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % floor_eq2
% 5.25/5.58 thf(fact_9163_floor__divide__real__eq__div,axiom,
% 5.25/5.58 ! [B: int,A: real] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.58 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 5.25/5.58 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % floor_divide_real_eq_div
% 5.25/5.58 thf(fact_9164_ln__powr__bound,axiom,
% 5.25/5.58 ! [X3: real,A: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ one_one_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ord_less_eq_real @ ( ln_ln_real @ X3 ) @ ( divide_divide_real @ ( powr_real @ X3 @ A ) @ A ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ln_powr_bound
% 5.25/5.58 thf(fact_9165_ln__powr__bound2,axiom,
% 5.25/5.58 ! [X3: real,A: real] :
% 5.25/5.58 ( ( ord_less_real @ one_one_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X3 ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ln_powr_bound2
% 5.25/5.58 thf(fact_9166_log__add__eq__powr,axiom,
% 5.25/5.58 ! [B: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.58 => ( ( B != one_one_real )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( plus_plus_real @ ( log @ B @ X3 ) @ Y )
% 5.25/5.58 = ( log @ B @ ( times_times_real @ X3 @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_add_eq_powr
% 5.25/5.58 thf(fact_9167_add__log__eq__powr,axiom,
% 5.25/5.58 ! [B: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.58 => ( ( B != one_one_real )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( plus_plus_real @ Y @ ( log @ B @ X3 ) )
% 5.25/5.58 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X3 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % add_log_eq_powr
% 5.25/5.58 thf(fact_9168_minus__log__eq__powr,axiom,
% 5.25/5.58 ! [B: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.58 => ( ( B != one_one_real )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( minus_minus_real @ Y @ ( log @ B @ X3 ) )
% 5.25/5.58 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X3 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % minus_log_eq_powr
% 5.25/5.58 thf(fact_9169_log__minus__eq__powr,axiom,
% 5.25/5.58 ! [B: real,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.58 => ( ( B != one_one_real )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( minus_minus_real @ ( log @ B @ X3 ) @ Y )
% 5.25/5.58 = ( log @ B @ ( times_times_real @ X3 @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_minus_eq_powr
% 5.25/5.58 thf(fact_9170_powr__half__sqrt,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( powr_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.58 = ( sqrt @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_half_sqrt
% 5.25/5.58 thf(fact_9171_powr__neg__numeral,axiom,
% 5.25/5.58 ! [X3: real,N: num] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( powr_real @ X3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.25/5.58 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_neg_numeral
% 5.25/5.58 thf(fact_9172_floor__log2__div2,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.58 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.25/5.58 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % floor_log2_div2
% 5.25/5.58 thf(fact_9173_bij__betw__roots__unity,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( bij_betw_nat_complex
% 5.25/5.58 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.25/5.58 @ ( set_ord_lessThan_nat @ N )
% 5.25/5.58 @ ( collect_complex
% 5.25/5.58 @ ^ [Z5: complex] :
% 5.25/5.58 ( ( power_power_complex @ Z5 @ N )
% 5.25/5.58 = one_one_complex ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % bij_betw_roots_unity
% 5.25/5.58 thf(fact_9174_exp__pi__i,axiom,
% 5.25/5.58 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 5.25/5.58 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_pi_i
% 5.25/5.58 thf(fact_9175_exp__pi__i_H,axiom,
% 5.25/5.58 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 5.25/5.58 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_pi_i'
% 5.25/5.58 thf(fact_9176_exp__two__pi__i_H,axiom,
% 5.25/5.58 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.25/5.58 = one_one_complex ) ).
% 5.25/5.58
% 5.25/5.58 % exp_two_pi_i'
% 5.25/5.58 thf(fact_9177_exp__two__pi__i,axiom,
% 5.25/5.58 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.25/5.58 = one_one_complex ) ).
% 5.25/5.58
% 5.25/5.58 % exp_two_pi_i
% 5.25/5.58 thf(fact_9178_complex__exp__exists,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ? [A5: complex,R3: real] :
% 5.25/5.58 ( Z
% 5.25/5.58 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( exp_complex @ A5 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_exp_exists
% 5.25/5.58 thf(fact_9179_complex__of__real__mult__Complex,axiom,
% 5.25/5.58 ! [R2: real,X3: real,Y: real] :
% 5.25/5.58 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X3 @ Y ) )
% 5.25/5.58 = ( complex2 @ ( times_times_real @ R2 @ X3 ) @ ( times_times_real @ R2 @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_of_real_mult_Complex
% 5.25/5.58 thf(fact_9180_Complex__mult__complex__of__real,axiom,
% 5.25/5.58 ! [X3: real,Y: real,R2: real] :
% 5.25/5.58 ( ( times_times_complex @ ( complex2 @ X3 @ Y ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.25/5.58 = ( complex2 @ ( times_times_real @ X3 @ R2 ) @ ( times_times_real @ Y @ R2 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Complex_mult_complex_of_real
% 5.25/5.58 thf(fact_9181_complex__of__real__add__Complex,axiom,
% 5.25/5.58 ! [R2: real,X3: real,Y: real] :
% 5.25/5.58 ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X3 @ Y ) )
% 5.25/5.58 = ( complex2 @ ( plus_plus_real @ R2 @ X3 ) @ Y ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_of_real_add_Complex
% 5.25/5.58 thf(fact_9182_Complex__add__complex__of__real,axiom,
% 5.25/5.58 ! [X3: real,Y: real,R2: real] :
% 5.25/5.58 ( ( plus_plus_complex @ ( complex2 @ X3 @ Y ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.25/5.58 = ( complex2 @ ( plus_plus_real @ X3 @ R2 ) @ Y ) ) ).
% 5.25/5.58
% 5.25/5.58 % Complex_add_complex_of_real
% 5.25/5.58 thf(fact_9183_cis__conv__exp,axiom,
% 5.25/5.58 ( cis
% 5.25/5.58 = ( ^ [B2: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cis_conv_exp
% 5.25/5.58 thf(fact_9184_complex__of__real__i,axiom,
% 5.25/5.58 ! [R2: real] :
% 5.25/5.58 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ imaginary_unit )
% 5.25/5.58 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_of_real_i
% 5.25/5.58 thf(fact_9185_i__complex__of__real,axiom,
% 5.25/5.58 ! [R2: real] :
% 5.25/5.58 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.25/5.58 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.25/5.58
% 5.25/5.58 % i_complex_of_real
% 5.25/5.58 thf(fact_9186_Complex__eq,axiom,
% 5.25/5.58 ( complex2
% 5.25/5.58 = ( ^ [A3: real,B2: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A3 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Complex_eq
% 5.25/5.58 thf(fact_9187_complex__split__polar,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ? [R3: real,A5: real] :
% 5.25/5.58 ( Z
% 5.25/5.58 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A5 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A5 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_split_polar
% 5.25/5.58 thf(fact_9188_cmod__unit__one,axiom,
% 5.25/5.58 ! [A: real] :
% 5.25/5.58 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.25/5.58 = one_one_real ) ).
% 5.25/5.58
% 5.25/5.58 % cmod_unit_one
% 5.25/5.58 thf(fact_9189_cmod__complex__polar,axiom,
% 5.25/5.58 ! [R2: real,A: real] :
% 5.25/5.58 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) ) )
% 5.25/5.58 = ( abs_abs_real @ R2 ) ) ).
% 5.25/5.58
% 5.25/5.58 % cmod_complex_polar
% 5.25/5.58 thf(fact_9190_csqrt__ii,axiom,
% 5.25/5.58 ( ( csqrt @ imaginary_unit )
% 5.25/5.58 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % csqrt_ii
% 5.25/5.58 thf(fact_9191_arctan__def,axiom,
% 5.25/5.58 ( arctan
% 5.25/5.58 = ( ^ [Y6: real] :
% 5.25/5.58 ( the_real
% 5.25/5.58 @ ^ [X2: real] :
% 5.25/5.58 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.25/5.58 & ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.58 & ( ( tan_real @ X2 )
% 5.25/5.58 = Y6 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arctan_def
% 5.25/5.58 thf(fact_9192_arcsin__def,axiom,
% 5.25/5.58 ( arcsin
% 5.25/5.58 = ( ^ [Y6: real] :
% 5.25/5.58 ( the_real
% 5.25/5.58 @ ^ [X2: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.25/5.58 & ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.58 & ( ( sin_real @ X2 )
% 5.25/5.58 = Y6 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arcsin_def
% 5.25/5.58 thf(fact_9193_modulo__int__unfold,axiom,
% 5.25/5.58 ! [L2: int,K: int,N: nat,M: nat] :
% 5.25/5.58 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.25/5.58 = zero_zero_int )
% 5.25/5.58 | ( ( sgn_sgn_int @ K )
% 5.25/5.58 = zero_zero_int )
% 5.25/5.58 | ( N = zero_zero_nat ) )
% 5.25/5.58 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.25/5.58 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.25/5.58 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.25/5.58 = zero_zero_int )
% 5.25/5.58 | ( ( sgn_sgn_int @ K )
% 5.25/5.58 = zero_zero_int )
% 5.25/5.58 | ( N = zero_zero_nat ) )
% 5.25/5.58 => ( ( ( ( sgn_sgn_int @ K )
% 5.25/5.58 = ( sgn_sgn_int @ L2 ) )
% 5.25/5.58 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.25/5.58 = ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 5.25/5.58 & ( ( ( sgn_sgn_int @ K )
% 5.25/5.58 != ( sgn_sgn_int @ L2 ) )
% 5.25/5.58 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.25/5.58 = ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.25/5.58 @ ( minus_minus_int
% 5.25/5.58 @ ( semiri1314217659103216013at_int
% 5.25/5.58 @ ( times_times_nat @ N
% 5.25/5.58 @ ( zero_n2687167440665602831ol_nat
% 5.25/5.58 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 5.25/5.58 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % modulo_int_unfold
% 5.25/5.58 thf(fact_9194_csqrt__eq__1,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( ( csqrt @ Z )
% 5.25/5.58 = one_one_complex )
% 5.25/5.58 = ( Z = one_one_complex ) ) ).
% 5.25/5.58
% 5.25/5.58 % csqrt_eq_1
% 5.25/5.58 thf(fact_9195_csqrt__1,axiom,
% 5.25/5.58 ( ( csqrt @ one_one_complex )
% 5.25/5.58 = one_one_complex ) ).
% 5.25/5.58
% 5.25/5.58 % csqrt_1
% 5.25/5.58 thf(fact_9196_sgn__mult__dvd__iff,axiom,
% 5.25/5.58 ! [R2: int,L2: int,K: int] :
% 5.25/5.58 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L2 ) @ K )
% 5.25/5.58 = ( ( dvd_dvd_int @ L2 @ K )
% 5.25/5.58 & ( ( R2 = zero_zero_int )
% 5.25/5.58 => ( K = zero_zero_int ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sgn_mult_dvd_iff
% 5.25/5.58 thf(fact_9197_mult__sgn__dvd__iff,axiom,
% 5.25/5.58 ! [L2: int,R2: int,K: int] :
% 5.25/5.58 ( ( dvd_dvd_int @ ( times_times_int @ L2 @ ( sgn_sgn_int @ R2 ) ) @ K )
% 5.25/5.58 = ( ( dvd_dvd_int @ L2 @ K )
% 5.25/5.58 & ( ( R2 = zero_zero_int )
% 5.25/5.58 => ( K = zero_zero_int ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % mult_sgn_dvd_iff
% 5.25/5.58 thf(fact_9198_dvd__sgn__mult__iff,axiom,
% 5.25/5.58 ! [L2: int,R2: int,K: int] :
% 5.25/5.58 ( ( dvd_dvd_int @ L2 @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 5.25/5.58 = ( ( dvd_dvd_int @ L2 @ K )
% 5.25/5.58 | ( R2 = zero_zero_int ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % dvd_sgn_mult_iff
% 5.25/5.58 thf(fact_9199_dvd__mult__sgn__iff,axiom,
% 5.25/5.58 ! [L2: int,K: int,R2: int] :
% 5.25/5.58 ( ( dvd_dvd_int @ L2 @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 5.25/5.58 = ( ( dvd_dvd_int @ L2 @ K )
% 5.25/5.58 | ( R2 = zero_zero_int ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % dvd_mult_sgn_iff
% 5.25/5.58 thf(fact_9200_power2__csqrt,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.58 = Z ) ).
% 5.25/5.58
% 5.25/5.58 % power2_csqrt
% 5.25/5.58 thf(fact_9201_int__sgnE,axiom,
% 5.25/5.58 ! [K: int] :
% 5.25/5.58 ~ ! [N3: nat,L4: int] :
% 5.25/5.58 ( K
% 5.25/5.58 != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % int_sgnE
% 5.25/5.58 thf(fact_9202_div__eq__sgn__abs,axiom,
% 5.25/5.58 ! [K: int,L2: int] :
% 5.25/5.58 ( ( ( sgn_sgn_int @ K )
% 5.25/5.58 = ( sgn_sgn_int @ L2 ) )
% 5.25/5.58 => ( ( divide_divide_int @ K @ L2 )
% 5.25/5.58 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % div_eq_sgn_abs
% 5.25/5.58 thf(fact_9203_sgn__mod,axiom,
% 5.25/5.58 ! [L2: int,K: int] :
% 5.25/5.58 ( ( L2 != zero_zero_int )
% 5.25/5.58 => ( ~ ( dvd_dvd_int @ L2 @ K )
% 5.25/5.58 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L2 ) )
% 5.25/5.58 = ( sgn_sgn_int @ L2 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sgn_mod
% 5.25/5.58 thf(fact_9204_ln__neg__is__const,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.58 => ( ( ln_ln_real @ X3 )
% 5.25/5.58 = ( the_real
% 5.25/5.58 @ ^ [X2: real] : $false ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ln_neg_is_const
% 5.25/5.58 thf(fact_9205_zsgn__def,axiom,
% 5.25/5.58 ( sgn_sgn_int
% 5.25/5.58 = ( ^ [I3: int] : ( if_int @ ( I3 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % zsgn_def
% 5.25/5.58 thf(fact_9206_div__sgn__abs__cancel,axiom,
% 5.25/5.58 ! [V: int,K: int,L2: int] :
% 5.25/5.58 ( ( V != zero_zero_int )
% 5.25/5.58 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L2 ) ) )
% 5.25/5.58 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % div_sgn_abs_cancel
% 5.25/5.58 thf(fact_9207_div__dvd__sgn__abs,axiom,
% 5.25/5.58 ! [L2: int,K: int] :
% 5.25/5.58 ( ( dvd_dvd_int @ L2 @ K )
% 5.25/5.58 => ( ( divide_divide_int @ K @ L2 )
% 5.25/5.58 = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L2 ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % div_dvd_sgn_abs
% 5.25/5.58 thf(fact_9208_of__real__sqrt,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X3 ) )
% 5.25/5.58 = ( csqrt @ ( real_V4546457046886955230omplex @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % of_real_sqrt
% 5.25/5.58 thf(fact_9209_arccos__def,axiom,
% 5.25/5.58 ( arccos
% 5.25/5.58 = ( ^ [Y6: real] :
% 5.25/5.58 ( the_real
% 5.25/5.58 @ ^ [X2: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.25/5.58 & ( ord_less_eq_real @ X2 @ pi )
% 5.25/5.58 & ( ( cos_real @ X2 )
% 5.25/5.58 = Y6 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arccos_def
% 5.25/5.58 thf(fact_9210_eucl__rel__int__remainderI,axiom,
% 5.25/5.58 ! [R2: int,L2: int,K: int,Q2: int] :
% 5.25/5.58 ( ( ( sgn_sgn_int @ R2 )
% 5.25/5.58 = ( sgn_sgn_int @ L2 ) )
% 5.25/5.58 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L2 ) )
% 5.25/5.58 => ( ( K
% 5.25/5.58 = ( plus_plus_int @ ( times_times_int @ Q2 @ L2 ) @ R2 ) )
% 5.25/5.58 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % eucl_rel_int_remainderI
% 5.25/5.58 thf(fact_9211_eucl__rel__int_Osimps,axiom,
% 5.25/5.58 ( eucl_rel_int
% 5.25/5.58 = ( ^ [A1: int,A22: int,A32: product_prod_int_int] :
% 5.25/5.58 ( ? [K3: int] :
% 5.25/5.58 ( ( A1 = K3 )
% 5.25/5.58 & ( A22 = zero_zero_int )
% 5.25/5.58 & ( A32
% 5.25/5.58 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 5.25/5.58 | ? [L: int,K3: int,Q4: int] :
% 5.25/5.58 ( ( A1 = K3 )
% 5.25/5.58 & ( A22 = L )
% 5.25/5.58 & ( A32
% 5.25/5.58 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.25/5.58 & ( L != zero_zero_int )
% 5.25/5.58 & ( K3
% 5.25/5.58 = ( times_times_int @ Q4 @ L ) ) )
% 5.25/5.58 | ? [R5: int,L: int,K3: int,Q4: int] :
% 5.25/5.58 ( ( A1 = K3 )
% 5.25/5.58 & ( A22 = L )
% 5.25/5.58 & ( A32
% 5.25/5.58 = ( product_Pair_int_int @ Q4 @ R5 ) )
% 5.25/5.58 & ( ( sgn_sgn_int @ R5 )
% 5.25/5.58 = ( sgn_sgn_int @ L ) )
% 5.25/5.58 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L ) )
% 5.25/5.58 & ( K3
% 5.25/5.58 = ( plus_plus_int @ ( times_times_int @ Q4 @ L ) @ R5 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % eucl_rel_int.simps
% 5.25/5.58 thf(fact_9212_eucl__rel__int_Ocases,axiom,
% 5.25/5.58 ! [A12: int,A23: int,A33: product_prod_int_int] :
% 5.25/5.58 ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 5.25/5.58 => ( ( ( A23 = zero_zero_int )
% 5.25/5.58 => ( A33
% 5.25/5.58 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 5.25/5.58 => ( ! [Q3: int] :
% 5.25/5.58 ( ( A33
% 5.25/5.58 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 5.25/5.58 => ( ( A23 != zero_zero_int )
% 5.25/5.58 => ( A12
% 5.25/5.58 != ( times_times_int @ Q3 @ A23 ) ) ) )
% 5.25/5.58 => ~ ! [R3: int,Q3: int] :
% 5.25/5.58 ( ( A33
% 5.25/5.58 = ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.25/5.58 => ( ( ( sgn_sgn_int @ R3 )
% 5.25/5.58 = ( sgn_sgn_int @ A23 ) )
% 5.25/5.58 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A23 ) )
% 5.25/5.58 => ( A12
% 5.25/5.58 != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R3 ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % eucl_rel_int.cases
% 5.25/5.58 thf(fact_9213_div__noneq__sgn__abs,axiom,
% 5.25/5.58 ! [L2: int,K: int] :
% 5.25/5.58 ( ( L2 != zero_zero_int )
% 5.25/5.58 => ( ( ( sgn_sgn_int @ K )
% 5.25/5.58 != ( sgn_sgn_int @ L2 ) )
% 5.25/5.58 => ( ( divide_divide_int @ K @ L2 )
% 5.25/5.58 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) )
% 5.25/5.58 @ ( zero_n2684676970156552555ol_int
% 5.25/5.58 @ ~ ( dvd_dvd_int @ L2 @ K ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % div_noneq_sgn_abs
% 5.25/5.58 thf(fact_9214_pi__half,axiom,
% 5.25/5.58 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.25/5.58 = ( the_real
% 5.25/5.58 @ ^ [X2: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.25/5.58 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.25/5.58 & ( ( cos_real @ X2 )
% 5.25/5.58 = zero_zero_real ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % pi_half
% 5.25/5.58 thf(fact_9215_pi__def,axiom,
% 5.25/5.58 ( pi
% 5.25/5.58 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.25/5.58 @ ( the_real
% 5.25/5.58 @ ^ [X2: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.25/5.58 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.25/5.58 & ( ( cos_real @ X2 )
% 5.25/5.58 = zero_zero_real ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % pi_def
% 5.25/5.58 thf(fact_9216_divide__int__unfold,axiom,
% 5.25/5.58 ! [L2: int,K: int,N: nat,M: nat] :
% 5.25/5.58 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.25/5.58 = zero_zero_int )
% 5.25/5.58 | ( ( sgn_sgn_int @ K )
% 5.25/5.58 = zero_zero_int )
% 5.25/5.58 | ( N = zero_zero_nat ) )
% 5.25/5.58 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.25/5.58 = zero_zero_int ) )
% 5.25/5.58 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.25/5.58 = zero_zero_int )
% 5.25/5.58 | ( ( sgn_sgn_int @ K )
% 5.25/5.58 = zero_zero_int )
% 5.25/5.58 | ( N = zero_zero_nat ) )
% 5.25/5.58 => ( ( ( ( sgn_sgn_int @ K )
% 5.25/5.58 = ( sgn_sgn_int @ L2 ) )
% 5.25/5.58 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.25/5.58 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 5.25/5.58 & ( ( ( sgn_sgn_int @ K )
% 5.25/5.58 != ( sgn_sgn_int @ L2 ) )
% 5.25/5.58 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.25/5.58 = ( uminus_uminus_int
% 5.25/5.58 @ ( semiri1314217659103216013at_int
% 5.25/5.58 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 5.25/5.58 @ ( zero_n2687167440665602831ol_nat
% 5.25/5.58 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % divide_int_unfold
% 5.25/5.58 thf(fact_9217_modulo__int__def,axiom,
% 5.25/5.58 ( modulo_modulo_int
% 5.25/5.58 = ( ^ [K3: int,L: int] :
% 5.25/5.58 ( if_int @ ( L = zero_zero_int ) @ K3
% 5.25/5.58 @ ( if_int
% 5.25/5.58 @ ( ( sgn_sgn_int @ K3 )
% 5.25/5.58 = ( sgn_sgn_int @ L ) )
% 5.25/5.58 @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) )
% 5.25/5.58 @ ( times_times_int @ ( sgn_sgn_int @ L )
% 5.25/5.58 @ ( minus_minus_int
% 5.25/5.58 @ ( times_times_int @ ( abs_abs_int @ L )
% 5.25/5.58 @ ( zero_n2684676970156552555ol_int
% 5.25/5.58 @ ~ ( dvd_dvd_int @ L @ K3 ) ) )
% 5.25/5.58 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % modulo_int_def
% 5.25/5.58 thf(fact_9218_divide__int__def,axiom,
% 5.25/5.58 ( divide_divide_int
% 5.25/5.58 = ( ^ [K3: int,L: int] :
% 5.25/5.58 ( if_int @ ( L = zero_zero_int ) @ zero_zero_int
% 5.25/5.58 @ ( if_int
% 5.25/5.58 @ ( ( sgn_sgn_int @ K3 )
% 5.25/5.58 = ( sgn_sgn_int @ L ) )
% 5.25/5.58 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) )
% 5.25/5.58 @ ( uminus_uminus_int
% 5.25/5.58 @ ( semiri1314217659103216013at_int
% 5.25/5.58 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) )
% 5.25/5.58 @ ( zero_n2687167440665602831ol_nat
% 5.25/5.58 @ ~ ( dvd_dvd_int @ L @ K3 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % divide_int_def
% 5.25/5.58 thf(fact_9219_powr__int,axiom,
% 5.25/5.58 ! [X3: real,I2: int] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.25/5.58 => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ I2 ) )
% 5.25/5.58 = ( power_power_real @ X3 @ ( nat2 @ I2 ) ) ) )
% 5.25/5.58 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.25/5.58 => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ I2 ) )
% 5.25/5.58 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X3 @ ( nat2 @ ( uminus_uminus_int @ I2 ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_int
% 5.25/5.58 thf(fact_9220_or__int__unfold,axiom,
% 5.25/5.58 ( bit_se1409905431419307370or_int
% 5.25/5.58 = ( ^ [K3: int,L: int] :
% 5.25/5.58 ( if_int
% 5.25/5.58 @ ( ( K3
% 5.25/5.58 = ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.58 | ( L
% 5.25/5.58 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.25/5.58 @ ( uminus_uminus_int @ one_one_int )
% 5.25/5.58 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_int_unfold
% 5.25/5.58 thf(fact_9221_sgn__le__0__iff,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X3 ) @ zero_zero_real )
% 5.25/5.58 = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % sgn_le_0_iff
% 5.25/5.58 thf(fact_9222_zero__le__sgn__iff,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X3 ) )
% 5.25/5.58 = ( ord_less_eq_real @ zero_zero_real @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % zero_le_sgn_iff
% 5.25/5.58 thf(fact_9223_nat__numeral,axiom,
% 5.25/5.58 ! [K: num] :
% 5.25/5.58 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.25/5.58 = ( numeral_numeral_nat @ K ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_numeral
% 5.25/5.58 thf(fact_9224_or__nonnegative__int__iff,axiom,
% 5.25/5.58 ! [K: int,L2: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 5.25/5.58 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.58 & ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_nonnegative_int_iff
% 5.25/5.58 thf(fact_9225_or__negative__int__iff,axiom,
% 5.25/5.58 ! [K: int,L2: int] :
% 5.25/5.58 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ zero_zero_int )
% 5.25/5.58 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.25/5.58 | ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_negative_int_iff
% 5.25/5.58 thf(fact_9226_nat__1,axiom,
% 5.25/5.58 ( ( nat2 @ one_one_int )
% 5.25/5.58 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_1
% 5.25/5.58 thf(fact_9227_nat__le__0,axiom,
% 5.25/5.58 ! [Z: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.25/5.58 => ( ( nat2 @ Z )
% 5.25/5.58 = zero_zero_nat ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_le_0
% 5.25/5.58 thf(fact_9228_nat__0__iff,axiom,
% 5.25/5.58 ! [I2: int] :
% 5.25/5.58 ( ( ( nat2 @ I2 )
% 5.25/5.58 = zero_zero_nat )
% 5.25/5.58 = ( ord_less_eq_int @ I2 @ zero_zero_int ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_0_iff
% 5.25/5.58 thf(fact_9229_zless__nat__conj,axiom,
% 5.25/5.58 ! [W: int,Z: int] :
% 5.25/5.58 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.25/5.58 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.25/5.58 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % zless_nat_conj
% 5.25/5.58 thf(fact_9230_nat__neg__numeral,axiom,
% 5.25/5.58 ! [K: num] :
% 5.25/5.58 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.25/5.58 = zero_zero_nat ) ).
% 5.25/5.58
% 5.25/5.58 % nat_neg_numeral
% 5.25/5.58 thf(fact_9231_int__nat__eq,axiom,
% 5.25/5.58 ! [Z: int] :
% 5.25/5.58 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.58 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.25/5.58 = Z ) )
% 5.25/5.58 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.58 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.25/5.58 = zero_zero_int ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % int_nat_eq
% 5.25/5.58 thf(fact_9232_zero__less__nat__eq,axiom,
% 5.25/5.58 ! [Z: int] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.25/5.58 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.25/5.58
% 5.25/5.58 % zero_less_nat_eq
% 5.25/5.58 thf(fact_9233_diff__nat__numeral,axiom,
% 5.25/5.58 ! [V: num,V3: num] :
% 5.25/5.58 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 5.25/5.58 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % diff_nat_numeral
% 5.25/5.58 thf(fact_9234_nat__eq__numeral__power__cancel__iff,axiom,
% 5.25/5.58 ! [Y: int,X3: num,N: nat] :
% 5.25/5.58 ( ( ( nat2 @ Y )
% 5.25/5.58 = ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) )
% 5.25/5.58 = ( Y
% 5.25/5.58 = ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_eq_numeral_power_cancel_iff
% 5.25/5.58 thf(fact_9235_numeral__power__eq__nat__cancel__iff,axiom,
% 5.25/5.58 ! [X3: num,N: nat,Y: int] :
% 5.25/5.58 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N )
% 5.25/5.58 = ( nat2 @ Y ) )
% 5.25/5.58 = ( ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N )
% 5.25/5.58 = Y ) ) ).
% 5.25/5.58
% 5.25/5.58 % numeral_power_eq_nat_cancel_iff
% 5.25/5.58 thf(fact_9236_or__minus__numerals_I6_J,axiom,
% 5.25/5.58 ! [N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.25/5.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_minus_numerals(6)
% 5.25/5.58 thf(fact_9237_or__minus__numerals_I2_J,axiom,
% 5.25/5.58 ! [N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.25/5.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_minus_numerals(2)
% 5.25/5.58 thf(fact_9238_nat__ceiling__le__eq,axiom,
% 5.25/5.58 ! [X3: real,A: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X3 ) ) @ A )
% 5.25/5.58 = ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_ceiling_le_eq
% 5.25/5.58 thf(fact_9239_one__less__nat__eq,axiom,
% 5.25/5.58 ! [Z: int] :
% 5.25/5.58 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.25/5.58 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.25/5.58
% 5.25/5.58 % one_less_nat_eq
% 5.25/5.58 thf(fact_9240_nat__numeral__diff__1,axiom,
% 5.25/5.58 ! [V: num] :
% 5.25/5.58 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.25/5.58 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_numeral_diff_1
% 5.25/5.58 thf(fact_9241_nat__less__numeral__power__cancel__iff,axiom,
% 5.25/5.58 ! [A: int,X3: num,N: nat] :
% 5.25/5.58 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) )
% 5.25/5.58 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_less_numeral_power_cancel_iff
% 5.25/5.58 thf(fact_9242_numeral__power__less__nat__cancel__iff,axiom,
% 5.25/5.58 ! [X3: num,N: nat,A: int] :
% 5.25/5.58 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) @ ( nat2 @ A ) )
% 5.25/5.58 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 5.25/5.58
% 5.25/5.58 % numeral_power_less_nat_cancel_iff
% 5.25/5.58 thf(fact_9243_nat__le__numeral__power__cancel__iff,axiom,
% 5.25/5.58 ! [A: int,X3: num,N: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) )
% 5.25/5.58 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_le_numeral_power_cancel_iff
% 5.25/5.58 thf(fact_9244_numeral__power__le__nat__cancel__iff,axiom,
% 5.25/5.58 ! [X3: num,N: nat,A: int] :
% 5.25/5.58 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X3 ) @ N ) @ ( nat2 @ A ) )
% 5.25/5.58 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X3 ) @ N ) @ A ) ) ).
% 5.25/5.58
% 5.25/5.58 % numeral_power_le_nat_cancel_iff
% 5.25/5.58 thf(fact_9245_bit__or__int__iff,axiom,
% 5.25/5.58 ! [K: int,L2: int,N: nat] :
% 5.25/5.58 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ N )
% 5.25/5.58 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.25/5.58 | ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % bit_or_int_iff
% 5.25/5.58 thf(fact_9246_or__greater__eq,axiom,
% 5.25/5.58 ! [L2: int,K: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 5.25/5.58 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L2 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_greater_eq
% 5.25/5.58 thf(fact_9247_OR__lower,axiom,
% 5.25/5.58 ! [X3: int,Y: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.58 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X3 @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % OR_lower
% 5.25/5.58 thf(fact_9248_nat__numeral__as__int,axiom,
% 5.25/5.58 ( numeral_numeral_nat
% 5.25/5.58 = ( ^ [I3: num] : ( nat2 @ ( numeral_numeral_int @ I3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_numeral_as_int
% 5.25/5.58 thf(fact_9249_nat__mono,axiom,
% 5.25/5.58 ! [X3: int,Y: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ X3 @ Y )
% 5.25/5.58 => ( ord_less_eq_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_mono
% 5.25/5.58 thf(fact_9250_eq__nat__nat__iff,axiom,
% 5.25/5.58 ! [Z: int,Z6: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.58 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.25/5.58 => ( ( ( nat2 @ Z )
% 5.25/5.58 = ( nat2 @ Z6 ) )
% 5.25/5.58 = ( Z = Z6 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % eq_nat_nat_iff
% 5.25/5.58 thf(fact_9251_all__nat,axiom,
% 5.25/5.58 ( ( ^ [P5: nat > $o] :
% 5.25/5.58 ! [X7: nat] : ( P5 @ X7 ) )
% 5.25/5.58 = ( ^ [P6: nat > $o] :
% 5.25/5.58 ! [X2: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.25/5.58 => ( P6 @ ( nat2 @ X2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % all_nat
% 5.25/5.58 thf(fact_9252_ex__nat,axiom,
% 5.25/5.58 ( ( ^ [P5: nat > $o] :
% 5.25/5.58 ? [X7: nat] : ( P5 @ X7 ) )
% 5.25/5.58 = ( ^ [P6: nat > $o] :
% 5.25/5.58 ? [X2: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.25/5.58 & ( P6 @ ( nat2 @ X2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ex_nat
% 5.25/5.58 thf(fact_9253_nat__one__as__int,axiom,
% 5.25/5.58 ( one_one_nat
% 5.25/5.58 = ( nat2 @ one_one_int ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_one_as_int
% 5.25/5.58 thf(fact_9254_plus__and__or,axiom,
% 5.25/5.58 ! [X3: int,Y: int] :
% 5.25/5.58 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X3 @ Y ) @ ( bit_se1409905431419307370or_int @ X3 @ Y ) )
% 5.25/5.58 = ( plus_plus_int @ X3 @ Y ) ) ).
% 5.25/5.58
% 5.25/5.58 % plus_and_or
% 5.25/5.58 thf(fact_9255_unset__bit__nat__def,axiom,
% 5.25/5.58 ( bit_se4205575877204974255it_nat
% 5.25/5.58 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M6 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % unset_bit_nat_def
% 5.25/5.58 thf(fact_9256_nat__mask__eq,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.25/5.58 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_mask_eq
% 5.25/5.58 thf(fact_9257_nat__mono__iff,axiom,
% 5.25/5.58 ! [Z: int,W: int] :
% 5.25/5.58 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.25/5.58 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.25/5.58 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_mono_iff
% 5.25/5.58 thf(fact_9258_zless__nat__eq__int__zless,axiom,
% 5.25/5.58 ! [M: nat,Z: int] :
% 5.25/5.58 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.25/5.58 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.25/5.58
% 5.25/5.58 % zless_nat_eq_int_zless
% 5.25/5.58 thf(fact_9259_nat__le__iff,axiom,
% 5.25/5.58 ! [X3: int,N: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ ( nat2 @ X3 ) @ N )
% 5.25/5.58 = ( ord_less_eq_int @ X3 @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_le_iff
% 5.25/5.58 thf(fact_9260_int__eq__iff,axiom,
% 5.25/5.58 ! [M: nat,Z: int] :
% 5.25/5.58 ( ( ( semiri1314217659103216013at_int @ M )
% 5.25/5.58 = Z )
% 5.25/5.58 = ( ( M
% 5.25/5.58 = ( nat2 @ Z ) )
% 5.25/5.58 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % int_eq_iff
% 5.25/5.58 thf(fact_9261_nat__0__le,axiom,
% 5.25/5.58 ! [Z: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.58 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.25/5.58 = Z ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_0_le
% 5.25/5.58 thf(fact_9262_nat__int__add,axiom,
% 5.25/5.58 ! [A: nat,B: nat] :
% 5.25/5.58 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.25/5.58 = ( plus_plus_nat @ A @ B ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_int_add
% 5.25/5.58 thf(fact_9263_nat__abs__mult__distrib,axiom,
% 5.25/5.58 ! [W: int,Z: int] :
% 5.25/5.58 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 5.25/5.58 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_abs_mult_distrib
% 5.25/5.58 thf(fact_9264_and__nat__def,axiom,
% 5.25/5.58 ( bit_se727722235901077358nd_nat
% 5.25/5.58 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % and_nat_def
% 5.25/5.58 thf(fact_9265_nat__plus__as__int,axiom,
% 5.25/5.58 ( plus_plus_nat
% 5.25/5.58 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_plus_as_int
% 5.25/5.58 thf(fact_9266_nat__times__as__int,axiom,
% 5.25/5.58 ( times_times_nat
% 5.25/5.58 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_times_as_int
% 5.25/5.58 thf(fact_9267_real__nat__ceiling__ge,axiom,
% 5.25/5.58 ! [X3: real] : ( ord_less_eq_real @ X3 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_nat_ceiling_ge
% 5.25/5.58 thf(fact_9268_nat__div__as__int,axiom,
% 5.25/5.58 ( divide_divide_nat
% 5.25/5.58 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_div_as_int
% 5.25/5.58 thf(fact_9269_nat__mod__as__int,axiom,
% 5.25/5.58 ( modulo_modulo_nat
% 5.25/5.58 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_mod_as_int
% 5.25/5.58 thf(fact_9270_sgn__real__def,axiom,
% 5.25/5.58 ( sgn_sgn_real
% 5.25/5.58 = ( ^ [A3: real] : ( if_real @ ( A3 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A3 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sgn_real_def
% 5.25/5.58 thf(fact_9271_nat__less__eq__zless,axiom,
% 5.25/5.58 ! [W: int,Z: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.25/5.58 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.25/5.58 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_less_eq_zless
% 5.25/5.58 thf(fact_9272_nat__le__eq__zle,axiom,
% 5.25/5.58 ! [W: int,Z: int] :
% 5.25/5.58 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.25/5.58 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.25/5.58 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.25/5.58 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_le_eq_zle
% 5.25/5.58 thf(fact_9273_nat__eq__iff2,axiom,
% 5.25/5.58 ! [M: nat,W: int] :
% 5.25/5.58 ( ( M
% 5.25/5.58 = ( nat2 @ W ) )
% 5.25/5.58 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.25/5.58 => ( W
% 5.25/5.58 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.25/5.58 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.25/5.58 => ( M = zero_zero_nat ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_eq_iff2
% 5.25/5.58 thf(fact_9274_nat__eq__iff,axiom,
% 5.25/5.58 ! [W: int,M: nat] :
% 5.25/5.58 ( ( ( nat2 @ W )
% 5.25/5.58 = M )
% 5.25/5.58 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.25/5.58 => ( W
% 5.25/5.58 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.25/5.58 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.25/5.58 => ( M = zero_zero_nat ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_eq_iff
% 5.25/5.58 thf(fact_9275_le__nat__iff,axiom,
% 5.25/5.58 ! [K: int,N: nat] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.58 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 5.25/5.58 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % le_nat_iff
% 5.25/5.58 thf(fact_9276_nat__add__distrib,axiom,
% 5.25/5.58 ! [Z: int,Z6: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.58 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.25/5.58 => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 5.25/5.58 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_add_distrib
% 5.25/5.58 thf(fact_9277_nat__mult__distrib,axiom,
% 5.25/5.58 ! [Z: int,Z6: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.58 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 5.25/5.58 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_mult_distrib
% 5.25/5.58 thf(fact_9278_Suc__as__int,axiom,
% 5.25/5.58 ( suc
% 5.25/5.58 = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Suc_as_int
% 5.25/5.58 thf(fact_9279_nat__diff__distrib,axiom,
% 5.25/5.58 ! [Z6: int,Z: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.25/5.58 => ( ( ord_less_eq_int @ Z6 @ Z )
% 5.25/5.58 => ( ( nat2 @ ( minus_minus_int @ Z @ Z6 ) )
% 5.25/5.58 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_diff_distrib
% 5.25/5.58 thf(fact_9280_nat__diff__distrib_H,axiom,
% 5.25/5.58 ! [X3: int,Y: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.58 => ( ( nat2 @ ( minus_minus_int @ X3 @ Y ) )
% 5.25/5.58 = ( minus_minus_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_diff_distrib'
% 5.25/5.58 thf(fact_9281_nat__abs__triangle__ineq,axiom,
% 5.25/5.58 ! [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 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_abs_triangle_ineq
% 5.25/5.58 thf(fact_9282_nat__div__distrib,axiom,
% 5.25/5.58 ! [X3: int,Y: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.58 => ( ( nat2 @ ( divide_divide_int @ X3 @ Y ) )
% 5.25/5.58 = ( divide_divide_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_div_distrib
% 5.25/5.58 thf(fact_9283_nat__div__distrib_H,axiom,
% 5.25/5.58 ! [Y: int,X3: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.58 => ( ( nat2 @ ( divide_divide_int @ X3 @ Y ) )
% 5.25/5.58 = ( divide_divide_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_div_distrib'
% 5.25/5.58 thf(fact_9284_nat__floor__neg,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ X3 @ zero_zero_real )
% 5.25/5.58 => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 5.25/5.58 = zero_zero_nat ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_floor_neg
% 5.25/5.58 thf(fact_9285_nat__power__eq,axiom,
% 5.25/5.58 ! [Z: int,N: nat] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.58 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 5.25/5.58 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_power_eq
% 5.25/5.58 thf(fact_9286_nat__mod__distrib,axiom,
% 5.25/5.58 ! [X3: int,Y: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.58 => ( ( nat2 @ ( modulo_modulo_int @ X3 @ Y ) )
% 5.25/5.58 = ( modulo_modulo_nat @ ( nat2 @ X3 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_mod_distrib
% 5.25/5.58 thf(fact_9287_div__abs__eq__div__nat,axiom,
% 5.25/5.58 ! [K: int,L2: int] :
% 5.25/5.58 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 5.25/5.58 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % div_abs_eq_div_nat
% 5.25/5.58 thf(fact_9288_floor__eq3,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.25/5.58 => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 5.25/5.58 = N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % floor_eq3
% 5.25/5.58 thf(fact_9289_le__nat__floor,axiom,
% 5.25/5.58 ! [X3: nat,A: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X3 ) @ A )
% 5.25/5.58 => ( ord_less_eq_nat @ X3 @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % le_nat_floor
% 5.25/5.58 thf(fact_9290_mod__abs__eq__div__nat,axiom,
% 5.25/5.58 ! [K: int,L2: int] :
% 5.25/5.58 ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 5.25/5.58 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % mod_abs_eq_div_nat
% 5.25/5.58 thf(fact_9291_take__bit__nat__eq,axiom,
% 5.25/5.58 ! [K: int,N: nat] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.58 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 5.25/5.58 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % take_bit_nat_eq
% 5.25/5.58 thf(fact_9292_nat__take__bit__eq,axiom,
% 5.25/5.58 ! [K: int,N: nat] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.58 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.25/5.58 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_take_bit_eq
% 5.25/5.58 thf(fact_9293_bit__nat__iff,axiom,
% 5.25/5.58 ! [K: int,N: nat] :
% 5.25/5.58 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 5.25/5.58 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.58 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % bit_nat_iff
% 5.25/5.58 thf(fact_9294_nat__2,axiom,
% 5.25/5.58 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.58 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_2
% 5.25/5.58 thf(fact_9295_sgn__power__injE,axiom,
% 5.25/5.58 ! [A: real,N: nat,X3: real,B: real] :
% 5.25/5.58 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.25/5.58 = X3 )
% 5.25/5.58 => ( ( X3
% 5.25/5.58 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 5.25/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( A = B ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sgn_power_injE
% 5.25/5.58 thf(fact_9296_Suc__nat__eq__nat__zadd1,axiom,
% 5.25/5.58 ! [Z: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.58 => ( ( suc @ ( nat2 @ Z ) )
% 5.25/5.58 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Suc_nat_eq_nat_zadd1
% 5.25/5.58 thf(fact_9297_nat__less__iff,axiom,
% 5.25/5.58 ! [W: int,M: nat] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.25/5.58 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.25/5.58 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_less_iff
% 5.25/5.58 thf(fact_9298_nat__mult__distrib__neg,axiom,
% 5.25/5.58 ! [Z: int,Z6: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.25/5.58 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 5.25/5.58 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_mult_distrib_neg
% 5.25/5.58 thf(fact_9299_nat__abs__int__diff,axiom,
% 5.25/5.58 ! [A: nat,B: nat] :
% 5.25/5.58 ( ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.58 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.25/5.58 = ( minus_minus_nat @ B @ A ) ) )
% 5.25/5.58 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.25/5.58 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.25/5.58 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_abs_int_diff
% 5.25/5.58 thf(fact_9300_floor__eq4,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.25/5.58 => ( ( nat2 @ ( archim6058952711729229775r_real @ X3 ) )
% 5.25/5.58 = N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % floor_eq4
% 5.25/5.58 thf(fact_9301_nat__dvd__iff,axiom,
% 5.25/5.58 ! [Z: int,M: nat] :
% 5.25/5.58 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 5.25/5.58 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.58 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.25/5.58 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.58 => ( M = zero_zero_nat ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % nat_dvd_iff
% 5.25/5.58 thf(fact_9302_cis__Arg__unique,axiom,
% 5.25/5.58 ! [Z: complex,X3: real] :
% 5.25/5.58 ( ( ( sgn_sgn_complex @ Z )
% 5.25/5.58 = ( cis @ X3 ) )
% 5.25/5.58 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ pi )
% 5.25/5.58 => ( ( arg @ Z )
% 5.25/5.58 = X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cis_Arg_unique
% 5.25/5.58 thf(fact_9303_OR__upper,axiom,
% 5.25/5.58 ! [X3: int,N: nat,Y: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.58 => ( ( ord_less_int @ X3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.58 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.58 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X3 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % OR_upper
% 5.25/5.58 thf(fact_9304_Arg__correct,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( Z != zero_zero_complex )
% 5.25/5.58 => ( ( ( sgn_sgn_complex @ Z )
% 5.25/5.58 = ( cis @ ( arg @ Z ) ) )
% 5.25/5.58 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.25/5.58 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Arg_correct
% 5.25/5.58 thf(fact_9305_even__nat__iff,axiom,
% 5.25/5.58 ! [K: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.58 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.25/5.58 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % even_nat_iff
% 5.25/5.58 thf(fact_9306_or__int__rec,axiom,
% 5.25/5.58 ( bit_se1409905431419307370or_int
% 5.25/5.58 = ( ^ [K3: int,L: int] :
% 5.25/5.58 ( plus_plus_int
% 5.25/5.58 @ ( zero_n2684676970156552555ol_int
% 5.25/5.58 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.25/5.58 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.25/5.58 @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_int_rec
% 5.25/5.58 thf(fact_9307_powr__real__of__int,axiom,
% 5.25/5.58 ! [X3: real,N: int] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.25/5.58 => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N ) )
% 5.25/5.58 = ( power_power_real @ X3 @ ( nat2 @ N ) ) ) )
% 5.25/5.58 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 5.25/5.58 => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N ) )
% 5.25/5.58 = ( inverse_inverse_real @ ( power_power_real @ X3 @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % powr_real_of_int
% 5.25/5.58 thf(fact_9308_arctan__inverse,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( X3 != zero_zero_real )
% 5.25/5.58 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X3 ) )
% 5.25/5.58 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X3 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % arctan_inverse
% 5.25/5.58 thf(fact_9309_or__minus__numerals_I5_J,axiom,
% 5.25/5.58 ! [N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.25/5.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_minus_numerals(5)
% 5.25/5.58 thf(fact_9310_or__minus__numerals_I1_J,axiom,
% 5.25/5.58 ! [N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.25/5.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_minus_numerals(1)
% 5.25/5.58 thf(fact_9311_Arg__def,axiom,
% 5.25/5.58 ( arg
% 5.25/5.58 = ( ^ [Z5: complex] :
% 5.25/5.58 ( if_real @ ( Z5 = zero_zero_complex ) @ zero_zero_real
% 5.25/5.58 @ ( fChoice_real
% 5.25/5.58 @ ^ [A3: real] :
% 5.25/5.58 ( ( ( sgn_sgn_complex @ Z5 )
% 5.25/5.58 = ( cis @ A3 ) )
% 5.25/5.58 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 5.25/5.58 & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Arg_def
% 5.25/5.58 thf(fact_9312_cis__multiple__2pi,axiom,
% 5.25/5.58 ! [N: real] :
% 5.25/5.58 ( ( member_real @ N @ ring_1_Ints_real )
% 5.25/5.58 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.25/5.58 = one_one_complex ) ) ).
% 5.25/5.58
% 5.25/5.58 % cis_multiple_2pi
% 5.25/5.58 thf(fact_9313_or__nat__numerals_I2_J,axiom,
% 5.25/5.58 ! [Y: num] :
% 5.25/5.58 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.25/5.58 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_nat_numerals(2)
% 5.25/5.58 thf(fact_9314_or__nat__numerals_I4_J,axiom,
% 5.25/5.58 ! [X3: num] :
% 5.25/5.58 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 5.25/5.58 = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_nat_numerals(4)
% 5.25/5.58 thf(fact_9315_or__nat__numerals_I1_J,axiom,
% 5.25/5.58 ! [Y: num] :
% 5.25/5.58 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.25/5.58 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_nat_numerals(1)
% 5.25/5.58 thf(fact_9316_or__nat__numerals_I3_J,axiom,
% 5.25/5.58 ! [X3: num] :
% 5.25/5.58 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 5.25/5.58 = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_nat_numerals(3)
% 5.25/5.58 thf(fact_9317_or__minus__numerals_I8_J,axiom,
% 5.25/5.58 ! [N: num,M: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.25/5.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_minus_numerals(8)
% 5.25/5.58 thf(fact_9318_or__minus__numerals_I4_J,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.25/5.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_minus_numerals(4)
% 5.25/5.58 thf(fact_9319_or__minus__numerals_I7_J,axiom,
% 5.25/5.58 ! [N: num,M: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.25/5.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_minus_numerals(7)
% 5.25/5.58 thf(fact_9320_or__minus__numerals_I3_J,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.25/5.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_minus_numerals(3)
% 5.25/5.58 thf(fact_9321_or__not__num__neg_Osimps_I1_J,axiom,
% 5.25/5.58 ( ( bit_or_not_num_neg @ one @ one )
% 5.25/5.58 = one ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_num_neg.simps(1)
% 5.25/5.58 thf(fact_9322_or__not__num__neg_Osimps_I4_J,axiom,
% 5.25/5.58 ! [N: num] :
% 5.25/5.58 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 5.25/5.58 = ( bit0 @ one ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_num_neg.simps(4)
% 5.25/5.58 thf(fact_9323_or__not__num__neg_Osimps_I6_J,axiom,
% 5.25/5.58 ! [N: num,M: num] :
% 5.25/5.58 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 5.25/5.58 = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_num_neg.simps(6)
% 5.25/5.58 thf(fact_9324_or__not__num__neg_Osimps_I3_J,axiom,
% 5.25/5.58 ! [M: num] :
% 5.25/5.58 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.25/5.58 = ( bit1 @ M ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_num_neg.simps(3)
% 5.25/5.58 thf(fact_9325_or__not__num__neg_Osimps_I7_J,axiom,
% 5.25/5.58 ! [N: num] :
% 5.25/5.58 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 5.25/5.58 = one ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_num_neg.simps(7)
% 5.25/5.58 thf(fact_9326_or__not__num__neg_Osimps_I5_J,axiom,
% 5.25/5.58 ! [N: num,M: num] :
% 5.25/5.58 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 5.25/5.58 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_num_neg.simps(5)
% 5.25/5.58 thf(fact_9327_or__not__num__neg_Osimps_I9_J,axiom,
% 5.25/5.58 ! [N: num,M: num] :
% 5.25/5.58 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 5.25/5.58 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_num_neg.simps(9)
% 5.25/5.58 thf(fact_9328_or__nat__def,axiom,
% 5.25/5.58 ( bit_se1412395901928357646or_nat
% 5.25/5.58 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_nat_def
% 5.25/5.58 thf(fact_9329_or__not__num__neg_Osimps_I2_J,axiom,
% 5.25/5.58 ! [M: num] :
% 5.25/5.58 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.25/5.58 = ( bit1 @ M ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_num_neg.simps(2)
% 5.25/5.58 thf(fact_9330_or__not__num__neg_Osimps_I8_J,axiom,
% 5.25/5.58 ! [N: num,M: num] :
% 5.25/5.58 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 5.25/5.58 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_num_neg.simps(8)
% 5.25/5.58 thf(fact_9331_sin__times__pi__eq__0,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( ( sin_real @ ( times_times_real @ X3 @ pi ) )
% 5.25/5.58 = zero_zero_real )
% 5.25/5.58 = ( member_real @ X3 @ ring_1_Ints_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % sin_times_pi_eq_0
% 5.25/5.58 thf(fact_9332_or__not__num__neg_Oelims,axiom,
% 5.25/5.58 ! [X3: num,Xa2: num,Y: num] :
% 5.25/5.58 ( ( ( bit_or_not_num_neg @ X3 @ Xa2 )
% 5.25/5.58 = Y )
% 5.25/5.58 => ( ( ( X3 = one )
% 5.25/5.58 => ( ( Xa2 = one )
% 5.25/5.58 => ( Y != one ) ) )
% 5.25/5.58 => ( ( ( X3 = one )
% 5.25/5.58 => ! [M5: num] :
% 5.25/5.58 ( ( Xa2
% 5.25/5.58 = ( bit0 @ M5 ) )
% 5.25/5.58 => ( Y
% 5.25/5.58 != ( bit1 @ M5 ) ) ) )
% 5.25/5.58 => ( ( ( X3 = one )
% 5.25/5.58 => ! [M5: num] :
% 5.25/5.58 ( ( Xa2
% 5.25/5.58 = ( bit1 @ M5 ) )
% 5.25/5.58 => ( Y
% 5.25/5.58 != ( bit1 @ M5 ) ) ) )
% 5.25/5.58 => ( ( ? [N3: num] :
% 5.25/5.58 ( X3
% 5.25/5.58 = ( bit0 @ N3 ) )
% 5.25/5.58 => ( ( Xa2 = one )
% 5.25/5.58 => ( Y
% 5.25/5.58 != ( bit0 @ one ) ) ) )
% 5.25/5.58 => ( ! [N3: num] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( bit0 @ N3 ) )
% 5.25/5.58 => ! [M5: num] :
% 5.25/5.58 ( ( Xa2
% 5.25/5.58 = ( bit0 @ M5 ) )
% 5.25/5.58 => ( Y
% 5.25/5.58 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 5.25/5.58 => ( ! [N3: num] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( bit0 @ N3 ) )
% 5.25/5.58 => ! [M5: num] :
% 5.25/5.58 ( ( Xa2
% 5.25/5.58 = ( bit1 @ M5 ) )
% 5.25/5.58 => ( Y
% 5.25/5.58 != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 5.25/5.58 => ( ( ? [N3: num] :
% 5.25/5.58 ( X3
% 5.25/5.58 = ( bit1 @ N3 ) )
% 5.25/5.58 => ( ( Xa2 = one )
% 5.25/5.58 => ( Y != one ) ) )
% 5.25/5.58 => ( ! [N3: num] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( bit1 @ N3 ) )
% 5.25/5.58 => ! [M5: num] :
% 5.25/5.58 ( ( Xa2
% 5.25/5.58 = ( bit0 @ M5 ) )
% 5.25/5.58 => ( Y
% 5.25/5.58 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 5.25/5.58 => ~ ! [N3: num] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( bit1 @ N3 ) )
% 5.25/5.58 => ! [M5: num] :
% 5.25/5.58 ( ( Xa2
% 5.25/5.58 = ( bit1 @ M5 ) )
% 5.25/5.58 => ( Y
% 5.25/5.58 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_num_neg.elims
% 5.25/5.58 thf(fact_9333_sin__integer__2pi,axiom,
% 5.25/5.58 ! [N: real] :
% 5.25/5.58 ( ( member_real @ N @ ring_1_Ints_real )
% 5.25/5.58 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.25/5.58 = zero_zero_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % sin_integer_2pi
% 5.25/5.58 thf(fact_9334_cos__integer__2pi,axiom,
% 5.25/5.58 ! [N: real] :
% 5.25/5.58 ( ( member_real @ N @ ring_1_Ints_real )
% 5.25/5.58 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.25/5.58 = one_one_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % cos_integer_2pi
% 5.25/5.58 thf(fact_9335_Suc__0__or__eq,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.25/5.58 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Suc_0_or_eq
% 5.25/5.58 thf(fact_9336_or__Suc__0__eq,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.25/5.58 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_Suc_0_eq
% 5.25/5.58 thf(fact_9337_or__nat__rec,axiom,
% 5.25/5.58 ( bit_se1412395901928357646or_nat
% 5.25/5.58 = ( ^ [M6: nat,N2: nat] :
% 5.25/5.58 ( plus_plus_nat
% 5.25/5.58 @ ( zero_n2687167440665602831ol_nat
% 5.25/5.58 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.25/5.58 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.25/5.58 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_nat_rec
% 5.25/5.58 thf(fact_9338_or__nat__unfold,axiom,
% 5.25/5.58 ( bit_se1412395901928357646or_nat
% 5.25/5.58 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_nat_unfold
% 5.25/5.58 thf(fact_9339_Suc__0__xor__eq,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.25/5.58 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.58 @ ( zero_n2687167440665602831ol_nat
% 5.25/5.58 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Suc_0_xor_eq
% 5.25/5.58 thf(fact_9340_xor__Suc__0__eq,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.25/5.58 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.58 @ ( zero_n2687167440665602831ol_nat
% 5.25/5.58 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % xor_Suc_0_eq
% 5.25/5.58 thf(fact_9341_horner__sum__of__bool__2__less,axiom,
% 5.25/5.58 ! [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 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % horner_sum_of_bool_2_less
% 5.25/5.58 thf(fact_9342_xor__nat__numerals_I4_J,axiom,
% 5.25/5.58 ! [X3: num] :
% 5.25/5.58 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 5.25/5.58 = ( numeral_numeral_nat @ ( bit0 @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % xor_nat_numerals(4)
% 5.25/5.58 thf(fact_9343_xor__nat__numerals_I3_J,axiom,
% 5.25/5.58 ! [X3: num] :
% 5.25/5.58 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X3 ) ) @ ( suc @ zero_zero_nat ) )
% 5.25/5.58 = ( numeral_numeral_nat @ ( bit1 @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % xor_nat_numerals(3)
% 5.25/5.58 thf(fact_9344_xor__nat__numerals_I2_J,axiom,
% 5.25/5.58 ! [Y: num] :
% 5.25/5.58 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.25/5.58 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % xor_nat_numerals(2)
% 5.25/5.58 thf(fact_9345_xor__nat__numerals_I1_J,axiom,
% 5.25/5.58 ! [Y: num] :
% 5.25/5.58 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.25/5.58 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % xor_nat_numerals(1)
% 5.25/5.58 thf(fact_9346_xor__nat__unfold,axiom,
% 5.25/5.58 ( bit_se6528837805403552850or_nat
% 5.25/5.58 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % xor_nat_unfold
% 5.25/5.58 thf(fact_9347_xor__nat__rec,axiom,
% 5.25/5.58 ( bit_se6528837805403552850or_nat
% 5.25/5.58 = ( ^ [M6: nat,N2: nat] :
% 5.25/5.58 ( plus_plus_nat
% 5.25/5.58 @ ( zero_n2687167440665602831ol_nat
% 5.25/5.58 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 5.25/5.58 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.25/5.58 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % xor_nat_rec
% 5.25/5.58 thf(fact_9348_set__encode__def,axiom,
% 5.25/5.58 ( nat_set_encode
% 5.25/5.58 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % set_encode_def
% 5.25/5.58 thf(fact_9349_valid__eq,axiom,
% 5.25/5.58 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.25/5.58
% 5.25/5.58 % valid_eq
% 5.25/5.58 thf(fact_9350_valid__eq1,axiom,
% 5.25/5.58 ! [T: vEBT_VEBT,D: nat] :
% 5.25/5.58 ( ( vEBT_invar_vebt @ T @ D )
% 5.25/5.58 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 5.25/5.58
% 5.25/5.58 % valid_eq1
% 5.25/5.58 thf(fact_9351_valid__eq2,axiom,
% 5.25/5.58 ! [T: vEBT_VEBT,D: nat] :
% 5.25/5.58 ( ( vEBT_VEBT_valid @ T @ D )
% 5.25/5.58 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 5.25/5.58
% 5.25/5.58 % valid_eq2
% 5.25/5.58 thf(fact_9352_push__bit__nonnegative__int__iff,axiom,
% 5.25/5.58 ! [N: nat,K: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.25/5.58 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.25/5.58
% 5.25/5.58 % push_bit_nonnegative_int_iff
% 5.25/5.58 thf(fact_9353_push__bit__negative__int__iff,axiom,
% 5.25/5.58 ! [N: nat,K: int] :
% 5.25/5.58 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 5.25/5.58 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.25/5.58
% 5.25/5.58 % push_bit_negative_int_iff
% 5.25/5.58 thf(fact_9354_concat__bit__of__zero__1,axiom,
% 5.25/5.58 ! [N: nat,L2: int] :
% 5.25/5.58 ( ( bit_concat_bit @ N @ zero_zero_int @ L2 )
% 5.25/5.58 = ( bit_se545348938243370406it_int @ N @ L2 ) ) ).
% 5.25/5.58
% 5.25/5.58 % concat_bit_of_zero_1
% 5.25/5.58 thf(fact_9355_xor__nonnegative__int__iff,axiom,
% 5.25/5.58 ! [K: int,L2: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) )
% 5.25/5.58 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.58 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % xor_nonnegative_int_iff
% 5.25/5.58 thf(fact_9356_xor__negative__int__iff,axiom,
% 5.25/5.58 ! [K: int,L2: int] :
% 5.25/5.58 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ zero_zero_int )
% 5.25/5.58 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.25/5.58 != ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % xor_negative_int_iff
% 5.25/5.58 thf(fact_9357_push__bit__of__Suc__0,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.25/5.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.25/5.58
% 5.25/5.58 % push_bit_of_Suc_0
% 5.25/5.58 thf(fact_9358_flip__bit__int__def,axiom,
% 5.25/5.58 ( bit_se2159334234014336723it_int
% 5.25/5.58 = ( ^ [N2: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % flip_bit_int_def
% 5.25/5.58 thf(fact_9359_bit__xor__int__iff,axiom,
% 5.25/5.58 ! [K: int,L2: int,N: nat] :
% 5.25/5.58 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ N )
% 5.25/5.58 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.25/5.58 != ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % bit_xor_int_iff
% 5.25/5.58 thf(fact_9360_push__bit__nat__eq,axiom,
% 5.25/5.58 ! [N: nat,K: int] :
% 5.25/5.58 ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 5.25/5.58 = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % push_bit_nat_eq
% 5.25/5.58 thf(fact_9361_XOR__lower,axiom,
% 5.25/5.58 ! [X3: int,Y: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.58 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X3 @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % XOR_lower
% 5.25/5.58 thf(fact_9362_set__bit__nat__def,axiom,
% 5.25/5.58 ( bit_se7882103937844011126it_nat
% 5.25/5.58 = ( ^ [M6: nat,N2: nat] : ( bit_se1412395901928357646or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % set_bit_nat_def
% 5.25/5.58 thf(fact_9363_flip__bit__nat__def,axiom,
% 5.25/5.58 ( bit_se2161824704523386999it_nat
% 5.25/5.58 = ( ^ [M6: nat,N2: nat] : ( bit_se6528837805403552850or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % flip_bit_nat_def
% 5.25/5.58 thf(fact_9364_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.25/5.58 ! [Uu2: $o,Uv2: $o,D: nat] :
% 5.25/5.58 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D )
% 5.25/5.58 = ( D = one_one_nat ) ) ).
% 5.25/5.58
% 5.25/5.58 % VEBT_internal.valid'.simps(1)
% 5.25/5.58 thf(fact_9365_bit__push__bit__iff__int,axiom,
% 5.25/5.58 ! [M: nat,K: int,N: nat] :
% 5.25/5.58 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 5.25/5.58 = ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.58 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % bit_push_bit_iff_int
% 5.25/5.58 thf(fact_9366_xor__nat__def,axiom,
% 5.25/5.58 ( bit_se6528837805403552850or_nat
% 5.25/5.58 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % xor_nat_def
% 5.25/5.58 thf(fact_9367_bit__push__bit__iff__nat,axiom,
% 5.25/5.58 ! [M: nat,Q2: nat,N: nat] :
% 5.25/5.58 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 5.25/5.58 = ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.58 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % bit_push_bit_iff_nat
% 5.25/5.58 thf(fact_9368_concat__bit__eq,axiom,
% 5.25/5.58 ( bit_concat_bit
% 5.25/5.58 = ( ^ [N2: nat,K3: int,L: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % concat_bit_eq
% 5.25/5.58 thf(fact_9369_concat__bit__def,axiom,
% 5.25/5.58 ( bit_concat_bit
% 5.25/5.58 = ( ^ [N2: nat,K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % concat_bit_def
% 5.25/5.58 thf(fact_9370_set__bit__int__def,axiom,
% 5.25/5.58 ( bit_se7879613467334960850it_int
% 5.25/5.58 = ( ^ [N2: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % set_bit_int_def
% 5.25/5.58 thf(fact_9371_push__bit__int__def,axiom,
% 5.25/5.58 ( bit_se545348938243370406it_int
% 5.25/5.58 = ( ^ [N2: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % push_bit_int_def
% 5.25/5.58 thf(fact_9372_push__bit__nat__def,axiom,
% 5.25/5.58 ( bit_se547839408752420682it_nat
% 5.25/5.58 = ( ^ [N2: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % push_bit_nat_def
% 5.25/5.58 thf(fact_9373_push__bit__minus__one,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.58 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % push_bit_minus_one
% 5.25/5.58 thf(fact_9374_XOR__upper,axiom,
% 5.25/5.58 ! [X3: int,N: nat,Y: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.58 => ( ( ord_less_int @ X3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.58 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.58 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X3 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % XOR_upper
% 5.25/5.58 thf(fact_9375_xor__int__rec,axiom,
% 5.25/5.58 ( bit_se6526347334894502574or_int
% 5.25/5.58 = ( ^ [K3: int,L: int] :
% 5.25/5.58 ( plus_plus_int
% 5.25/5.58 @ ( zero_n2684676970156552555ol_int
% 5.25/5.58 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 5.25/5.58 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.25/5.58 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % xor_int_rec
% 5.25/5.58 thf(fact_9376_xor__int__unfold,axiom,
% 5.25/5.58 ( bit_se6526347334894502574or_int
% 5.25/5.58 = ( ^ [K3: int,L: int] :
% 5.25/5.58 ( if_int
% 5.25/5.58 @ ( K3
% 5.25/5.58 = ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.58 @ ( bit_ri7919022796975470100ot_int @ L )
% 5.25/5.58 @ ( if_int
% 5.25/5.58 @ ( L
% 5.25/5.58 = ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.58 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 5.25/5.58 @ ( if_int @ ( K3 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % xor_int_unfold
% 5.25/5.58 thf(fact_9377_set__encode__insert,axiom,
% 5.25/5.58 ! [A2: set_nat,N: nat] :
% 5.25/5.58 ( ( finite_finite_nat @ A2 )
% 5.25/5.58 => ( ~ ( member_nat @ N @ A2 )
% 5.25/5.58 => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 5.25/5.58 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % set_encode_insert
% 5.25/5.58 thf(fact_9378_set__vebt__finite,axiom,
% 5.25/5.58 ! [T: vEBT_VEBT,N: nat] :
% 5.25/5.58 ( ( vEBT_invar_vebt @ T @ N )
% 5.25/5.58 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % set_vebt_finite
% 5.25/5.58 thf(fact_9379_finite__atLeastAtMost,axiom,
% 5.25/5.58 ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_atLeastAtMost
% 5.25/5.58 thf(fact_9380_finite__lessThan,axiom,
% 5.25/5.58 ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_lessThan
% 5.25/5.58 thf(fact_9381_finite__atMost,axiom,
% 5.25/5.58 ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_atMost
% 5.25/5.58 thf(fact_9382_not__nonnegative__int__iff,axiom,
% 5.25/5.58 ! [K: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.25/5.58 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.25/5.58
% 5.25/5.58 % not_nonnegative_int_iff
% 5.25/5.58 thf(fact_9383_not__negative__int__iff,axiom,
% 5.25/5.58 ! [K: int] :
% 5.25/5.58 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.25/5.58 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.25/5.58
% 5.25/5.58 % not_negative_int_iff
% 5.25/5.58 thf(fact_9384_or__minus__minus__numerals,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.58 = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_minus_minus_numerals
% 5.25/5.58 thf(fact_9385_and__minus__minus__numerals,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.58 = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % and_minus_minus_numerals
% 5.25/5.58 thf(fact_9386_finite__less__ub,axiom,
% 5.25/5.58 ! [F: nat > nat,U: nat] :
% 5.25/5.58 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 5.25/5.58 => ( finite_finite_nat
% 5.25/5.58 @ ( collect_nat
% 5.25/5.58 @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ U ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_less_ub
% 5.25/5.58 thf(fact_9387_finite__nat__set__iff__bounded__le,axiom,
% 5.25/5.58 ( finite_finite_nat
% 5.25/5.58 = ( ^ [N9: set_nat] :
% 5.25/5.58 ? [M6: nat] :
% 5.25/5.58 ! [X2: nat] :
% 5.25/5.58 ( ( member_nat @ X2 @ N9 )
% 5.25/5.58 => ( ord_less_eq_nat @ X2 @ M6 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_nat_set_iff_bounded_le
% 5.25/5.58 thf(fact_9388_bit__not__int__iff,axiom,
% 5.25/5.58 ! [K: int,N: nat] :
% 5.25/5.58 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 5.25/5.58 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % bit_not_int_iff
% 5.25/5.58 thf(fact_9389_finite__nat__set__iff__bounded,axiom,
% 5.25/5.58 ( finite_finite_nat
% 5.25/5.58 = ( ^ [N9: set_nat] :
% 5.25/5.58 ? [M6: nat] :
% 5.25/5.58 ! [X2: nat] :
% 5.25/5.58 ( ( member_nat @ X2 @ N9 )
% 5.25/5.58 => ( ord_less_nat @ X2 @ M6 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_nat_set_iff_bounded
% 5.25/5.58 thf(fact_9390_bounded__nat__set__is__finite,axiom,
% 5.25/5.58 ! [N5: set_nat,N: nat] :
% 5.25/5.58 ( ! [X5: nat] :
% 5.25/5.58 ( ( member_nat @ X5 @ N5 )
% 5.25/5.58 => ( ord_less_nat @ X5 @ N ) )
% 5.25/5.58 => ( finite_finite_nat @ N5 ) ) ).
% 5.25/5.58
% 5.25/5.58 % bounded_nat_set_is_finite
% 5.25/5.58 thf(fact_9391_finite__M__bounded__by__nat,axiom,
% 5.25/5.58 ! [P: nat > $o,I2: nat] :
% 5.25/5.58 ( finite_finite_nat
% 5.25/5.58 @ ( collect_nat
% 5.25/5.58 @ ^ [K3: nat] :
% 5.25/5.58 ( ( P @ K3 )
% 5.25/5.58 & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_M_bounded_by_nat
% 5.25/5.58 thf(fact_9392_or__int__def,axiom,
% 5.25/5.58 ( bit_se1409905431419307370or_int
% 5.25/5.58 = ( ^ [K3: int,L: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_int_def
% 5.25/5.58 thf(fact_9393_not__int__def,axiom,
% 5.25/5.58 ( bit_ri7919022796975470100ot_int
% 5.25/5.58 = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % not_int_def
% 5.25/5.58 thf(fact_9394_and__not__numerals_I1_J,axiom,
% 5.25/5.58 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.25/5.58 = zero_zero_int ) ).
% 5.25/5.58
% 5.25/5.58 % and_not_numerals(1)
% 5.25/5.58 thf(fact_9395_or__not__numerals_I1_J,axiom,
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.25/5.58 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_numerals(1)
% 5.25/5.58 thf(fact_9396_unset__bit__int__def,axiom,
% 5.25/5.58 ( bit_se4203085406695923979it_int
% 5.25/5.58 = ( ^ [N2: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % unset_bit_int_def
% 5.25/5.58 thf(fact_9397_xor__int__def,axiom,
% 5.25/5.58 ( bit_se6526347334894502574or_int
% 5.25/5.58 = ( ^ [K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % xor_int_def
% 5.25/5.58 thf(fact_9398_finite__divisors__nat,axiom,
% 5.25/5.58 ! [M: nat] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.58 => ( finite_finite_nat
% 5.25/5.58 @ ( collect_nat
% 5.25/5.58 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_divisors_nat
% 5.25/5.58 thf(fact_9399_subset__eq__atLeast0__atMost__finite,axiom,
% 5.25/5.58 ! [N5: set_nat,N: nat] :
% 5.25/5.58 ( ( ord_less_eq_set_nat @ N5 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.25/5.58 => ( finite_finite_nat @ N5 ) ) ).
% 5.25/5.58
% 5.25/5.58 % subset_eq_atLeast0_atMost_finite
% 5.25/5.58 thf(fact_9400_not__int__div__2,axiom,
% 5.25/5.58 ! [K: int] :
% 5.25/5.58 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.58 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % not_int_div_2
% 5.25/5.58 thf(fact_9401_even__not__iff__int,axiom,
% 5.25/5.58 ! [K: int] :
% 5.25/5.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.25/5.58 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % even_not_iff_int
% 5.25/5.58 thf(fact_9402_and__not__numerals_I4_J,axiom,
% 5.25/5.58 ! [M: num] :
% 5.25/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.25/5.58 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % and_not_numerals(4)
% 5.25/5.58 thf(fact_9403_and__not__numerals_I2_J,axiom,
% 5.25/5.58 ! [N: num] :
% 5.25/5.58 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.25/5.58 = one_one_int ) ).
% 5.25/5.58
% 5.25/5.58 % and_not_numerals(2)
% 5.25/5.58 thf(fact_9404_or__not__numerals_I4_J,axiom,
% 5.25/5.58 ! [M: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.25/5.58 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_numerals(4)
% 5.25/5.58 thf(fact_9405_or__not__numerals_I2_J,axiom,
% 5.25/5.58 ! [N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.25/5.58 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_numerals(2)
% 5.25/5.58 thf(fact_9406_bit__minus__int__iff,axiom,
% 5.25/5.58 ! [K: int,N: nat] :
% 5.25/5.58 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 5.25/5.58 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 5.25/5.58
% 5.25/5.58 % bit_minus_int_iff
% 5.25/5.58 thf(fact_9407_numeral__or__not__num__eq,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 5.25/5.58 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % numeral_or_not_num_eq
% 5.25/5.58 thf(fact_9408_int__numeral__not__or__num__neg,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % int_numeral_not_or_num_neg
% 5.25/5.58 thf(fact_9409_int__numeral__or__not__num__neg,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % int_numeral_or_not_num_neg
% 5.25/5.58 thf(fact_9410_and__not__numerals_I5_J,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.25/5.58 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % and_not_numerals(5)
% 5.25/5.58 thf(fact_9411_and__not__numerals_I7_J,axiom,
% 5.25/5.58 ! [M: num] :
% 5.25/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.25/5.58 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % and_not_numerals(7)
% 5.25/5.58 thf(fact_9412_or__not__numerals_I3_J,axiom,
% 5.25/5.58 ! [N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.25/5.58 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_numerals(3)
% 5.25/5.58 thf(fact_9413_and__not__numerals_I3_J,axiom,
% 5.25/5.58 ! [N: num] :
% 5.25/5.58 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.25/5.58 = zero_zero_int ) ).
% 5.25/5.58
% 5.25/5.58 % and_not_numerals(3)
% 5.25/5.58 thf(fact_9414_or__not__numerals_I7_J,axiom,
% 5.25/5.58 ! [M: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.25/5.58 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_numerals(7)
% 5.25/5.58 thf(fact_9415_and__not__numerals_I6_J,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.25/5.58 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % and_not_numerals(6)
% 5.25/5.58 thf(fact_9416_and__not__numerals_I9_J,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.25/5.58 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % and_not_numerals(9)
% 5.25/5.58 thf(fact_9417_or__not__numerals_I6_J,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.25/5.58 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_numerals(6)
% 5.25/5.58 thf(fact_9418_even__set__encode__iff,axiom,
% 5.25/5.58 ! [A2: set_nat] :
% 5.25/5.58 ( ( finite_finite_nat @ A2 )
% 5.25/5.58 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 5.25/5.58 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % even_set_encode_iff
% 5.25/5.58 thf(fact_9419_or__not__numerals_I5_J,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.25/5.58 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_numerals(5)
% 5.25/5.58 thf(fact_9420_and__not__numerals_I8_J,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.25/5.58 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % and_not_numerals(8)
% 5.25/5.58 thf(fact_9421_or__not__numerals_I8_J,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.25/5.58 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_numerals(8)
% 5.25/5.58 thf(fact_9422_or__not__numerals_I9_J,axiom,
% 5.25/5.58 ! [M: num,N: num] :
% 5.25/5.58 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.25/5.58 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_numerals(9)
% 5.25/5.58 thf(fact_9423_not__int__rec,axiom,
% 5.25/5.58 ( bit_ri7919022796975470100ot_int
% 5.25/5.58 = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % not_int_rec
% 5.25/5.58 thf(fact_9424_finite__Collect__le__nat,axiom,
% 5.25/5.58 ! [K: nat] :
% 5.25/5.58 ( finite_finite_nat
% 5.25/5.58 @ ( collect_nat
% 5.25/5.58 @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_Collect_le_nat
% 5.25/5.58 thf(fact_9425_finite__Collect__less__nat,axiom,
% 5.25/5.58 ! [K: nat] :
% 5.25/5.58 ( finite_finite_nat
% 5.25/5.58 @ ( collect_nat
% 5.25/5.58 @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_Collect_less_nat
% 5.25/5.58 thf(fact_9426_finite__atLeastAtMost__int,axiom,
% 5.25/5.58 ! [L2: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L2 @ U ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_atLeastAtMost_int
% 5.25/5.58 thf(fact_9427_finite__interval__int1,axiom,
% 5.25/5.58 ! [A: int,B: int] :
% 5.25/5.58 ( finite_finite_int
% 5.25/5.58 @ ( collect_int
% 5.25/5.58 @ ^ [I3: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ A @ I3 )
% 5.25/5.58 & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_interval_int1
% 5.25/5.58 thf(fact_9428_finite__interval__int3,axiom,
% 5.25/5.58 ! [A: int,B: int] :
% 5.25/5.58 ( finite_finite_int
% 5.25/5.58 @ ( collect_int
% 5.25/5.58 @ ^ [I3: int] :
% 5.25/5.58 ( ( ord_less_int @ A @ I3 )
% 5.25/5.58 & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_interval_int3
% 5.25/5.58 thf(fact_9429_finite__interval__int2,axiom,
% 5.25/5.58 ! [A: int,B: int] :
% 5.25/5.58 ( finite_finite_int
% 5.25/5.58 @ ( collect_int
% 5.25/5.58 @ ^ [I3: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ A @ I3 )
% 5.25/5.58 & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_interval_int2
% 5.25/5.58 thf(fact_9430_finite__nth__roots,axiom,
% 5.25/5.58 ! [N: nat,C: complex] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( finite3207457112153483333omplex
% 5.25/5.58 @ ( collect_complex
% 5.25/5.58 @ ^ [Z5: complex] :
% 5.25/5.58 ( ( power_power_complex @ Z5 @ N )
% 5.25/5.58 = C ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_nth_roots
% 5.25/5.58 thf(fact_9431_finite__nat__iff__bounded__le,axiom,
% 5.25/5.58 ( finite_finite_nat
% 5.25/5.58 = ( ^ [S4: set_nat] :
% 5.25/5.58 ? [K3: nat] : ( ord_less_eq_set_nat @ S4 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_nat_iff_bounded_le
% 5.25/5.58 thf(fact_9432_bij__betw__nth__root__unity,axiom,
% 5.25/5.58 ! [C: complex,N: nat] :
% 5.25/5.58 ( ( C != zero_zero_complex )
% 5.25/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.25/5.58 @ ( collect_complex
% 5.25/5.58 @ ^ [Z5: complex] :
% 5.25/5.58 ( ( power_power_complex @ Z5 @ N )
% 5.25/5.58 = one_one_complex ) )
% 5.25/5.58 @ ( collect_complex
% 5.25/5.58 @ ^ [Z5: complex] :
% 5.25/5.58 ( ( power_power_complex @ Z5 @ N )
% 5.25/5.58 = C ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % bij_betw_nth_root_unity
% 5.25/5.58 thf(fact_9433_finite__nat__bounded,axiom,
% 5.25/5.58 ! [S3: set_nat] :
% 5.25/5.58 ( ( finite_finite_nat @ S3 )
% 5.25/5.58 => ? [K2: nat] : ( ord_less_eq_set_nat @ S3 @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_nat_bounded
% 5.25/5.58 thf(fact_9434_real__root__zero,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( root @ N @ zero_zero_real )
% 5.25/5.58 = zero_zero_real ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_zero
% 5.25/5.58 thf(fact_9435_real__root__Suc__0,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( root @ ( suc @ zero_zero_nat ) @ X3 )
% 5.25/5.58 = X3 ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_Suc_0
% 5.25/5.58 thf(fact_9436_root__0,axiom,
% 5.25/5.58 ! [X3: real] :
% 5.25/5.58 ( ( root @ zero_zero_nat @ X3 )
% 5.25/5.58 = zero_zero_real ) ).
% 5.25/5.58
% 5.25/5.58 % root_0
% 5.25/5.58 thf(fact_9437_real__root__eq__iff,axiom,
% 5.25/5.58 ! [N: nat,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ( root @ N @ X3 )
% 5.25/5.58 = ( root @ N @ Y ) )
% 5.25/5.58 = ( X3 = Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_eq_iff
% 5.25/5.58 thf(fact_9438_real__root__eq__0__iff,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ( root @ N @ X3 )
% 5.25/5.58 = zero_zero_real )
% 5.25/5.58 = ( X3 = zero_zero_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_eq_0_iff
% 5.25/5.58 thf(fact_9439_real__root__less__iff,axiom,
% 5.25/5.58 ! [N: nat,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_real @ ( root @ N @ X3 ) @ ( root @ N @ Y ) )
% 5.25/5.58 = ( ord_less_real @ X3 @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_less_iff
% 5.25/5.58 thf(fact_9440_real__root__le__iff,axiom,
% 5.25/5.58 ! [N: nat,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( root @ N @ X3 ) @ ( root @ N @ Y ) )
% 5.25/5.58 = ( ord_less_eq_real @ X3 @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_le_iff
% 5.25/5.58 thf(fact_9441_real__root__eq__1__iff,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ( root @ N @ X3 )
% 5.25/5.58 = one_one_real )
% 5.25/5.58 = ( X3 = one_one_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_eq_1_iff
% 5.25/5.58 thf(fact_9442_real__root__one,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( root @ N @ one_one_real )
% 5.25/5.58 = one_one_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_one
% 5.25/5.58 thf(fact_9443_real__root__gt__0__iff,axiom,
% 5.25/5.58 ! [N: nat,Y: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y ) )
% 5.25/5.58 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_gt_0_iff
% 5.25/5.58 thf(fact_9444_real__root__lt__0__iff,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_real @ ( root @ N @ X3 ) @ zero_zero_real )
% 5.25/5.58 = ( ord_less_real @ X3 @ zero_zero_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_lt_0_iff
% 5.25/5.58 thf(fact_9445_real__root__ge__0__iff,axiom,
% 5.25/5.58 ! [N: nat,Y: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y ) )
% 5.25/5.58 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_ge_0_iff
% 5.25/5.58 thf(fact_9446_real__root__le__0__iff,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( root @ N @ X3 ) @ zero_zero_real )
% 5.25/5.58 = ( ord_less_eq_real @ X3 @ zero_zero_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_le_0_iff
% 5.25/5.58 thf(fact_9447_real__root__lt__1__iff,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_real @ ( root @ N @ X3 ) @ one_one_real )
% 5.25/5.58 = ( ord_less_real @ X3 @ one_one_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_lt_1_iff
% 5.25/5.58 thf(fact_9448_real__root__gt__1__iff,axiom,
% 5.25/5.58 ! [N: nat,Y: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y ) )
% 5.25/5.58 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_gt_1_iff
% 5.25/5.58 thf(fact_9449_real__root__le__1__iff,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( root @ N @ X3 ) @ one_one_real )
% 5.25/5.58 = ( ord_less_eq_real @ X3 @ one_one_real ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_le_1_iff
% 5.25/5.58 thf(fact_9450_real__root__ge__1__iff,axiom,
% 5.25/5.58 ! [N: nat,Y: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y ) )
% 5.25/5.58 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_ge_1_iff
% 5.25/5.58 thf(fact_9451_real__root__pow__pos2,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( power_power_real @ ( root @ N @ X3 ) @ N )
% 5.25/5.58 = X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_pow_pos2
% 5.25/5.58 thf(fact_9452_real__root__minus,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( root @ N @ ( uminus_uminus_real @ X3 ) )
% 5.25/5.58 = ( uminus_uminus_real @ ( root @ N @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_minus
% 5.25/5.58 thf(fact_9453_real__root__inverse,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( root @ N @ ( inverse_inverse_real @ X3 ) )
% 5.25/5.58 = ( inverse_inverse_real @ ( root @ N @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_inverse
% 5.25/5.58 thf(fact_9454_real__root__divide,axiom,
% 5.25/5.58 ! [N: nat,X3: real,Y: real] :
% 5.25/5.58 ( ( root @ N @ ( divide_divide_real @ X3 @ Y ) )
% 5.25/5.58 = ( divide_divide_real @ ( root @ N @ X3 ) @ ( root @ N @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_divide
% 5.25/5.58 thf(fact_9455_real__root__commute,axiom,
% 5.25/5.58 ! [M: nat,N: nat,X3: real] :
% 5.25/5.58 ( ( root @ M @ ( root @ N @ X3 ) )
% 5.25/5.58 = ( root @ N @ ( root @ M @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_commute
% 5.25/5.58 thf(fact_9456_real__root__mult,axiom,
% 5.25/5.58 ! [N: nat,X3: real,Y: real] :
% 5.25/5.58 ( ( root @ N @ ( times_times_real @ X3 @ Y ) )
% 5.25/5.58 = ( times_times_real @ ( root @ N @ X3 ) @ ( root @ N @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_mult
% 5.25/5.58 thf(fact_9457_real__root__mult__exp,axiom,
% 5.25/5.58 ! [M: nat,N: nat,X3: real] :
% 5.25/5.58 ( ( root @ ( times_times_nat @ M @ N ) @ X3 )
% 5.25/5.58 = ( root @ M @ ( root @ N @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_mult_exp
% 5.25/5.58 thf(fact_9458_real__root__pos__pos__le,axiom,
% 5.25/5.58 ! [X3: real,N: nat] :
% 5.25/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_pos_pos_le
% 5.25/5.58 thf(fact_9459_real__root__less__mono,axiom,
% 5.25/5.58 ! [N: nat,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ Y )
% 5.25/5.58 => ( ord_less_real @ ( root @ N @ X3 ) @ ( root @ N @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_less_mono
% 5.25/5.58 thf(fact_9460_real__root__le__mono,axiom,
% 5.25/5.58 ! [N: nat,X3: real,Y: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ Y )
% 5.25/5.58 => ( ord_less_eq_real @ ( root @ N @ X3 ) @ ( root @ N @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_le_mono
% 5.25/5.58 thf(fact_9461_real__root__power,axiom,
% 5.25/5.58 ! [N: nat,X3: real,K: nat] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( root @ N @ ( power_power_real @ X3 @ K ) )
% 5.25/5.58 = ( power_power_real @ ( root @ N @ X3 ) @ K ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_power
% 5.25/5.58 thf(fact_9462_real__root__abs,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( root @ N @ ( abs_abs_real @ X3 ) )
% 5.25/5.58 = ( abs_abs_real @ ( root @ N @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_abs
% 5.25/5.58 thf(fact_9463_sgn__root,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( sgn_sgn_real @ ( root @ N @ X3 ) )
% 5.25/5.58 = ( sgn_sgn_real @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sgn_root
% 5.25/5.58 thf(fact_9464_real__root__gt__zero,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_gt_zero
% 5.25/5.58 thf(fact_9465_real__root__strict__decreasing,axiom,
% 5.25/5.58 ! [N: nat,N5: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_nat @ N @ N5 )
% 5.25/5.58 => ( ( ord_less_real @ one_one_real @ X3 )
% 5.25/5.58 => ( ord_less_real @ ( root @ N5 @ X3 ) @ ( root @ N @ X3 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_strict_decreasing
% 5.25/5.58 thf(fact_9466_sqrt__def,axiom,
% 5.25/5.58 ( sqrt
% 5.25/5.58 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sqrt_def
% 5.25/5.58 thf(fact_9467_root__abs__power,axiom,
% 5.25/5.58 ! [N: nat,Y: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y @ N ) ) )
% 5.25/5.58 = ( abs_abs_real @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % root_abs_power
% 5.25/5.58 thf(fact_9468_real__root__pos__pos,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_pos_pos
% 5.25/5.58 thf(fact_9469_real__root__strict__increasing,axiom,
% 5.25/5.58 ! [N: nat,N5: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_nat @ N @ N5 )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_real @ X3 @ one_one_real )
% 5.25/5.58 => ( ord_less_real @ ( root @ N @ X3 ) @ ( root @ N5 @ X3 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_strict_increasing
% 5.25/5.58 thf(fact_9470_real__root__decreasing,axiom,
% 5.25/5.58 ! [N: nat,N5: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.25/5.58 => ( ( ord_less_eq_real @ one_one_real @ X3 )
% 5.25/5.58 => ( ord_less_eq_real @ ( root @ N5 @ X3 ) @ ( root @ N @ X3 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_decreasing
% 5.25/5.58 thf(fact_9471_real__root__pow__pos,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( power_power_real @ ( root @ N @ X3 ) @ N )
% 5.25/5.58 = X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_pow_pos
% 5.25/5.58 thf(fact_9472_real__root__pos__unique,axiom,
% 5.25/5.58 ! [N: nat,Y: real,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.58 => ( ( ( power_power_real @ Y @ N )
% 5.25/5.58 = X3 )
% 5.25/5.58 => ( ( root @ N @ X3 )
% 5.25/5.58 = Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_pos_unique
% 5.25/5.58 thf(fact_9473_real__root__power__cancel,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( root @ N @ ( power_power_real @ X3 @ N ) )
% 5.25/5.58 = X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_power_cancel
% 5.25/5.58 thf(fact_9474_odd__real__root__pow,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.58 => ( ( power_power_real @ ( root @ N @ X3 ) @ N )
% 5.25/5.58 = X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % odd_real_root_pow
% 5.25/5.58 thf(fact_9475_odd__real__root__unique,axiom,
% 5.25/5.58 ! [N: nat,Y: real,X3: real] :
% 5.25/5.58 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.58 => ( ( ( power_power_real @ Y @ N )
% 5.25/5.58 = X3 )
% 5.25/5.58 => ( ( root @ N @ X3 )
% 5.25/5.58 = Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % odd_real_root_unique
% 5.25/5.58 thf(fact_9476_odd__real__root__power__cancel,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.58 => ( ( root @ N @ ( power_power_real @ X3 @ N ) )
% 5.25/5.58 = X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % odd_real_root_power_cancel
% 5.25/5.58 thf(fact_9477_real__root__increasing,axiom,
% 5.25/5.58 ! [N: nat,N5: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 5.25/5.58 => ( ord_less_eq_real @ ( root @ N @ X3 ) @ ( root @ N5 @ X3 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_root_increasing
% 5.25/5.58 thf(fact_9478_root__sgn__power,axiom,
% 5.25/5.58 ! [N: nat,Y: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) ) )
% 5.25/5.58 = Y ) ) ).
% 5.25/5.58
% 5.25/5.58 % root_sgn_power
% 5.25/5.58 thf(fact_9479_sgn__power__root,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X3 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X3 ) ) @ N ) )
% 5.25/5.58 = X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % sgn_power_root
% 5.25/5.58 thf(fact_9480_ln__root,axiom,
% 5.25/5.58 ! [N: nat,B: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.58 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 5.25/5.58 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ln_root
% 5.25/5.58 thf(fact_9481_log__root,axiom,
% 5.25/5.58 ! [N: nat,A: real,B: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.58 => ( ( log @ B @ ( root @ N @ A ) )
% 5.25/5.58 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_root
% 5.25/5.58 thf(fact_9482_log__base__root,axiom,
% 5.25/5.58 ! [N: nat,B: real,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.58 => ( ( log @ ( root @ N @ B ) @ X3 )
% 5.25/5.58 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X3 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % log_base_root
% 5.25/5.58 thf(fact_9483_split__root,axiom,
% 5.25/5.58 ! [P: real > $o,N: nat,X3: real] :
% 5.25/5.58 ( ( P @ ( root @ N @ X3 ) )
% 5.25/5.58 = ( ( ( N = zero_zero_nat )
% 5.25/5.58 => ( P @ zero_zero_real ) )
% 5.25/5.58 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ! [Y6: real] :
% 5.25/5.58 ( ( ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N ) )
% 5.25/5.58 = X3 )
% 5.25/5.58 => ( P @ Y6 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % split_root
% 5.25/5.58 thf(fact_9484_infinite__int__iff__unbounded__le,axiom,
% 5.25/5.58 ! [S3: set_int] :
% 5.25/5.58 ( ( ~ ( finite_finite_int @ S3 ) )
% 5.25/5.58 = ( ! [M6: int] :
% 5.25/5.58 ? [N2: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ M6 @ ( abs_abs_int @ N2 ) )
% 5.25/5.58 & ( member_int @ N2 @ S3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % infinite_int_iff_unbounded_le
% 5.25/5.58 thf(fact_9485_infinite__nat__iff__unbounded,axiom,
% 5.25/5.58 ! [S3: set_nat] :
% 5.25/5.58 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.25/5.58 = ( ! [M6: nat] :
% 5.25/5.58 ? [N2: nat] :
% 5.25/5.58 ( ( ord_less_nat @ M6 @ N2 )
% 5.25/5.58 & ( member_nat @ N2 @ S3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % infinite_nat_iff_unbounded
% 5.25/5.58 thf(fact_9486_unbounded__k__infinite,axiom,
% 5.25/5.58 ! [K: nat,S3: set_nat] :
% 5.25/5.58 ( ! [M5: nat] :
% 5.25/5.58 ( ( ord_less_nat @ K @ M5 )
% 5.25/5.58 => ? [N8: nat] :
% 5.25/5.58 ( ( ord_less_nat @ M5 @ N8 )
% 5.25/5.58 & ( member_nat @ N8 @ S3 ) ) )
% 5.25/5.58 => ~ ( finite_finite_nat @ S3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % unbounded_k_infinite
% 5.25/5.58 thf(fact_9487_infinite__nat__iff__unbounded__le,axiom,
% 5.25/5.58 ! [S3: set_nat] :
% 5.25/5.58 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.25/5.58 = ( ! [M6: nat] :
% 5.25/5.58 ? [N2: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.25/5.58 & ( member_nat @ N2 @ S3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % infinite_nat_iff_unbounded_le
% 5.25/5.58 thf(fact_9488_root__powr__inverse,axiom,
% 5.25/5.58 ! [N: nat,X3: real] :
% 5.25/5.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.58 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.58 => ( ( root @ N @ X3 )
% 5.25/5.58 = ( powr_real @ X3 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % root_powr_inverse
% 5.25/5.58 thf(fact_9489_finite__nat__iff__bounded,axiom,
% 5.25/5.58 ( finite_finite_nat
% 5.25/5.58 = ( ^ [S4: set_nat] :
% 5.25/5.58 ? [K3: nat] : ( ord_less_eq_set_nat @ S4 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_nat_iff_bounded
% 5.25/5.58 thf(fact_9490_or__not__num__neg_Opelims,axiom,
% 5.25/5.58 ! [X3: num,Xa2: num,Y: num] :
% 5.25/5.58 ( ( ( bit_or_not_num_neg @ X3 @ Xa2 )
% 5.25/5.58 = Y )
% 5.25/5.58 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X3 @ Xa2 ) )
% 5.25/5.58 => ( ( ( X3 = one )
% 5.25/5.58 => ( ( Xa2 = one )
% 5.25/5.58 => ( ( Y = one )
% 5.25/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.25/5.58 => ( ( ( X3 = one )
% 5.25/5.58 => ! [M5: num] :
% 5.25/5.58 ( ( Xa2
% 5.25/5.58 = ( bit0 @ M5 ) )
% 5.25/5.58 => ( ( Y
% 5.25/5.58 = ( bit1 @ M5 ) )
% 5.25/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M5 ) ) ) ) ) )
% 5.25/5.58 => ( ( ( X3 = one )
% 5.25/5.58 => ! [M5: num] :
% 5.25/5.58 ( ( Xa2
% 5.25/5.58 = ( bit1 @ M5 ) )
% 5.25/5.58 => ( ( Y
% 5.25/5.58 = ( bit1 @ M5 ) )
% 5.25/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M5 ) ) ) ) ) )
% 5.25/5.58 => ( ! [N3: num] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( bit0 @ N3 ) )
% 5.25/5.58 => ( ( Xa2 = one )
% 5.25/5.58 => ( ( Y
% 5.25/5.58 = ( bit0 @ one ) )
% 5.25/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 5.25/5.58 => ( ! [N3: num] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( bit0 @ N3 ) )
% 5.25/5.58 => ! [M5: num] :
% 5.25/5.58 ( ( Xa2
% 5.25/5.58 = ( bit0 @ M5 ) )
% 5.25/5.58 => ( ( Y
% 5.25/5.58 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.25/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M5 ) ) ) ) ) )
% 5.25/5.58 => ( ! [N3: num] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( bit0 @ N3 ) )
% 5.25/5.58 => ! [M5: num] :
% 5.25/5.58 ( ( Xa2
% 5.25/5.58 = ( bit1 @ M5 ) )
% 5.25/5.58 => ( ( Y
% 5.25/5.58 = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.25/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M5 ) ) ) ) ) )
% 5.25/5.58 => ( ! [N3: num] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( bit1 @ N3 ) )
% 5.25/5.58 => ( ( Xa2 = one )
% 5.25/5.58 => ( ( Y = one )
% 5.25/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 5.25/5.58 => ( ! [N3: num] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( bit1 @ N3 ) )
% 5.25/5.58 => ! [M5: num] :
% 5.25/5.58 ( ( Xa2
% 5.25/5.58 = ( bit0 @ M5 ) )
% 5.25/5.58 => ( ( Y
% 5.25/5.58 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.25/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M5 ) ) ) ) ) )
% 5.25/5.58 => ~ ! [N3: num] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( bit1 @ N3 ) )
% 5.25/5.58 => ! [M5: num] :
% 5.25/5.58 ( ( Xa2
% 5.25/5.58 = ( bit1 @ M5 ) )
% 5.25/5.58 => ( ( Y
% 5.25/5.58 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.25/5.58 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % or_not_num_neg.pelims
% 5.25/5.58 thf(fact_9491_int__ge__less__than__def,axiom,
% 5.25/5.58 ( int_ge_less_than
% 5.25/5.58 = ( ^ [D2: int] :
% 5.25/5.58 ( collec213857154873943460nt_int
% 5.25/5.58 @ ( produc4947309494688390418_int_o
% 5.25/5.58 @ ^ [Z7: int,Z5: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ D2 @ Z7 )
% 5.25/5.58 & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % int_ge_less_than_def
% 5.25/5.58 thf(fact_9492_int__ge__less__than2__def,axiom,
% 5.25/5.58 ( int_ge_less_than2
% 5.25/5.58 = ( ^ [D2: int] :
% 5.25/5.58 ( collec213857154873943460nt_int
% 5.25/5.58 @ ( produc4947309494688390418_int_o
% 5.25/5.58 @ ^ [Z7: int,Z5: int] :
% 5.25/5.58 ( ( ord_less_eq_int @ D2 @ Z5 )
% 5.25/5.58 & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % int_ge_less_than2_def
% 5.25/5.58 thf(fact_9493_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 5.25/5.58 ! [X3: vEBT_VEBT,Y: $o] :
% 5.25/5.58 ( ( ( vEBT_VEBT_minNull @ X3 )
% 5.25/5.58 = Y )
% 5.25/5.58 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X3 )
% 5.25/5.58 => ( ( ( X3
% 5.25/5.58 = ( vEBT_Leaf @ $false @ $false ) )
% 5.25/5.58 => ( Y
% 5.25/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.25/5.58 => ( ! [Uv: $o] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( vEBT_Leaf @ $true @ Uv ) )
% 5.25/5.58 => ( ~ Y
% 5.25/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv ) ) ) )
% 5.25/5.58 => ( ! [Uu: $o] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( vEBT_Leaf @ Uu @ $true ) )
% 5.25/5.58 => ( ~ Y
% 5.25/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu @ $true ) ) ) )
% 5.25/5.58 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) )
% 5.25/5.58 => ( Y
% 5.25/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) ) ) )
% 5.25/5.58 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.25/5.58 => ( ~ Y
% 5.25/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % VEBT_internal.minNull.pelims(1)
% 5.25/5.58 thf(fact_9494_Sum__Ico__nat,axiom,
% 5.25/5.58 ! [M: nat,N: nat] :
% 5.25/5.58 ( ( groups3542108847815614940at_nat
% 5.25/5.58 @ ^ [X2: nat] : X2
% 5.25/5.58 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.25/5.58 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Sum_Ico_nat
% 5.25/5.58 thf(fact_9495_finite__atLeastLessThan,axiom,
% 5.25/5.58 ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L2 @ U ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_atLeastLessThan
% 5.25/5.58 thf(fact_9496_atLeastLessThan__singleton,axiom,
% 5.25/5.58 ! [M: nat] :
% 5.25/5.58 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.25/5.58 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.25/5.58
% 5.25/5.58 % atLeastLessThan_singleton
% 5.25/5.58 thf(fact_9497_ex__nat__less__eq,axiom,
% 5.25/5.58 ! [N: nat,P: nat > $o] :
% 5.25/5.58 ( ( ? [M6: nat] :
% 5.25/5.58 ( ( ord_less_nat @ M6 @ N )
% 5.25/5.58 & ( P @ M6 ) ) )
% 5.25/5.58 = ( ? [X2: nat] :
% 5.25/5.58 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.25/5.58 & ( P @ X2 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % ex_nat_less_eq
% 5.25/5.58 thf(fact_9498_all__nat__less__eq,axiom,
% 5.25/5.58 ! [N: nat,P: nat > $o] :
% 5.25/5.58 ( ( ! [M6: nat] :
% 5.25/5.58 ( ( ord_less_nat @ M6 @ N )
% 5.25/5.58 => ( P @ M6 ) ) )
% 5.25/5.58 = ( ! [X2: nat] :
% 5.25/5.58 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.25/5.58 => ( P @ X2 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % all_nat_less_eq
% 5.25/5.58 thf(fact_9499_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.25/5.58 ! [L2: nat,U: nat] :
% 5.25/5.58 ( ( set_or4665077453230672383an_nat @ L2 @ ( suc @ U ) )
% 5.25/5.58 = ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 5.25/5.58
% 5.25/5.58 % atLeastLessThanSuc_atLeastAtMost
% 5.25/5.58 thf(fact_9500_lessThan__atLeast0,axiom,
% 5.25/5.58 ( set_ord_lessThan_nat
% 5.25/5.58 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 5.25/5.58
% 5.25/5.58 % lessThan_atLeast0
% 5.25/5.58 thf(fact_9501_atLeastLessThan0,axiom,
% 5.25/5.58 ! [M: nat] :
% 5.25/5.58 ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 5.25/5.58 = bot_bot_set_nat ) ).
% 5.25/5.58
% 5.25/5.58 % atLeastLessThan0
% 5.25/5.58 thf(fact_9502_atLeast0__lessThan__Suc,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.25/5.58 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % atLeast0_lessThan_Suc
% 5.25/5.58 thf(fact_9503_subset__eq__atLeast0__lessThan__finite,axiom,
% 5.25/5.58 ! [N5: set_nat,N: nat] :
% 5.25/5.58 ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.25/5.58 => ( finite_finite_nat @ N5 ) ) ).
% 5.25/5.58
% 5.25/5.58 % subset_eq_atLeast0_lessThan_finite
% 5.25/5.58 thf(fact_9504_atLeastLessThanSuc,axiom,
% 5.25/5.58 ! [M: nat,N: nat] :
% 5.25/5.58 ( ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.58 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.25/5.58 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 5.25/5.58 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.25/5.58 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.25/5.58 = bot_bot_set_nat ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % atLeastLessThanSuc
% 5.25/5.58 thf(fact_9505_prod__Suc__fact,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.25/5.58 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.25/5.58
% 5.25/5.58 % prod_Suc_fact
% 5.25/5.58 thf(fact_9506_prod__Suc__Suc__fact,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.25/5.58 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.25/5.58
% 5.25/5.58 % prod_Suc_Suc_fact
% 5.25/5.58 thf(fact_9507_atLeastLessThan__nat__numeral,axiom,
% 5.25/5.58 ! [M: nat,K: num] :
% 5.25/5.58 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.25/5.58 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.25/5.58 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.25/5.58 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.25/5.58 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.25/5.58 = bot_bot_set_nat ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % atLeastLessThan_nat_numeral
% 5.25/5.58 thf(fact_9508_atLeast1__lessThan__eq__remove0,axiom,
% 5.25/5.58 ! [N: nat] :
% 5.25/5.58 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.25/5.58 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % atLeast1_lessThan_eq_remove0
% 5.25/5.58 thf(fact_9509_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 5.25/5.58 ! [X3: vEBT_VEBT] :
% 5.25/5.58 ( ~ ( vEBT_VEBT_minNull @ X3 )
% 5.25/5.58 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X3 )
% 5.25/5.58 => ( ! [Uv: $o] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( vEBT_Leaf @ $true @ Uv ) )
% 5.25/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv ) ) )
% 5.25/5.58 => ( ! [Uu: $o] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( vEBT_Leaf @ Uu @ $true ) )
% 5.25/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu @ $true ) ) )
% 5.25/5.58 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.25/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % VEBT_internal.minNull.pelims(3)
% 5.25/5.58 thf(fact_9510_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 5.25/5.58 ! [X3: vEBT_VEBT] :
% 5.25/5.58 ( ( vEBT_VEBT_minNull @ X3 )
% 5.25/5.58 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X3 )
% 5.25/5.58 => ( ( ( X3
% 5.25/5.58 = ( vEBT_Leaf @ $false @ $false ) )
% 5.25/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 5.25/5.58 => ~ ! [Uw: nat,Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.25/5.58 ( ( X3
% 5.25/5.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) )
% 5.25/5.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % VEBT_internal.minNull.pelims(2)
% 5.25/5.58 thf(fact_9511_sum__power2,axiom,
% 5.25/5.58 ! [K: nat] :
% 5.25/5.58 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.25/5.58 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.25/5.58
% 5.25/5.58 % sum_power2
% 5.25/5.58 thf(fact_9512_Chebyshev__sum__upper__nat,axiom,
% 5.25/5.58 ! [N: nat,A: nat > nat,B: nat > nat] :
% 5.25/5.58 ( ! [I4: nat,J: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ I4 @ J )
% 5.25/5.58 => ( ( ord_less_nat @ J @ N )
% 5.25/5.58 => ( ord_less_eq_nat @ ( A @ I4 ) @ ( A @ J ) ) ) )
% 5.25/5.58 => ( ! [I4: nat,J: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ I4 @ J )
% 5.25/5.58 => ( ( ord_less_nat @ J @ N )
% 5.25/5.58 => ( ord_less_eq_nat @ ( B @ J ) @ ( B @ I4 ) ) ) )
% 5.25/5.58 => ( ord_less_eq_nat
% 5.25/5.58 @ ( times_times_nat @ N
% 5.25/5.58 @ ( groups3542108847815614940at_nat
% 5.25/5.58 @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( B @ I3 ) )
% 5.25/5.58 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.25/5.58 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Chebyshev_sum_upper_nat
% 5.25/5.58 thf(fact_9513_finite__atLeastLessThan__int,axiom,
% 5.25/5.58 ! [L2: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_atLeastLessThan_int
% 5.25/5.58 thf(fact_9514_finite__atLeastZeroLessThan__int,axiom,
% 5.25/5.58 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 5.25/5.58
% 5.25/5.58 % finite_atLeastZeroLessThan_int
% 5.25/5.58 thf(fact_9515_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 5.25/5.58 ! [L2: int,U: int] :
% 5.25/5.58 ( ( set_or4662586982721622107an_int @ L2 @ ( plus_plus_int @ U @ one_one_int ) )
% 5.25/5.58 = ( set_or1266510415728281911st_int @ L2 @ U ) ) ).
% 5.25/5.58
% 5.25/5.58 % atLeastLessThanPlusOne_atLeastAtMost_int
% 5.25/5.58 thf(fact_9516_Cauchy__iff2,axiom,
% 5.25/5.58 ( topolo4055970368930404560y_real
% 5.25/5.58 = ( ^ [X4: nat > real] :
% 5.25/5.58 ! [J3: nat] :
% 5.25/5.58 ? [M9: nat] :
% 5.25/5.58 ! [M6: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ M9 @ M6 )
% 5.25/5.58 => ! [N2: nat] :
% 5.25/5.58 ( ( ord_less_eq_nat @ M9 @ N2 )
% 5.25/5.58 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X4 @ M6 ) @ ( X4 @ N2 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Cauchy_iff2
% 5.25/5.58 thf(fact_9517_Code__Target__Int_Opositive__def,axiom,
% 5.25/5.58 code_Target_positive = numeral_numeral_int ).
% 5.25/5.58
% 5.25/5.58 % Code_Target_Int.positive_def
% 5.25/5.58 thf(fact_9518_divmod__step__integer__def,axiom,
% 5.25/5.58 ( unique4921790084139445826nteger
% 5.25/5.58 = ( ^ [L: num] :
% 5.25/5.58 ( produc6916734918728496179nteger
% 5.25/5.58 @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % divmod_step_integer_def
% 5.25/5.58 thf(fact_9519_csqrt_Osimps_I1_J,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( re @ ( csqrt @ Z ) )
% 5.25/5.58 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % csqrt.simps(1)
% 5.25/5.58 thf(fact_9520_complex__Re__numeral,axiom,
% 5.25/5.58 ! [V: num] :
% 5.25/5.58 ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 5.25/5.58 = ( numeral_numeral_real @ V ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_Re_numeral
% 5.25/5.58 thf(fact_9521_Re__divide__numeral,axiom,
% 5.25/5.58 ! [Z: complex,W: num] :
% 5.25/5.58 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.25/5.58 = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Re_divide_numeral
% 5.25/5.58 thf(fact_9522_sgn__integer__code,axiom,
% 5.25/5.58 ( sgn_sgn_Code_integer
% 5.25/5.58 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sgn_integer_code
% 5.25/5.58 thf(fact_9523_less__eq__integer__code_I1_J,axiom,
% 5.25/5.58 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 5.25/5.58
% 5.25/5.58 % less_eq_integer_code(1)
% 5.25/5.58 thf(fact_9524_divmod__integer_H__def,axiom,
% 5.25/5.58 ( unique3479559517661332726nteger
% 5.25/5.58 = ( ^ [M6: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % divmod_integer'_def
% 5.25/5.58 thf(fact_9525_plus__integer__code_I1_J,axiom,
% 5.25/5.58 ! [K: code_integer] :
% 5.25/5.58 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 5.25/5.58 = K ) ).
% 5.25/5.58
% 5.25/5.58 % plus_integer_code(1)
% 5.25/5.58 thf(fact_9526_plus__integer__code_I2_J,axiom,
% 5.25/5.58 ! [L2: code_integer] :
% 5.25/5.58 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.25/5.58 = L2 ) ).
% 5.25/5.58
% 5.25/5.58 % plus_integer_code(2)
% 5.25/5.58 thf(fact_9527_times__integer__code_I1_J,axiom,
% 5.25/5.58 ! [K: code_integer] :
% 5.25/5.58 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 5.25/5.58 = zero_z3403309356797280102nteger ) ).
% 5.25/5.58
% 5.25/5.58 % times_integer_code(1)
% 5.25/5.58 thf(fact_9528_times__integer__code_I2_J,axiom,
% 5.25/5.58 ! [L2: code_integer] :
% 5.25/5.58 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.25/5.58 = zero_z3403309356797280102nteger ) ).
% 5.25/5.58
% 5.25/5.58 % times_integer_code(2)
% 5.25/5.58 thf(fact_9529_complex__Re__le__cmod,axiom,
% 5.25/5.58 ! [X3: complex] : ( ord_less_eq_real @ ( re @ X3 ) @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_Re_le_cmod
% 5.25/5.58 thf(fact_9530_one__complex_Osimps_I1_J,axiom,
% 5.25/5.58 ( ( re @ one_one_complex )
% 5.25/5.58 = one_one_real ) ).
% 5.25/5.58
% 5.25/5.58 % one_complex.simps(1)
% 5.25/5.58 thf(fact_9531_plus__complex_Osimps_I1_J,axiom,
% 5.25/5.58 ! [X3: complex,Y: complex] :
% 5.25/5.58 ( ( re @ ( plus_plus_complex @ X3 @ Y ) )
% 5.25/5.58 = ( plus_plus_real @ ( re @ X3 ) @ ( re @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % plus_complex.simps(1)
% 5.25/5.58 thf(fact_9532_scaleR__complex_Osimps_I1_J,axiom,
% 5.25/5.58 ! [R2: real,X3: complex] :
% 5.25/5.58 ( ( re @ ( real_V2046097035970521341omplex @ R2 @ X3 ) )
% 5.25/5.58 = ( times_times_real @ R2 @ ( re @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % scaleR_complex.simps(1)
% 5.25/5.58 thf(fact_9533_abs__Re__le__cmod,axiom,
% 5.25/5.58 ! [X3: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X3 ) ) @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % abs_Re_le_cmod
% 5.25/5.58 thf(fact_9534_Re__csqrt,axiom,
% 5.25/5.58 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Re_csqrt
% 5.25/5.58 thf(fact_9535_one__integer_Orsp,axiom,
% 5.25/5.58 one_one_int = one_one_int ).
% 5.25/5.58
% 5.25/5.58 % one_integer.rsp
% 5.25/5.58 thf(fact_9536_one__natural_Orsp,axiom,
% 5.25/5.58 one_one_nat = one_one_nat ).
% 5.25/5.58
% 5.25/5.58 % one_natural.rsp
% 5.25/5.58 thf(fact_9537_cmod__plus__Re__le__0__iff,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 5.25/5.58 = ( ( re @ Z )
% 5.25/5.58 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cmod_plus_Re_le_0_iff
% 5.25/5.58 thf(fact_9538_cos__n__Re__cis__pow__n,axiom,
% 5.25/5.58 ! [N: nat,A: real] :
% 5.25/5.58 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.25/5.58 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cos_n_Re_cis_pow_n
% 5.25/5.58 thf(fact_9539_csqrt_Ocode,axiom,
% 5.25/5.58 ( csqrt
% 5.25/5.58 = ( ^ [Z5: complex] :
% 5.25/5.58 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.58 @ ( times_times_real
% 5.25/5.58 @ ( if_real
% 5.25/5.58 @ ( ( im @ Z5 )
% 5.25/5.58 = zero_zero_real )
% 5.25/5.58 @ one_one_real
% 5.25/5.58 @ ( sgn_sgn_real @ ( im @ Z5 ) ) )
% 5.25/5.58 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % csqrt.code
% 5.25/5.58 thf(fact_9540_csqrt_Osimps_I2_J,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( im @ ( csqrt @ Z ) )
% 5.25/5.58 = ( times_times_real
% 5.25/5.58 @ ( if_real
% 5.25/5.58 @ ( ( im @ Z )
% 5.25/5.58 = zero_zero_real )
% 5.25/5.58 @ one_one_real
% 5.25/5.58 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 5.25/5.58 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % csqrt.simps(2)
% 5.25/5.58 thf(fact_9541_integer__of__int__code,axiom,
% 5.25/5.58 ( code_integer_of_int
% 5.25/5.58 = ( ^ [K3: int] :
% 5.25/5.58 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.25/5.58 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.25/5.58 @ ( if_Code_integer
% 5.25/5.58 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.58 = zero_zero_int )
% 5.25/5.58 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.25/5.58 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % integer_of_int_code
% 5.25/5.58 thf(fact_9542_Im__power__real,axiom,
% 5.25/5.58 ! [X3: complex,N: nat] :
% 5.25/5.58 ( ( ( im @ X3 )
% 5.25/5.58 = zero_zero_real )
% 5.25/5.58 => ( ( im @ ( power_power_complex @ X3 @ N ) )
% 5.25/5.58 = zero_zero_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % Im_power_real
% 5.25/5.58 thf(fact_9543_complex__Im__numeral,axiom,
% 5.25/5.58 ! [V: num] :
% 5.25/5.58 ( ( im @ ( numera6690914467698888265omplex @ V ) )
% 5.25/5.58 = zero_zero_real ) ).
% 5.25/5.58
% 5.25/5.58 % complex_Im_numeral
% 5.25/5.58 thf(fact_9544_Im__i__times,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( im @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.25/5.58 = ( re @ Z ) ) ).
% 5.25/5.58
% 5.25/5.58 % Im_i_times
% 5.25/5.58 thf(fact_9545_Re__power__real,axiom,
% 5.25/5.58 ! [X3: complex,N: nat] :
% 5.25/5.58 ( ( ( im @ X3 )
% 5.25/5.58 = zero_zero_real )
% 5.25/5.58 => ( ( re @ ( power_power_complex @ X3 @ N ) )
% 5.25/5.58 = ( power_power_real @ ( re @ X3 ) @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Re_power_real
% 5.25/5.58 thf(fact_9546_Re__i__times,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( re @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.25/5.58 = ( uminus_uminus_real @ ( im @ Z ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Re_i_times
% 5.25/5.58 thf(fact_9547_Im__divide__numeral,axiom,
% 5.25/5.58 ! [Z: complex,W: num] :
% 5.25/5.58 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.25/5.58 = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Im_divide_numeral
% 5.25/5.58 thf(fact_9548_csqrt__of__real__nonneg,axiom,
% 5.25/5.58 ! [X3: complex] :
% 5.25/5.58 ( ( ( im @ X3 )
% 5.25/5.58 = zero_zero_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X3 ) )
% 5.25/5.58 => ( ( csqrt @ X3 )
% 5.25/5.58 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X3 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % csqrt_of_real_nonneg
% 5.25/5.58 thf(fact_9549_csqrt__minus,axiom,
% 5.25/5.58 ! [X3: complex] :
% 5.25/5.58 ( ( ( ord_less_real @ ( im @ X3 ) @ zero_zero_real )
% 5.25/5.58 | ( ( ( im @ X3 )
% 5.25/5.58 = zero_zero_real )
% 5.25/5.58 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X3 ) ) ) )
% 5.25/5.58 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X3 ) )
% 5.25/5.58 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X3 ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % csqrt_minus
% 5.25/5.58 thf(fact_9550_csqrt__of__real__nonpos,axiom,
% 5.25/5.58 ! [X3: complex] :
% 5.25/5.58 ( ( ( im @ X3 )
% 5.25/5.58 = zero_zero_real )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( re @ X3 ) @ zero_zero_real )
% 5.25/5.58 => ( ( csqrt @ X3 )
% 5.25/5.58 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X3 ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % csqrt_of_real_nonpos
% 5.25/5.58 thf(fact_9551_modulo__integer_Oabs__eq,axiom,
% 5.25/5.58 ! [Xa2: int,X3: int] :
% 5.25/5.58 ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X3 ) )
% 5.25/5.58 = ( code_integer_of_int @ ( modulo_modulo_int @ Xa2 @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % modulo_integer.abs_eq
% 5.25/5.58 thf(fact_9552_imaginary__unit_Osimps_I2_J,axiom,
% 5.25/5.58 ( ( im @ imaginary_unit )
% 5.25/5.58 = one_one_real ) ).
% 5.25/5.58
% 5.25/5.58 % imaginary_unit.simps(2)
% 5.25/5.58 thf(fact_9553_one__complex_Osimps_I2_J,axiom,
% 5.25/5.58 ( ( im @ one_one_complex )
% 5.25/5.58 = zero_zero_real ) ).
% 5.25/5.58
% 5.25/5.58 % one_complex.simps(2)
% 5.25/5.58 thf(fact_9554_plus__integer_Oabs__eq,axiom,
% 5.25/5.58 ! [Xa2: int,X3: int] :
% 5.25/5.58 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X3 ) )
% 5.25/5.58 = ( code_integer_of_int @ ( plus_plus_int @ Xa2 @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % plus_integer.abs_eq
% 5.25/5.58 thf(fact_9555_times__integer_Oabs__eq,axiom,
% 5.25/5.58 ! [Xa2: int,X3: int] :
% 5.25/5.58 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X3 ) )
% 5.25/5.58 = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % times_integer.abs_eq
% 5.25/5.58 thf(fact_9556_one__integer__def,axiom,
% 5.25/5.58 ( one_one_Code_integer
% 5.25/5.58 = ( code_integer_of_int @ one_one_int ) ) ).
% 5.25/5.58
% 5.25/5.58 % one_integer_def
% 5.25/5.58 thf(fact_9557_less__eq__integer_Oabs__eq,axiom,
% 5.25/5.58 ! [Xa2: int,X3: int] :
% 5.25/5.58 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X3 ) )
% 5.25/5.58 = ( ord_less_eq_int @ Xa2 @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % less_eq_integer.abs_eq
% 5.25/5.58 thf(fact_9558_plus__complex_Osimps_I2_J,axiom,
% 5.25/5.58 ! [X3: complex,Y: complex] :
% 5.25/5.58 ( ( im @ ( plus_plus_complex @ X3 @ Y ) )
% 5.25/5.58 = ( plus_plus_real @ ( im @ X3 ) @ ( im @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % plus_complex.simps(2)
% 5.25/5.58 thf(fact_9559_scaleR__complex_Osimps_I2_J,axiom,
% 5.25/5.58 ! [R2: real,X3: complex] :
% 5.25/5.58 ( ( im @ ( real_V2046097035970521341omplex @ R2 @ X3 ) )
% 5.25/5.58 = ( times_times_real @ R2 @ ( im @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % scaleR_complex.simps(2)
% 5.25/5.58 thf(fact_9560_abs__Im__le__cmod,axiom,
% 5.25/5.58 ! [X3: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X3 ) ) @ ( real_V1022390504157884413omplex @ X3 ) ) ).
% 5.25/5.58
% 5.25/5.58 % abs_Im_le_cmod
% 5.25/5.58 thf(fact_9561_times__complex_Osimps_I2_J,axiom,
% 5.25/5.58 ! [X3: complex,Y: complex] :
% 5.25/5.58 ( ( im @ ( times_times_complex @ X3 @ Y ) )
% 5.25/5.58 = ( plus_plus_real @ ( times_times_real @ ( re @ X3 ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X3 ) @ ( re @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % times_complex.simps(2)
% 5.25/5.58 thf(fact_9562_cmod__Re__le__iff,axiom,
% 5.25/5.58 ! [X3: complex,Y: complex] :
% 5.25/5.58 ( ( ( im @ X3 )
% 5.25/5.58 = ( im @ Y ) )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y ) )
% 5.25/5.58 = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X3 ) ) @ ( abs_abs_real @ ( re @ Y ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cmod_Re_le_iff
% 5.25/5.58 thf(fact_9563_cmod__Im__le__iff,axiom,
% 5.25/5.58 ! [X3: complex,Y: complex] :
% 5.25/5.58 ( ( ( re @ X3 )
% 5.25/5.58 = ( re @ Y ) )
% 5.25/5.58 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X3 ) @ ( real_V1022390504157884413omplex @ Y ) )
% 5.25/5.58 = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X3 ) ) @ ( abs_abs_real @ ( im @ Y ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cmod_Im_le_iff
% 5.25/5.58 thf(fact_9564_times__complex_Osimps_I1_J,axiom,
% 5.25/5.58 ! [X3: complex,Y: complex] :
% 5.25/5.58 ( ( re @ ( times_times_complex @ X3 @ Y ) )
% 5.25/5.58 = ( minus_minus_real @ ( times_times_real @ ( re @ X3 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X3 ) @ ( im @ Y ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % times_complex.simps(1)
% 5.25/5.58 thf(fact_9565_plus__complex_Ocode,axiom,
% 5.25/5.58 ( plus_plus_complex
% 5.25/5.58 = ( ^ [X2: complex,Y6: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X2 ) @ ( re @ Y6 ) ) @ ( plus_plus_real @ ( im @ X2 ) @ ( im @ Y6 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % plus_complex.code
% 5.25/5.58 thf(fact_9566_scaleR__complex_Ocode,axiom,
% 5.25/5.58 ( real_V2046097035970521341omplex
% 5.25/5.58 = ( ^ [R5: real,X2: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X2 ) ) @ ( times_times_real @ R5 @ ( im @ X2 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % scaleR_complex.code
% 5.25/5.58 thf(fact_9567_csqrt__principal,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 5.25/5.58 | ( ( ( re @ ( csqrt @ Z ) )
% 5.25/5.58 = zero_zero_real )
% 5.25/5.58 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % csqrt_principal
% 5.25/5.58 thf(fact_9568_cmod__le,axiom,
% 5.25/5.58 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cmod_le
% 5.25/5.58 thf(fact_9569_sin__n__Im__cis__pow__n,axiom,
% 5.25/5.58 ! [N: nat,A: real] :
% 5.25/5.58 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.25/5.58 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % sin_n_Im_cis_pow_n
% 5.25/5.58 thf(fact_9570_Re__exp,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( re @ ( exp_complex @ Z ) )
% 5.25/5.58 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Re_exp
% 5.25/5.58 thf(fact_9571_Im__exp,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( im @ ( exp_complex @ Z ) )
% 5.25/5.58 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Im_exp
% 5.25/5.58 thf(fact_9572_complex__eq,axiom,
% 5.25/5.58 ! [A: complex] :
% 5.25/5.58 ( A
% 5.25/5.58 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_eq
% 5.25/5.58 thf(fact_9573_times__complex_Ocode,axiom,
% 5.25/5.58 ( times_times_complex
% 5.25/5.58 = ( ^ [X2: complex,Y6: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y6 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y6 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y6 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % times_complex.code
% 5.25/5.58 thf(fact_9574_exp__eq__polar,axiom,
% 5.25/5.58 ( exp_complex
% 5.25/5.58 = ( ^ [Z5: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z5 ) ) ) @ ( cis @ ( im @ Z5 ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % exp_eq_polar
% 5.25/5.58 thf(fact_9575_cmod__power2,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.58 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % cmod_power2
% 5.25/5.58 thf(fact_9576_Im__power2,axiom,
% 5.25/5.58 ! [X3: complex] :
% 5.25/5.58 ( ( im @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.58 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X3 ) ) @ ( im @ X3 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Im_power2
% 5.25/5.58 thf(fact_9577_Re__power2,axiom,
% 5.25/5.58 ! [X3: complex] :
% 5.25/5.58 ( ( re @ ( power_power_complex @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.58 = ( minus_minus_real @ ( power_power_real @ ( re @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Re_power2
% 5.25/5.58 thf(fact_9578_complex__eq__0,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( Z = zero_zero_complex )
% 5.25/5.58 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.58 = zero_zero_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_eq_0
% 5.25/5.58 thf(fact_9579_norm__complex__def,axiom,
% 5.25/5.58 ( real_V1022390504157884413omplex
% 5.25/5.58 = ( ^ [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 ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % norm_complex_def
% 5.25/5.58 thf(fact_9580_inverse__complex_Osimps_I1_J,axiom,
% 5.25/5.58 ! [X3: complex] :
% 5.25/5.58 ( ( re @ ( invers8013647133539491842omplex @ X3 ) )
% 5.25/5.58 = ( divide_divide_real @ ( re @ X3 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % inverse_complex.simps(1)
% 5.25/5.58 thf(fact_9581_complex__neq__0,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( Z != zero_zero_complex )
% 5.25/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_neq_0
% 5.25/5.58 thf(fact_9582_Re__divide,axiom,
% 5.25/5.58 ! [X3: complex,Y: complex] :
% 5.25/5.58 ( ( re @ ( divide1717551699836669952omplex @ X3 @ Y ) )
% 5.25/5.58 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X3 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X3 ) @ ( 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 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Re_divide
% 5.25/5.58 thf(fact_9583_csqrt__square,axiom,
% 5.25/5.58 ! [B: complex] :
% 5.25/5.58 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 5.25/5.58 | ( ( ( re @ B )
% 5.25/5.58 = zero_zero_real )
% 5.25/5.58 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 5.25/5.58 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.58 = B ) ) ).
% 5.25/5.58
% 5.25/5.58 % csqrt_square
% 5.25/5.58 thf(fact_9584_csqrt__unique,axiom,
% 5.25/5.58 ! [W: complex,Z: complex] :
% 5.25/5.58 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.58 = Z )
% 5.25/5.58 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 5.25/5.58 | ( ( ( re @ W )
% 5.25/5.58 = zero_zero_real )
% 5.25/5.58 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 5.25/5.58 => ( ( csqrt @ Z )
% 5.25/5.58 = W ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % csqrt_unique
% 5.25/5.58 thf(fact_9585_inverse__complex_Osimps_I2_J,axiom,
% 5.25/5.58 ! [X3: complex] :
% 5.25/5.58 ( ( im @ ( invers8013647133539491842omplex @ X3 ) )
% 5.25/5.58 = ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X3 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % inverse_complex.simps(2)
% 5.25/5.58 thf(fact_9586_Im__divide,axiom,
% 5.25/5.58 ! [X3: complex,Y: complex] :
% 5.25/5.58 ( ( im @ ( divide1717551699836669952omplex @ X3 @ Y ) )
% 5.25/5.58 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X3 ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X3 ) @ ( 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 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Im_divide
% 5.25/5.58 thf(fact_9587_complex__abs__le__norm,axiom,
% 5.25/5.58 ! [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 ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_abs_le_norm
% 5.25/5.58 thf(fact_9588_complex__unit__circle,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( Z != zero_zero_complex )
% 5.25/5.58 => ( ( 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 ) ) ) )
% 5.25/5.58 = one_one_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_unit_circle
% 5.25/5.58 thf(fact_9589_inverse__complex_Ocode,axiom,
% 5.25/5.58 ( invers8013647133539491842omplex
% 5.25/5.58 = ( ^ [X2: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X2 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X2 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % inverse_complex.code
% 5.25/5.58 thf(fact_9590_Complex__divide,axiom,
% 5.25/5.58 ( divide1717551699836669952omplex
% 5.25/5.58 = ( ^ [X2: complex,Y6: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y6 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y6 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Complex_divide
% 5.25/5.58 thf(fact_9591_Im__Reals__divide,axiom,
% 5.25/5.58 ! [R2: complex,Z: complex] :
% 5.25/5.58 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.25/5.58 => ( ( im @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.25/5.58 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R2 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Im_Reals_divide
% 5.25/5.58 thf(fact_9592_Re__Reals__divide,axiom,
% 5.25/5.58 ! [R2: complex,Z: complex] :
% 5.25/5.58 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.25/5.58 => ( ( re @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.25/5.58 = ( divide_divide_real @ ( times_times_real @ ( re @ R2 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % Re_Reals_divide
% 5.25/5.58 thf(fact_9593_Code__Numeral_Opositive__def,axiom,
% 5.25/5.58 code_positive = numera6620942414471956472nteger ).
% 5.25/5.58
% 5.25/5.58 % Code_Numeral.positive_def
% 5.25/5.58 thf(fact_9594_real__eq__imaginary__iff,axiom,
% 5.25/5.58 ! [Y: complex,X3: complex] :
% 5.25/5.58 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 5.25/5.58 => ( ( member_complex @ X3 @ real_V2521375963428798218omplex )
% 5.25/5.58 => ( ( X3
% 5.25/5.58 = ( times_times_complex @ imaginary_unit @ Y ) )
% 5.25/5.58 = ( ( X3 = zero_zero_complex )
% 5.25/5.58 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % real_eq_imaginary_iff
% 5.25/5.58 thf(fact_9595_imaginary__eq__real__iff,axiom,
% 5.25/5.58 ! [Y: complex,X3: complex] :
% 5.25/5.58 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 5.25/5.58 => ( ( member_complex @ X3 @ real_V2521375963428798218omplex )
% 5.25/5.58 => ( ( ( times_times_complex @ imaginary_unit @ Y )
% 5.25/5.58 = X3 )
% 5.25/5.58 = ( ( X3 = zero_zero_complex )
% 5.25/5.58 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % imaginary_eq_real_iff
% 5.25/5.58 thf(fact_9596_complex__mult__cnj,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 5.25/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_mult_cnj
% 5.25/5.58 thf(fact_9597_integer__of__num_I3_J,axiom,
% 5.25/5.58 ! [N: num] :
% 5.25/5.58 ( ( code_integer_of_num @ ( bit1 @ N ) )
% 5.25/5.58 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 5.25/5.58
% 5.25/5.58 % integer_of_num(3)
% 5.25/5.58 thf(fact_9598_complex__cnj__mult,axiom,
% 5.25/5.58 ! [X3: complex,Y: complex] :
% 5.25/5.58 ( ( cnj @ ( times_times_complex @ X3 @ Y ) )
% 5.25/5.58 = ( times_times_complex @ ( cnj @ X3 ) @ ( cnj @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_cnj_mult
% 5.25/5.58 thf(fact_9599_complex__cnj__one__iff,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( ( cnj @ Z )
% 5.25/5.58 = one_one_complex )
% 5.25/5.58 = ( Z = one_one_complex ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_cnj_one_iff
% 5.25/5.58 thf(fact_9600_complex__cnj__one,axiom,
% 5.25/5.58 ( ( cnj @ one_one_complex )
% 5.25/5.58 = one_one_complex ) ).
% 5.25/5.58
% 5.25/5.58 % complex_cnj_one
% 5.25/5.58 thf(fact_9601_complex__cnj__power,axiom,
% 5.25/5.58 ! [X3: complex,N: nat] :
% 5.25/5.58 ( ( cnj @ ( power_power_complex @ X3 @ N ) )
% 5.25/5.58 = ( power_power_complex @ ( cnj @ X3 ) @ N ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_cnj_power
% 5.25/5.58 thf(fact_9602_complex__cnj__add,axiom,
% 5.25/5.58 ! [X3: complex,Y: complex] :
% 5.25/5.58 ( ( cnj @ ( plus_plus_complex @ X3 @ Y ) )
% 5.25/5.58 = ( plus_plus_complex @ ( cnj @ X3 ) @ ( cnj @ Y ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_cnj_add
% 5.25/5.58 thf(fact_9603_complex__cnj__numeral,axiom,
% 5.25/5.58 ! [W: num] :
% 5.25/5.58 ( ( cnj @ ( numera6690914467698888265omplex @ W ) )
% 5.25/5.58 = ( numera6690914467698888265omplex @ W ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_cnj_numeral
% 5.25/5.58 thf(fact_9604_complex__cnj__neg__numeral,axiom,
% 5.25/5.58 ! [W: num] :
% 5.25/5.58 ( ( cnj @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.25/5.58 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.25/5.58
% 5.25/5.58 % complex_cnj_neg_numeral
% 5.25/5.58 thf(fact_9605_complex__In__mult__cnj__zero,axiom,
% 5.25/5.58 ! [Z: complex] :
% 5.25/5.58 ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.25/5.58 = zero_zero_real ) ).
% 5.25/5.58
% 5.25/5.58 % complex_In_mult_cnj_zero
% 5.25/5.58 thf(fact_9606_integer__of__num__def,axiom,
% 5.25/5.58 code_integer_of_num = numera6620942414471956472nteger ).
% 5.25/5.58
% 5.25/5.58 % integer_of_num_def
% 5.25/5.58 thf(fact_9607_Re__complex__div__eq__0,axiom,
% 5.25/5.58 ! [A: complex,B: complex] :
% 5.25/5.58 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.25/5.58 = zero_zero_real )
% 5.25/5.58 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.25/5.58 = zero_zero_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % Re_complex_div_eq_0
% 5.25/5.58 thf(fact_9608_Im__complex__div__eq__0,axiom,
% 5.25/5.58 ! [A: complex,B: complex] :
% 5.25/5.58 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.25/5.58 = zero_zero_real )
% 5.25/5.58 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.25/5.58 = zero_zero_real ) ) ).
% 5.25/5.58
% 5.25/5.58 % Im_complex_div_eq_0
% 5.25/5.58 thf(fact_9609_complex__mod__sqrt__Re__mult__cnj,axiom,
% 5.25/5.58 ( real_V1022390504157884413omplex
% 5.25/5.59 = ( ^ [Z5: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z5 @ ( cnj @ Z5 ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % complex_mod_sqrt_Re_mult_cnj
% 5.25/5.59 thf(fact_9610_integer__of__num__triv_I1_J,axiom,
% 5.25/5.59 ( ( code_integer_of_num @ one )
% 5.25/5.59 = one_one_Code_integer ) ).
% 5.25/5.59
% 5.25/5.59 % integer_of_num_triv(1)
% 5.25/5.59 thf(fact_9611_Re__complex__div__gt__0,axiom,
% 5.25/5.59 ! [A: complex,B: complex] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.25/5.59 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Re_complex_div_gt_0
% 5.25/5.59 thf(fact_9612_Re__complex__div__lt__0,axiom,
% 5.25/5.59 ! [A: complex,B: complex] :
% 5.25/5.59 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.25/5.59 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.25/5.59
% 5.25/5.59 % Re_complex_div_lt_0
% 5.25/5.59 thf(fact_9613_Re__complex__div__le__0,axiom,
% 5.25/5.59 ! [A: complex,B: complex] :
% 5.25/5.59 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.25/5.59 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.25/5.59
% 5.25/5.59 % Re_complex_div_le_0
% 5.25/5.59 thf(fact_9614_Re__complex__div__ge__0,axiom,
% 5.25/5.59 ! [A: complex,B: complex] :
% 5.25/5.59 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.25/5.59 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Re_complex_div_ge_0
% 5.25/5.59 thf(fact_9615_Im__complex__div__gt__0,axiom,
% 5.25/5.59 ! [A: complex,B: complex] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.25/5.59 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Im_complex_div_gt_0
% 5.25/5.59 thf(fact_9616_Im__complex__div__lt__0,axiom,
% 5.25/5.59 ! [A: complex,B: complex] :
% 5.25/5.59 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.25/5.59 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.25/5.59
% 5.25/5.59 % Im_complex_div_lt_0
% 5.25/5.59 thf(fact_9617_Im__complex__div__le__0,axiom,
% 5.25/5.59 ! [A: complex,B: complex] :
% 5.25/5.59 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.25/5.59 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.25/5.59
% 5.25/5.59 % Im_complex_div_le_0
% 5.25/5.59 thf(fact_9618_Im__complex__div__ge__0,axiom,
% 5.25/5.59 ! [A: complex,B: complex] :
% 5.25/5.59 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.25/5.59 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Im_complex_div_ge_0
% 5.25/5.59 thf(fact_9619_integer__of__num_I2_J,axiom,
% 5.25/5.59 ! [N: num] :
% 5.25/5.59 ( ( code_integer_of_num @ ( bit0 @ N ) )
% 5.25/5.59 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % integer_of_num(2)
% 5.25/5.59 thf(fact_9620_complex__mod__mult__cnj,axiom,
% 5.25/5.59 ! [Z: complex] :
% 5.25/5.59 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.25/5.59 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % complex_mod_mult_cnj
% 5.25/5.59 thf(fact_9621_complex__div__gt__0,axiom,
% 5.25/5.59 ! [A: complex,B: complex] :
% 5.25/5.59 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.25/5.59 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.25/5.59 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.25/5.59 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % complex_div_gt_0
% 5.25/5.59 thf(fact_9622_integer__of__num__triv_I2_J,axiom,
% 5.25/5.59 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.25/5.59 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % integer_of_num_triv(2)
% 5.25/5.59 thf(fact_9623_complex__norm__square,axiom,
% 5.25/5.59 ! [Z: complex] :
% 5.25/5.59 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.59 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % complex_norm_square
% 5.25/5.59 thf(fact_9624_complex__add__cnj,axiom,
% 5.25/5.59 ! [Z: complex] :
% 5.25/5.59 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 5.25/5.59 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % complex_add_cnj
% 5.25/5.59 thf(fact_9625_complex__diff__cnj,axiom,
% 5.25/5.59 ! [Z: complex] :
% 5.25/5.59 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 5.25/5.59 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 5.25/5.59
% 5.25/5.59 % complex_diff_cnj
% 5.25/5.59 thf(fact_9626_complex__div__cnj,axiom,
% 5.25/5.59 ( divide1717551699836669952omplex
% 5.25/5.59 = ( ^ [A3: complex,B2: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B2 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % complex_div_cnj
% 5.25/5.59 thf(fact_9627_cnj__add__mult__eq__Re,axiom,
% 5.25/5.59 ! [Z: complex,W: complex] :
% 5.25/5.59 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 5.25/5.59 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % cnj_add_mult_eq_Re
% 5.25/5.59 thf(fact_9628_bit__cut__integer__def,axiom,
% 5.25/5.59 ( code_bit_cut_integer
% 5.25/5.59 = ( ^ [K3: code_integer] :
% 5.25/5.59 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.59 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % bit_cut_integer_def
% 5.25/5.59 thf(fact_9629_divmod__integer__def,axiom,
% 5.25/5.59 ( code_divmod_integer
% 5.25/5.59 = ( ^ [K3: code_integer,L: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K3 @ L ) @ ( modulo364778990260209775nteger @ K3 @ L ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % divmod_integer_def
% 5.25/5.59 thf(fact_9630_card__lessThan,axiom,
% 5.25/5.59 ! [U: nat] :
% 5.25/5.59 ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 5.25/5.59 = U ) ).
% 5.25/5.59
% 5.25/5.59 % card_lessThan
% 5.25/5.59 thf(fact_9631_card__Collect__less__nat,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( finite_card_nat
% 5.25/5.59 @ ( collect_nat
% 5.25/5.59 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) )
% 5.25/5.59 = N ) ).
% 5.25/5.59
% 5.25/5.59 % card_Collect_less_nat
% 5.25/5.59 thf(fact_9632_card__atMost,axiom,
% 5.25/5.59 ! [U: nat] :
% 5.25/5.59 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.25/5.59 = ( suc @ U ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_atMost
% 5.25/5.59 thf(fact_9633_card__atLeastLessThan,axiom,
% 5.25/5.59 ! [L2: nat,U: nat] :
% 5.25/5.59 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L2 @ U ) )
% 5.25/5.59 = ( minus_minus_nat @ U @ L2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_atLeastLessThan
% 5.25/5.59 thf(fact_9634_card__Collect__le__nat,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( finite_card_nat
% 5.25/5.59 @ ( collect_nat
% 5.25/5.59 @ ^ [I3: nat] : ( ord_less_eq_nat @ I3 @ N ) ) )
% 5.25/5.59 = ( suc @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_Collect_le_nat
% 5.25/5.59 thf(fact_9635_card__atLeastAtMost,axiom,
% 5.25/5.59 ! [L2: nat,U: nat] :
% 5.25/5.59 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 5.25/5.59 = ( minus_minus_nat @ ( suc @ U ) @ L2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_atLeastAtMost
% 5.25/5.59 thf(fact_9636_card__atLeastLessThan__int,axiom,
% 5.25/5.59 ! [L2: int,U: int] :
% 5.25/5.59 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L2 @ U ) )
% 5.25/5.59 = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_atLeastLessThan_int
% 5.25/5.59 thf(fact_9637_card__atLeastAtMost__int,axiom,
% 5.25/5.59 ! [L2: int,U: int] :
% 5.25/5.59 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 5.25/5.59 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L2 ) @ one_one_int ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_atLeastAtMost_int
% 5.25/5.59 thf(fact_9638_card__less,axiom,
% 5.25/5.59 ! [M7: set_nat,I2: nat] :
% 5.25/5.59 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.25/5.59 => ( ( finite_card_nat
% 5.25/5.59 @ ( collect_nat
% 5.25/5.59 @ ^ [K3: nat] :
% 5.25/5.59 ( ( member_nat @ K3 @ M7 )
% 5.25/5.59 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 5.25/5.59 != zero_zero_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_less
% 5.25/5.59 thf(fact_9639_card__less__Suc,axiom,
% 5.25/5.59 ! [M7: set_nat,I2: nat] :
% 5.25/5.59 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.25/5.59 => ( ( suc
% 5.25/5.59 @ ( finite_card_nat
% 5.25/5.59 @ ( collect_nat
% 5.25/5.59 @ ^ [K3: nat] :
% 5.25/5.59 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.25/5.59 & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 5.25/5.59 = ( finite_card_nat
% 5.25/5.59 @ ( collect_nat
% 5.25/5.59 @ ^ [K3: nat] :
% 5.25/5.59 ( ( member_nat @ K3 @ M7 )
% 5.25/5.59 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_less_Suc
% 5.25/5.59 thf(fact_9640_card__less__Suc2,axiom,
% 5.25/5.59 ! [M7: set_nat,I2: nat] :
% 5.25/5.59 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.25/5.59 => ( ( finite_card_nat
% 5.25/5.59 @ ( collect_nat
% 5.25/5.59 @ ^ [K3: nat] :
% 5.25/5.59 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.25/5.59 & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 5.25/5.59 = ( finite_card_nat
% 5.25/5.59 @ ( collect_nat
% 5.25/5.59 @ ^ [K3: nat] :
% 5.25/5.59 ( ( member_nat @ K3 @ M7 )
% 5.25/5.59 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_less_Suc2
% 5.25/5.59 thf(fact_9641_card__atLeastZeroLessThan__int,axiom,
% 5.25/5.59 ! [U: int] :
% 5.25/5.59 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 5.25/5.59 = ( nat2 @ U ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_atLeastZeroLessThan_int
% 5.25/5.59 thf(fact_9642_subset__card__intvl__is__intvl,axiom,
% 5.25/5.59 ! [A2: set_nat,K: nat] :
% 5.25/5.59 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 5.25/5.59 => ( A2
% 5.25/5.59 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % subset_card_intvl_is_intvl
% 5.25/5.59 thf(fact_9643_subset__eq__atLeast0__lessThan__card,axiom,
% 5.25/5.59 ! [N5: set_nat,N: nat] :
% 5.25/5.59 ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.25/5.59 => ( ord_less_eq_nat @ ( finite_card_nat @ N5 ) @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % subset_eq_atLeast0_lessThan_card
% 5.25/5.59 thf(fact_9644_card__sum__le__nat__sum,axiom,
% 5.25/5.59 ! [S3: set_nat] :
% 5.25/5.59 ( ord_less_eq_nat
% 5.25/5.59 @ ( groups3542108847815614940at_nat
% 5.25/5.59 @ ^ [X2: nat] : X2
% 5.25/5.59 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 5.25/5.59 @ ( groups3542108847815614940at_nat
% 5.25/5.59 @ ^ [X2: nat] : X2
% 5.25/5.59 @ S3 ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_sum_le_nat_sum
% 5.25/5.59 thf(fact_9645_card__nth__roots,axiom,
% 5.25/5.59 ! [C: complex,N: nat] :
% 5.25/5.59 ( ( C != zero_zero_complex )
% 5.25/5.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( finite_card_complex
% 5.25/5.59 @ ( collect_complex
% 5.25/5.59 @ ^ [Z5: complex] :
% 5.25/5.59 ( ( power_power_complex @ Z5 @ N )
% 5.25/5.59 = C ) ) )
% 5.25/5.59 = N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_nth_roots
% 5.25/5.59 thf(fact_9646_card__roots__unity__eq,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( finite_card_complex
% 5.25/5.59 @ ( collect_complex
% 5.25/5.59 @ ^ [Z5: complex] :
% 5.25/5.59 ( ( power_power_complex @ Z5 @ N )
% 5.25/5.59 = one_one_complex ) ) )
% 5.25/5.59 = N ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_roots_unity_eq
% 5.25/5.59 thf(fact_9647_bit__cut__integer__code,axiom,
% 5.25/5.59 ( code_bit_cut_integer
% 5.25/5.59 = ( ^ [K3: code_integer] :
% 5.25/5.59 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.25/5.59 @ ( produc9125791028180074456eger_o
% 5.25/5.59 @ ^ [R5: code_integer,S5: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S5 ) ) @ ( S5 = one_one_Code_integer ) )
% 5.25/5.59 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % bit_cut_integer_code
% 5.25/5.59 thf(fact_9648_divmod__abs__def,axiom,
% 5.25/5.59 ( code_divmod_abs
% 5.25/5.59 = ( ^ [K3: code_integer,L: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % divmod_abs_def
% 5.25/5.59 thf(fact_9649_divmod__integer__code,axiom,
% 5.25/5.59 ( code_divmod_integer
% 5.25/5.59 = ( ^ [K3: code_integer,L: code_integer] :
% 5.25/5.59 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.25/5.59 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L )
% 5.25/5.59 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L )
% 5.25/5.59 @ ( produc6916734918728496179nteger
% 5.25/5.59 @ ^ [R5: code_integer,S5: code_integer] : ( if_Pro6119634080678213985nteger @ ( S5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L @ S5 ) ) )
% 5.25/5.59 @ ( code_divmod_abs @ K3 @ L ) ) )
% 5.25/5.59 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.25/5.59 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.25/5.59 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L )
% 5.25/5.59 @ ( produc6916734918728496179nteger
% 5.25/5.59 @ ^ [R5: code_integer,S5: code_integer] : ( if_Pro6119634080678213985nteger @ ( S5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L ) @ S5 ) ) )
% 5.25/5.59 @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % divmod_integer_code
% 5.25/5.59 thf(fact_9650_bezw__0,axiom,
% 5.25/5.59 ! [X3: nat] :
% 5.25/5.59 ( ( bezw @ X3 @ zero_zero_nat )
% 5.25/5.59 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % bezw_0
% 5.25/5.59 thf(fact_9651_nat_Odisc__eq__case_I2_J,axiom,
% 5.25/5.59 ! [Nat: nat] :
% 5.25/5.59 ( ( Nat != zero_zero_nat )
% 5.25/5.59 = ( case_nat_o @ $false
% 5.25/5.59 @ ^ [Uu3: nat] : $true
% 5.25/5.59 @ Nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % nat.disc_eq_case(2)
% 5.25/5.59 thf(fact_9652_nat_Odisc__eq__case_I1_J,axiom,
% 5.25/5.59 ! [Nat: nat] :
% 5.25/5.59 ( ( Nat = zero_zero_nat )
% 5.25/5.59 = ( case_nat_o @ $true
% 5.25/5.59 @ ^ [Uu3: nat] : $false
% 5.25/5.59 @ Nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % nat.disc_eq_case(1)
% 5.25/5.59 thf(fact_9653_less__eq__nat_Osimps_I2_J,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.25/5.59 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % less_eq_nat.simps(2)
% 5.25/5.59 thf(fact_9654_max__Suc1,axiom,
% 5.25/5.59 ! [N: nat,M: nat] :
% 5.25/5.59 ( ( ord_max_nat @ ( suc @ N ) @ M )
% 5.25/5.59 = ( case_nat_nat @ ( suc @ N )
% 5.25/5.59 @ ^ [M3: nat] : ( suc @ ( ord_max_nat @ N @ M3 ) )
% 5.25/5.59 @ M ) ) ).
% 5.25/5.59
% 5.25/5.59 % max_Suc1
% 5.25/5.59 thf(fact_9655_max__Suc2,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( ord_max_nat @ M @ ( suc @ N ) )
% 5.25/5.59 = ( case_nat_nat @ ( suc @ N )
% 5.25/5.59 @ ^ [M3: nat] : ( suc @ ( ord_max_nat @ M3 @ N ) )
% 5.25/5.59 @ M ) ) ).
% 5.25/5.59
% 5.25/5.59 % max_Suc2
% 5.25/5.59 thf(fact_9656_diff__Suc,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.25/5.59 = ( case_nat_nat @ zero_zero_nat
% 5.25/5.59 @ ^ [K3: nat] : K3
% 5.25/5.59 @ ( minus_minus_nat @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % diff_Suc
% 5.25/5.59 thf(fact_9657_floor__real__def,axiom,
% 5.25/5.59 ( archim6058952711729229775r_real
% 5.25/5.59 = ( ^ [X2: real] :
% 5.25/5.59 ( the_int
% 5.25/5.59 @ ^ [Z5: int] :
% 5.25/5.59 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z5 ) @ X2 )
% 5.25/5.59 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % floor_real_def
% 5.25/5.59 thf(fact_9658_floor__rat__def,axiom,
% 5.25/5.59 ( archim3151403230148437115or_rat
% 5.25/5.59 = ( ^ [X2: rat] :
% 5.25/5.59 ( the_int
% 5.25/5.59 @ ^ [Z5: int] :
% 5.25/5.59 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z5 ) @ X2 )
% 5.25/5.59 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % floor_rat_def
% 5.25/5.59 thf(fact_9659_obtain__pos__sum,axiom,
% 5.25/5.59 ! [R2: rat] :
% 5.25/5.59 ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.25/5.59 => ~ ! [S2: rat] :
% 5.25/5.59 ( ( ord_less_rat @ zero_zero_rat @ S2 )
% 5.25/5.59 => ! [T3: rat] :
% 5.25/5.59 ( ( ord_less_rat @ zero_zero_rat @ T3 )
% 5.25/5.59 => ( R2
% 5.25/5.59 != ( plus_plus_rat @ S2 @ T3 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % obtain_pos_sum
% 5.25/5.59 thf(fact_9660_sgn__rat__def,axiom,
% 5.25/5.59 ( sgn_sgn_rat
% 5.25/5.59 = ( ^ [A3: rat] : ( if_rat @ ( A3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % sgn_rat_def
% 5.25/5.59 thf(fact_9661_less__eq__rat__def,axiom,
% 5.25/5.59 ( ord_less_eq_rat
% 5.25/5.59 = ( ^ [X2: rat,Y6: rat] :
% 5.25/5.59 ( ( ord_less_rat @ X2 @ Y6 )
% 5.25/5.59 | ( X2 = Y6 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % less_eq_rat_def
% 5.25/5.59 thf(fact_9662_pred__def,axiom,
% 5.25/5.59 ( pred
% 5.25/5.59 = ( case_nat_nat @ zero_zero_nat
% 5.25/5.59 @ ^ [X24: nat] : X24 ) ) ).
% 5.25/5.59
% 5.25/5.59 % pred_def
% 5.25/5.59 thf(fact_9663_rat__inverse__code,axiom,
% 5.25/5.59 ! [P2: rat] :
% 5.25/5.59 ( ( quotient_of @ ( inverse_inverse_rat @ P2 ) )
% 5.25/5.59 = ( produc4245557441103728435nt_int
% 5.25/5.59 @ ^ [A3: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( A3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A3 ) @ B2 ) @ ( abs_abs_int @ A3 ) ) )
% 5.25/5.59 @ ( quotient_of @ P2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_inverse_code
% 5.25/5.59 thf(fact_9664_prod__decode__aux_Osimps,axiom,
% 5.25/5.59 ( nat_prod_decode_aux
% 5.25/5.59 = ( ^ [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 ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % prod_decode_aux.simps
% 5.25/5.59 thf(fact_9665_prod__decode__aux_Oelims,axiom,
% 5.25/5.59 ! [X3: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 5.25/5.59 ( ( ( nat_prod_decode_aux @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( ( ord_less_eq_nat @ Xa2 @ X3 )
% 5.25/5.59 => ( Y
% 5.25/5.59 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X3 @ Xa2 ) ) ) )
% 5.25/5.59 & ( ~ ( ord_less_eq_nat @ Xa2 @ X3 )
% 5.25/5.59 => ( Y
% 5.25/5.59 = ( nat_prod_decode_aux @ ( suc @ X3 ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X3 ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % prod_decode_aux.elims
% 5.25/5.59 thf(fact_9666_quotient__of__number_I3_J,axiom,
% 5.25/5.59 ! [K: num] :
% 5.25/5.59 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 5.25/5.59 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % quotient_of_number(3)
% 5.25/5.59 thf(fact_9667_rat__one__code,axiom,
% 5.25/5.59 ( ( quotient_of @ one_one_rat )
% 5.25/5.59 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_one_code
% 5.25/5.59 thf(fact_9668_rat__zero__code,axiom,
% 5.25/5.59 ( ( quotient_of @ zero_zero_rat )
% 5.25/5.59 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_zero_code
% 5.25/5.59 thf(fact_9669_quotient__of__number_I5_J,axiom,
% 5.25/5.59 ! [K: num] :
% 5.25/5.59 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.25/5.59 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % quotient_of_number(5)
% 5.25/5.59 thf(fact_9670_quotient__of__number_I4_J,axiom,
% 5.25/5.59 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.25/5.59 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % quotient_of_number(4)
% 5.25/5.59 thf(fact_9671_diff__rat__def,axiom,
% 5.25/5.59 ( minus_minus_rat
% 5.25/5.59 = ( ^ [Q4: rat,R5: rat] : ( plus_plus_rat @ Q4 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % diff_rat_def
% 5.25/5.59 thf(fact_9672_divide__rat__def,axiom,
% 5.25/5.59 ( divide_divide_rat
% 5.25/5.59 = ( ^ [Q4: rat,R5: rat] : ( times_times_rat @ Q4 @ ( inverse_inverse_rat @ R5 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % divide_rat_def
% 5.25/5.59 thf(fact_9673_rat__less__code,axiom,
% 5.25/5.59 ( ord_less_rat
% 5.25/5.59 = ( ^ [P4: rat,Q4: rat] :
% 5.25/5.59 ( produc4947309494688390418_int_o
% 5.25/5.59 @ ^ [A3: int,C2: int] :
% 5.25/5.59 ( produc4947309494688390418_int_o
% 5.25/5.59 @ ^ [B2: int,D2: int] : ( ord_less_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.25/5.59 @ ( quotient_of @ Q4 ) )
% 5.25/5.59 @ ( quotient_of @ P4 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_less_code
% 5.25/5.59 thf(fact_9674_rat__less__eq__code,axiom,
% 5.25/5.59 ( ord_less_eq_rat
% 5.25/5.59 = ( ^ [P4: rat,Q4: rat] :
% 5.25/5.59 ( produc4947309494688390418_int_o
% 5.25/5.59 @ ^ [A3: int,C2: int] :
% 5.25/5.59 ( produc4947309494688390418_int_o
% 5.25/5.59 @ ^ [B2: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.25/5.59 @ ( quotient_of @ Q4 ) )
% 5.25/5.59 @ ( quotient_of @ P4 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_less_eq_code
% 5.25/5.59 thf(fact_9675_prod__decode__aux_Opelims,axiom,
% 5.25/5.59 ! [X3: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 5.25/5.59 ( ( ( nat_prod_decode_aux @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X3 @ Xa2 ) )
% 5.25/5.59 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X3 )
% 5.25/5.59 => ( Y
% 5.25/5.59 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X3 @ Xa2 ) ) ) )
% 5.25/5.59 & ( ~ ( ord_less_eq_nat @ Xa2 @ X3 )
% 5.25/5.59 => ( Y
% 5.25/5.59 = ( nat_prod_decode_aux @ ( suc @ X3 ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X3 ) ) ) ) ) )
% 5.25/5.59 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X3 @ Xa2 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % prod_decode_aux.pelims
% 5.25/5.59 thf(fact_9676_quotient__of__int,axiom,
% 5.25/5.59 ! [A: int] :
% 5.25/5.59 ( ( quotient_of @ ( of_int @ A ) )
% 5.25/5.59 = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % quotient_of_int
% 5.25/5.59 thf(fact_9677_rat__plus__code,axiom,
% 5.25/5.59 ! [P2: rat,Q2: rat] :
% 5.25/5.59 ( ( quotient_of @ ( plus_plus_rat @ P2 @ Q2 ) )
% 5.25/5.59 = ( produc4245557441103728435nt_int
% 5.25/5.59 @ ^ [A3: int,C2: int] :
% 5.25/5.59 ( produc4245557441103728435nt_int
% 5.25/5.59 @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ B2 @ C2 ) ) @ ( times_times_int @ C2 @ D2 ) ) )
% 5.25/5.59 @ ( quotient_of @ Q2 ) )
% 5.25/5.59 @ ( quotient_of @ P2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_plus_code
% 5.25/5.59 thf(fact_9678_normalize__denom__zero,axiom,
% 5.25/5.59 ! [P2: int] :
% 5.25/5.59 ( ( normalize @ ( product_Pair_int_int @ P2 @ zero_zero_int ) )
% 5.25/5.59 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % normalize_denom_zero
% 5.25/5.59 thf(fact_9679_normalize__crossproduct,axiom,
% 5.25/5.59 ! [Q2: int,S: int,P2: int,R2: int] :
% 5.25/5.59 ( ( Q2 != zero_zero_int )
% 5.25/5.59 => ( ( S != zero_zero_int )
% 5.25/5.59 => ( ( ( normalize @ ( product_Pair_int_int @ P2 @ Q2 ) )
% 5.25/5.59 = ( normalize @ ( product_Pair_int_int @ R2 @ S ) ) )
% 5.25/5.59 => ( ( times_times_int @ P2 @ S )
% 5.25/5.59 = ( times_times_int @ R2 @ Q2 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % normalize_crossproduct
% 5.25/5.59 thf(fact_9680_rat__times__code,axiom,
% 5.25/5.59 ! [P2: rat,Q2: rat] :
% 5.25/5.59 ( ( quotient_of @ ( times_times_rat @ P2 @ Q2 ) )
% 5.25/5.59 = ( produc4245557441103728435nt_int
% 5.25/5.59 @ ^ [A3: int,C2: int] :
% 5.25/5.59 ( produc4245557441103728435nt_int
% 5.25/5.59 @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ B2 ) @ ( times_times_int @ C2 @ D2 ) ) )
% 5.25/5.59 @ ( quotient_of @ Q2 ) )
% 5.25/5.59 @ ( quotient_of @ P2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_times_code
% 5.25/5.59 thf(fact_9681_rat__divide__code,axiom,
% 5.25/5.59 ! [P2: rat,Q2: rat] :
% 5.25/5.59 ( ( quotient_of @ ( divide_divide_rat @ P2 @ Q2 ) )
% 5.25/5.59 = ( produc4245557441103728435nt_int
% 5.25/5.59 @ ^ [A3: int,C2: int] :
% 5.25/5.59 ( produc4245557441103728435nt_int
% 5.25/5.59 @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C2 @ B2 ) ) )
% 5.25/5.59 @ ( quotient_of @ Q2 ) )
% 5.25/5.59 @ ( quotient_of @ P2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_divide_code
% 5.25/5.59 thf(fact_9682_rat__minus__code,axiom,
% 5.25/5.59 ! [P2: rat,Q2: rat] :
% 5.25/5.59 ( ( quotient_of @ ( minus_minus_rat @ P2 @ Q2 ) )
% 5.25/5.59 = ( produc4245557441103728435nt_int
% 5.25/5.59 @ ^ [A3: int,C2: int] :
% 5.25/5.59 ( produc4245557441103728435nt_int
% 5.25/5.59 @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ B2 @ C2 ) ) @ ( times_times_int @ C2 @ D2 ) ) )
% 5.25/5.59 @ ( quotient_of @ Q2 ) )
% 5.25/5.59 @ ( quotient_of @ P2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_minus_code
% 5.25/5.59 thf(fact_9683_Frct__code__post_I5_J,axiom,
% 5.25/5.59 ! [K: num] :
% 5.25/5.59 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.25/5.59 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Frct_code_post(5)
% 5.25/5.59 thf(fact_9684_Frct__code__post_I6_J,axiom,
% 5.25/5.59 ! [K: num,L2: num] :
% 5.25/5.59 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L2 ) ) )
% 5.25/5.59 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Frct_code_post(6)
% 5.25/5.59 thf(fact_9685_Suc__0__div__numeral,axiom,
% 5.25/5.59 ! [K: num] :
% 5.25/5.59 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.25/5.59 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Suc_0_div_numeral
% 5.25/5.59 thf(fact_9686_fst__divmod__nat,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.25/5.59 = ( divide_divide_nat @ M @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % fst_divmod_nat
% 5.25/5.59 thf(fact_9687_Frct__code__post_I3_J,axiom,
% 5.25/5.59 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 5.25/5.59 = one_one_rat ) ).
% 5.25/5.59
% 5.25/5.59 % Frct_code_post(3)
% 5.25/5.59 thf(fact_9688_Frct__code__post_I4_J,axiom,
% 5.25/5.59 ! [K: num] :
% 5.25/5.59 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 5.25/5.59 = ( numeral_numeral_rat @ K ) ) ).
% 5.25/5.59
% 5.25/5.59 % Frct_code_post(4)
% 5.25/5.59 thf(fact_9689_drop__bit__numeral__minus__bit1,axiom,
% 5.25/5.59 ! [L2: num,K: num] :
% 5.25/5.59 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.25/5.59 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % drop_bit_numeral_minus_bit1
% 5.25/5.59 thf(fact_9690_Suc__0__mod__numeral,axiom,
% 5.25/5.59 ! [K: num] :
% 5.25/5.59 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.25/5.59 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Suc_0_mod_numeral
% 5.25/5.59 thf(fact_9691_finite__enumerate,axiom,
% 5.25/5.59 ! [S3: set_nat] :
% 5.25/5.59 ( ( finite_finite_nat @ S3 )
% 5.25/5.59 => ? [R3: nat > nat] :
% 5.25/5.59 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S3 ) ) )
% 5.25/5.59 & ! [N8: nat] :
% 5.25/5.59 ( ( ord_less_nat @ N8 @ ( finite_card_nat @ S3 ) )
% 5.25/5.59 => ( member_nat @ ( R3 @ N8 ) @ S3 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % finite_enumerate
% 5.25/5.59 thf(fact_9692_drop__bit__nonnegative__int__iff,axiom,
% 5.25/5.59 ! [N: nat,K: int] :
% 5.25/5.59 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 5.25/5.59 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.25/5.59
% 5.25/5.59 % drop_bit_nonnegative_int_iff
% 5.25/5.59 thf(fact_9693_drop__bit__negative__int__iff,axiom,
% 5.25/5.59 ! [N: nat,K: int] :
% 5.25/5.59 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 5.25/5.59 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % drop_bit_negative_int_iff
% 5.25/5.59 thf(fact_9694_drop__bit__minus__one,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.25/5.59 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % drop_bit_minus_one
% 5.25/5.59 thf(fact_9695_snd__divmod__nat,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.25/5.59 = ( modulo_modulo_nat @ M @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % snd_divmod_nat
% 5.25/5.59 thf(fact_9696_drop__bit__Suc__minus__bit0,axiom,
% 5.25/5.59 ! [N: nat,K: num] :
% 5.25/5.59 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.25/5.59 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % drop_bit_Suc_minus_bit0
% 5.25/5.59 thf(fact_9697_drop__bit__numeral__minus__bit0,axiom,
% 5.25/5.59 ! [L2: num,K: num] :
% 5.25/5.59 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.25/5.59 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % drop_bit_numeral_minus_bit0
% 5.25/5.59 thf(fact_9698_drop__bit__Suc__minus__bit1,axiom,
% 5.25/5.59 ! [N: nat,K: num] :
% 5.25/5.59 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.25/5.59 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % drop_bit_Suc_minus_bit1
% 5.25/5.59 thf(fact_9699_drop__bit__push__bit__int,axiom,
% 5.25/5.59 ! [M: nat,N: nat,K: int] :
% 5.25/5.59 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.25/5.59 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % drop_bit_push_bit_int
% 5.25/5.59 thf(fact_9700_drop__bit__int__def,axiom,
% 5.25/5.59 ( bit_se8568078237143864401it_int
% 5.25/5.59 = ( ^ [N2: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % drop_bit_int_def
% 5.25/5.59 thf(fact_9701_rat__sgn__code,axiom,
% 5.25/5.59 ! [P2: rat] :
% 5.25/5.59 ( ( quotient_of @ ( sgn_sgn_rat @ P2 ) )
% 5.25/5.59 = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P2 ) ) ) @ one_one_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_sgn_code
% 5.25/5.59 thf(fact_9702_bezw_Oelims,axiom,
% 5.25/5.59 ! [X3: nat,Xa2: nat,Y: product_prod_int_int] :
% 5.25/5.59 ( ( ( bezw @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.59 => ( Y
% 5.25/5.59 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.25/5.59 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.59 => ( Y
% 5.25/5.59 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X3 @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X3 @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X3 @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % bezw.elims
% 5.25/5.59 thf(fact_9703_bezw_Osimps,axiom,
% 5.25/5.59 ( bezw
% 5.25/5.59 = ( ^ [X2: nat,Y6: nat] : ( if_Pro3027730157355071871nt_int @ ( Y6 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y6 @ ( modulo_modulo_nat @ X2 @ Y6 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y6 @ ( modulo_modulo_nat @ X2 @ Y6 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y6 @ ( modulo_modulo_nat @ X2 @ Y6 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y6 ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % bezw.simps
% 5.25/5.59 thf(fact_9704_snd__divmod__integer,axiom,
% 5.25/5.59 ! [K: code_integer,L2: code_integer] :
% 5.25/5.59 ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L2 ) )
% 5.25/5.59 = ( modulo364778990260209775nteger @ K @ L2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % snd_divmod_integer
% 5.25/5.59 thf(fact_9705_snd__divmod__abs,axiom,
% 5.25/5.59 ! [K: code_integer,L2: code_integer] :
% 5.25/5.59 ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L2 ) )
% 5.25/5.59 = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % snd_divmod_abs
% 5.25/5.59 thf(fact_9706_drop__bit__of__Suc__0,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.25/5.59 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % drop_bit_of_Suc_0
% 5.25/5.59 thf(fact_9707_drop__bit__nat__eq,axiom,
% 5.25/5.59 ! [N: nat,K: int] :
% 5.25/5.59 ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 5.25/5.59 = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % drop_bit_nat_eq
% 5.25/5.59 thf(fact_9708_drop__bit__nat__def,axiom,
% 5.25/5.59 ( bit_se8570568707652914677it_nat
% 5.25/5.59 = ( ^ [N2: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % drop_bit_nat_def
% 5.25/5.59 thf(fact_9709_bezw__non__0,axiom,
% 5.25/5.59 ! [Y: nat,X3: nat] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 5.25/5.59 => ( ( bezw @ X3 @ Y )
% 5.25/5.59 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X3 @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X3 @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X3 @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Y ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % bezw_non_0
% 5.25/5.59 thf(fact_9710_bezw_Opelims,axiom,
% 5.25/5.59 ! [X3: nat,Xa2: nat,Y: product_prod_int_int] :
% 5.25/5.59 ( ( ( bezw @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X3 @ Xa2 ) )
% 5.25/5.59 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.59 => ( Y
% 5.25/5.59 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.25/5.59 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.59 => ( Y
% 5.25/5.59 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X3 @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X3 @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X3 @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Xa2 ) ) ) ) ) ) ) )
% 5.25/5.59 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X3 @ Xa2 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % bezw.pelims
% 5.25/5.59 thf(fact_9711_one__mod__minus__numeral,axiom,
% 5.25/5.59 ! [N: num] :
% 5.25/5.59 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % one_mod_minus_numeral
% 5.25/5.59 thf(fact_9712_minus__one__mod__numeral,axiom,
% 5.25/5.59 ! [N: num] :
% 5.25/5.59 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.59 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % minus_one_mod_numeral
% 5.25/5.59 thf(fact_9713_numeral__mod__minus__numeral,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % numeral_mod_minus_numeral
% 5.25/5.59 thf(fact_9714_minus__numeral__mod__numeral,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.59 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % minus_numeral_mod_numeral
% 5.25/5.59 thf(fact_9715_Divides_Oadjust__mod__def,axiom,
% 5.25/5.59 ( adjust_mod
% 5.25/5.59 = ( ^ [L: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L @ R5 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Divides.adjust_mod_def
% 5.25/5.59 thf(fact_9716_normalize__def,axiom,
% 5.25/5.59 ( normalize
% 5.25/5.59 = ( ^ [P4: product_prod_int_int] :
% 5.25/5.59 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P4 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P4 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P4 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) )
% 5.25/5.59 @ ( if_Pro3027730157355071871nt_int
% 5.25/5.59 @ ( ( product_snd_int_int @ P4 )
% 5.25/5.59 = zero_zero_int )
% 5.25/5.59 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.25/5.59 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P4 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P4 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P4 ) @ ( product_snd_int_int @ P4 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % normalize_def
% 5.25/5.59 thf(fact_9717_gcd__1__int,axiom,
% 5.25/5.59 ! [M: int] :
% 5.25/5.59 ( ( gcd_gcd_int @ M @ one_one_int )
% 5.25/5.59 = one_one_int ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_1_int
% 5.25/5.59 thf(fact_9718_gcd__neg__numeral__1__int,axiom,
% 5.25/5.59 ! [N: num,X3: int] :
% 5.25/5.59 ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X3 )
% 5.25/5.59 = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X3 ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_neg_numeral_1_int
% 5.25/5.59 thf(fact_9719_gcd__neg__numeral__2__int,axiom,
% 5.25/5.59 ! [X3: int,N: num] :
% 5.25/5.59 ( ( gcd_gcd_int @ X3 @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 = ( gcd_gcd_int @ X3 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_neg_numeral_2_int
% 5.25/5.59 thf(fact_9720_gcd__red__int,axiom,
% 5.25/5.59 ( gcd_gcd_int
% 5.25/5.59 = ( ^ [X2: int,Y6: int] : ( gcd_gcd_int @ Y6 @ ( modulo_modulo_int @ X2 @ Y6 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_red_int
% 5.25/5.59 thf(fact_9721_gcd__ge__0__int,axiom,
% 5.25/5.59 ! [X3: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X3 @ Y ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_ge_0_int
% 5.25/5.59 thf(fact_9722_bezout__int,axiom,
% 5.25/5.59 ! [X3: int,Y: int] :
% 5.25/5.59 ? [U3: int,V2: int] :
% 5.25/5.59 ( ( plus_plus_int @ ( times_times_int @ U3 @ X3 ) @ ( times_times_int @ V2 @ Y ) )
% 5.25/5.59 = ( gcd_gcd_int @ X3 @ Y ) ) ).
% 5.25/5.59
% 5.25/5.59 % bezout_int
% 5.25/5.59 thf(fact_9723_gcd__mult__distrib__int,axiom,
% 5.25/5.59 ! [K: int,M: int,N: int] :
% 5.25/5.59 ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N ) )
% 5.25/5.59 = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_mult_distrib_int
% 5.25/5.59 thf(fact_9724_gcd__le2__int,axiom,
% 5.25/5.59 ! [B: int,A: int] :
% 5.25/5.59 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.59 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_le2_int
% 5.25/5.59 thf(fact_9725_gcd__le1__int,axiom,
% 5.25/5.59 ! [A: int,B: int] :
% 5.25/5.59 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.59 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_le1_int
% 5.25/5.59 thf(fact_9726_gcd__cases__int,axiom,
% 5.25/5.59 ! [X3: int,Y: int,P: int > $o] :
% 5.25/5.59 ( ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.59 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.59 => ( P @ ( gcd_gcd_int @ X3 @ Y ) ) ) )
% 5.25/5.59 => ( ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.25/5.59 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.25/5.59 => ( P @ ( gcd_gcd_int @ X3 @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.25/5.59 => ( ( ( ord_less_eq_int @ X3 @ zero_zero_int )
% 5.25/5.59 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.59 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X3 ) @ Y ) ) ) )
% 5.25/5.59 => ( ( ( ord_less_eq_int @ X3 @ zero_zero_int )
% 5.25/5.59 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.25/5.59 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X3 ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.25/5.59 => ( P @ ( gcd_gcd_int @ X3 @ Y ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_cases_int
% 5.25/5.59 thf(fact_9727_gcd__unique__int,axiom,
% 5.25/5.59 ! [D: int,A: int,B: int] :
% 5.25/5.59 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 5.25/5.59 & ( dvd_dvd_int @ D @ A )
% 5.25/5.59 & ( dvd_dvd_int @ D @ B )
% 5.25/5.59 & ! [E3: int] :
% 5.25/5.59 ( ( ( dvd_dvd_int @ E3 @ A )
% 5.25/5.59 & ( dvd_dvd_int @ E3 @ B ) )
% 5.25/5.59 => ( dvd_dvd_int @ E3 @ D ) ) )
% 5.25/5.59 = ( D
% 5.25/5.59 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_unique_int
% 5.25/5.59 thf(fact_9728_gcd__non__0__int,axiom,
% 5.25/5.59 ! [Y: int,X3: int] :
% 5.25/5.59 ( ( ord_less_int @ zero_zero_int @ Y )
% 5.25/5.59 => ( ( gcd_gcd_int @ X3 @ Y )
% 5.25/5.59 = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X3 @ Y ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_non_0_int
% 5.25/5.59 thf(fact_9729_gcd__code__int,axiom,
% 5.25/5.59 ( gcd_gcd_int
% 5.25/5.59 = ( ^ [K3: int,L: int] : ( abs_abs_int @ ( if_int @ ( L = zero_zero_int ) @ K3 @ ( gcd_gcd_int @ L @ ( modulo_modulo_int @ ( abs_abs_int @ K3 ) @ ( abs_abs_int @ L ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_code_int
% 5.25/5.59 thf(fact_9730_divmod__integer__eq__cases,axiom,
% 5.25/5.59 ( code_divmod_integer
% 5.25/5.59 = ( ^ [K3: code_integer,L: code_integer] :
% 5.25/5.59 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.25/5.59 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.25/5.59 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L
% 5.25/5.59 @ ( if_Pro6119634080678213985nteger
% 5.25/5.59 @ ( ( sgn_sgn_Code_integer @ K3 )
% 5.25/5.59 = ( sgn_sgn_Code_integer @ L ) )
% 5.25/5.59 @ ( code_divmod_abs @ K3 @ L )
% 5.25/5.59 @ ( produc6916734918728496179nteger
% 5.25/5.59 @ ^ [R5: code_integer,S5: code_integer] : ( if_Pro6119634080678213985nteger @ ( S5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L ) @ S5 ) ) )
% 5.25/5.59 @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % divmod_integer_eq_cases
% 5.25/5.59 thf(fact_9731_gcd__1__nat,axiom,
% 5.25/5.59 ! [M: nat] :
% 5.25/5.59 ( ( gcd_gcd_nat @ M @ one_one_nat )
% 5.25/5.59 = one_one_nat ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_1_nat
% 5.25/5.59 thf(fact_9732_gcd__Suc__0,axiom,
% 5.25/5.59 ! [M: nat] :
% 5.25/5.59 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.25/5.59 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_Suc_0
% 5.25/5.59 thf(fact_9733_gcd__pos__nat,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 5.25/5.59 = ( ( M != zero_zero_nat )
% 5.25/5.59 | ( N != zero_zero_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_pos_nat
% 5.25/5.59 thf(fact_9734_gcd__mult__distrib__nat,axiom,
% 5.25/5.59 ! [K: nat,M: nat,N: nat] :
% 5.25/5.59 ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 5.25/5.59 = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_mult_distrib_nat
% 5.25/5.59 thf(fact_9735_gcd__red__nat,axiom,
% 5.25/5.59 ( gcd_gcd_nat
% 5.25/5.59 = ( ^ [X2: nat,Y6: nat] : ( gcd_gcd_nat @ Y6 @ ( modulo_modulo_nat @ X2 @ Y6 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_red_nat
% 5.25/5.59 thf(fact_9736_gcd__le2__nat,axiom,
% 5.25/5.59 ! [B: nat,A: nat] :
% 5.25/5.59 ( ( B != zero_zero_nat )
% 5.25/5.59 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_le2_nat
% 5.25/5.59 thf(fact_9737_gcd__le1__nat,axiom,
% 5.25/5.59 ! [A: nat,B: nat] :
% 5.25/5.59 ( ( A != zero_zero_nat )
% 5.25/5.59 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_le1_nat
% 5.25/5.59 thf(fact_9738_gcd__diff2__nat,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.59 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 5.25/5.59 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_diff2_nat
% 5.25/5.59 thf(fact_9739_gcd__diff1__nat,axiom,
% 5.25/5.59 ! [N: nat,M: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ N @ M )
% 5.25/5.59 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 5.25/5.59 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_diff1_nat
% 5.25/5.59 thf(fact_9740_gcd__nat_Oelims,axiom,
% 5.25/5.59 ! [X3: nat,Xa2: nat,Y: nat] :
% 5.25/5.59 ( ( ( gcd_gcd_nat @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.59 => ( Y = X3 ) )
% 5.25/5.59 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.59 => ( Y
% 5.25/5.59 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X3 @ Xa2 ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_nat.elims
% 5.25/5.59 thf(fact_9741_gcd__nat_Osimps,axiom,
% 5.25/5.59 ( gcd_gcd_nat
% 5.25/5.59 = ( ^ [X2: nat,Y6: nat] : ( if_nat @ ( Y6 = zero_zero_nat ) @ X2 @ ( gcd_gcd_nat @ Y6 @ ( modulo_modulo_nat @ X2 @ Y6 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_nat.simps
% 5.25/5.59 thf(fact_9742_gcd__non__0__nat,axiom,
% 5.25/5.59 ! [Y: nat,X3: nat] :
% 5.25/5.59 ( ( Y != zero_zero_nat )
% 5.25/5.59 => ( ( gcd_gcd_nat @ X3 @ Y )
% 5.25/5.59 = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X3 @ Y ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_non_0_nat
% 5.25/5.59 thf(fact_9743_bezout__nat,axiom,
% 5.25/5.59 ! [A: nat,B: nat] :
% 5.25/5.59 ( ( A != zero_zero_nat )
% 5.25/5.59 => ? [X5: nat,Y3: nat] :
% 5.25/5.59 ( ( times_times_nat @ A @ X5 )
% 5.25/5.59 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % bezout_nat
% 5.25/5.59 thf(fact_9744_bezout__gcd__nat_H,axiom,
% 5.25/5.59 ! [B: nat,A: nat] :
% 5.25/5.59 ? [X5: nat,Y3: nat] :
% 5.25/5.59 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X5 ) )
% 5.25/5.59 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X5 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.25/5.59 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.25/5.59 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X5 ) )
% 5.25/5.59 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X5 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.25/5.59 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % bezout_gcd_nat'
% 5.25/5.59 thf(fact_9745_gcd__code__integer,axiom,
% 5.25/5.59 ( gcd_gcd_Code_integer
% 5.25/5.59 = ( ^ [K3: code_integer,L: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L = zero_z3403309356797280102nteger ) @ K3 @ ( gcd_gcd_Code_integer @ L @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_code_integer
% 5.25/5.59 thf(fact_9746_bezw__aux,axiom,
% 5.25/5.59 ! [X3: nat,Y: nat] :
% 5.25/5.59 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X3 @ Y ) )
% 5.25/5.59 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X3 @ Y ) ) @ ( semiri1314217659103216013at_int @ X3 ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X3 @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % bezw_aux
% 5.25/5.59 thf(fact_9747_nat__descend__induct,axiom,
% 5.25/5.59 ! [N: nat,P: nat > $o,M: nat] :
% 5.25/5.59 ( ! [K2: nat] :
% 5.25/5.59 ( ( ord_less_nat @ N @ K2 )
% 5.25/5.59 => ( P @ K2 ) )
% 5.25/5.59 => ( ! [K2: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ K2 @ N )
% 5.25/5.59 => ( ! [I: nat] :
% 5.25/5.59 ( ( ord_less_nat @ K2 @ I )
% 5.25/5.59 => ( P @ I ) )
% 5.25/5.59 => ( P @ K2 ) ) )
% 5.25/5.59 => ( P @ M ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % nat_descend_induct
% 5.25/5.59 thf(fact_9748_gcd__nat_Opelims,axiom,
% 5.25/5.59 ! [X3: nat,Xa2: nat,Y: nat] :
% 5.25/5.59 ( ( ( gcd_gcd_nat @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X3 @ Xa2 ) )
% 5.25/5.59 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.25/5.59 => ( Y = X3 ) )
% 5.25/5.59 & ( ( Xa2 != zero_zero_nat )
% 5.25/5.59 => ( Y
% 5.25/5.59 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X3 @ Xa2 ) ) ) ) )
% 5.25/5.59 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X3 @ Xa2 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_nat.pelims
% 5.25/5.59 thf(fact_9749_card__greaterThanLessThan__int,axiom,
% 5.25/5.59 ! [L2: int,U: int] :
% 5.25/5.59 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L2 @ U ) )
% 5.25/5.59 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L2 @ one_one_int ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_greaterThanLessThan_int
% 5.25/5.59 thf(fact_9750_finite__greaterThanLessThan__int,axiom,
% 5.25/5.59 ! [L2: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L2 @ U ) ) ).
% 5.25/5.59
% 5.25/5.59 % finite_greaterThanLessThan_int
% 5.25/5.59 thf(fact_9751_card_Ocomp__fun__commute__on,axiom,
% 5.25/5.59 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.25/5.59 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.25/5.59
% 5.25/5.59 % card.comp_fun_commute_on
% 5.25/5.59 thf(fact_9752_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 5.25/5.59 ! [L2: int,U: int] :
% 5.25/5.59 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 5.25/5.59 = ( set_or5832277885323065728an_int @ L2 @ U ) ) ).
% 5.25/5.59
% 5.25/5.59 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 5.25/5.59 thf(fact_9753_Code__Numeral_Onegative__def,axiom,
% 5.25/5.59 ( code_negative
% 5.25/5.59 = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 5.25/5.59
% 5.25/5.59 % Code_Numeral.negative_def
% 5.25/5.59 thf(fact_9754_Code__Target__Int_Onegative__def,axiom,
% 5.25/5.59 ( code_Target_negative
% 5.25/5.59 = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % Code_Target_Int.negative_def
% 5.25/5.59 thf(fact_9755_xor__minus__numerals_I2_J,axiom,
% 5.25/5.59 ! [K: int,N: num] :
% 5.25/5.59 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % xor_minus_numerals(2)
% 5.25/5.59 thf(fact_9756_finite__greaterThanLessThan,axiom,
% 5.25/5.59 ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 5.25/5.59
% 5.25/5.59 % finite_greaterThanLessThan
% 5.25/5.59 thf(fact_9757_card__greaterThanLessThan,axiom,
% 5.25/5.59 ! [L2: nat,U: nat] :
% 5.25/5.59 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) )
% 5.25/5.59 = ( minus_minus_nat @ U @ ( suc @ L2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_greaterThanLessThan
% 5.25/5.59 thf(fact_9758_xor__minus__numerals_I1_J,axiom,
% 5.25/5.59 ! [N: num,K: int] :
% 5.25/5.59 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 5.25/5.59 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % xor_minus_numerals(1)
% 5.25/5.59 thf(fact_9759_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.25/5.59 ! [L2: nat,U: nat] :
% 5.25/5.59 ( ( set_or4665077453230672383an_nat @ ( suc @ L2 ) @ U )
% 5.25/5.59 = ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 5.25/5.59
% 5.25/5.59 % atLeastSucLessThan_greaterThanLessThan
% 5.25/5.59 thf(fact_9760_tanh__real__bounds,axiom,
% 5.25/5.59 ! [X3: real] : ( member_real @ ( tanh_real @ X3 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 5.25/5.59
% 5.25/5.59 % tanh_real_bounds
% 5.25/5.59 thf(fact_9761_sub__BitM__One__eq,axiom,
% 5.25/5.59 ! [N: num] :
% 5.25/5.59 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 5.25/5.59 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % sub_BitM_One_eq
% 5.25/5.59 thf(fact_9762_nat__of__integer__non__positive,axiom,
% 5.25/5.59 ! [K: code_integer] :
% 5.25/5.59 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 5.25/5.59 => ( ( code_nat_of_integer @ K )
% 5.25/5.59 = zero_zero_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % nat_of_integer_non_positive
% 5.25/5.59 thf(fact_9763_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.25/5.59 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.25/5.59 @ ^ [X2: nat,Y6: nat] : ( ord_less_eq_nat @ Y6 @ X2 )
% 5.25/5.59 @ ^ [X2: nat,Y6: nat] : ( ord_less_nat @ Y6 @ X2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % max_nat.semilattice_neutr_order_axioms
% 5.25/5.59 thf(fact_9764_Suc__funpow,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( compow_nat_nat @ N @ suc )
% 5.25/5.59 = ( plus_plus_nat @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % Suc_funpow
% 5.25/5.59 thf(fact_9765_nat__of__integer__code__post_I3_J,axiom,
% 5.25/5.59 ! [K: num] :
% 5.25/5.59 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.25/5.59 = ( numeral_numeral_nat @ K ) ) ).
% 5.25/5.59
% 5.25/5.59 % nat_of_integer_code_post(3)
% 5.25/5.59 thf(fact_9766_nat__of__integer__code__post_I2_J,axiom,
% 5.25/5.59 ( ( code_nat_of_integer @ one_one_Code_integer )
% 5.25/5.59 = one_one_nat ) ).
% 5.25/5.59
% 5.25/5.59 % nat_of_integer_code_post(2)
% 5.25/5.59 thf(fact_9767_nat__of__integer__code,axiom,
% 5.25/5.59 ( code_nat_of_integer
% 5.25/5.59 = ( ^ [K3: code_integer] :
% 5.25/5.59 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.25/5.59 @ ( produc1555791787009142072er_nat
% 5.25/5.59 @ ^ [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 ) )
% 5.25/5.59 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % nat_of_integer_code
% 5.25/5.59 thf(fact_9768_int__of__integer__code,axiom,
% 5.25/5.59 ( code_int_of_integer
% 5.25/5.59 = ( ^ [K3: code_integer] :
% 5.25/5.59 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 5.25/5.59 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.25/5.59 @ ( produc1553301316500091796er_int
% 5.25/5.59 @ ^ [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 ) )
% 5.25/5.59 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % int_of_integer_code
% 5.25/5.59 thf(fact_9769_int__of__integer__numeral,axiom,
% 5.25/5.59 ! [K: num] :
% 5.25/5.59 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.25/5.59 = ( numeral_numeral_int @ K ) ) ).
% 5.25/5.59
% 5.25/5.59 % int_of_integer_numeral
% 5.25/5.59 thf(fact_9770_plus__integer_Orep__eq,axiom,
% 5.25/5.59 ! [X3: code_integer,Xa2: code_integer] :
% 5.25/5.59 ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X3 @ Xa2 ) )
% 5.25/5.59 = ( plus_plus_int @ ( code_int_of_integer @ X3 ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % plus_integer.rep_eq
% 5.25/5.59 thf(fact_9771_times__integer_Orep__eq,axiom,
% 5.25/5.59 ! [X3: code_integer,Xa2: code_integer] :
% 5.25/5.59 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X3 @ Xa2 ) )
% 5.25/5.59 = ( times_times_int @ ( code_int_of_integer @ X3 ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % times_integer.rep_eq
% 5.25/5.59 thf(fact_9772_one__integer_Orep__eq,axiom,
% 5.25/5.59 ( ( code_int_of_integer @ one_one_Code_integer )
% 5.25/5.59 = one_one_int ) ).
% 5.25/5.59
% 5.25/5.59 % one_integer.rep_eq
% 5.25/5.59 thf(fact_9773_modulo__integer_Orep__eq,axiom,
% 5.25/5.59 ! [X3: code_integer,Xa2: code_integer] :
% 5.25/5.59 ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X3 @ Xa2 ) )
% 5.25/5.59 = ( modulo_modulo_int @ ( code_int_of_integer @ X3 ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % modulo_integer.rep_eq
% 5.25/5.59 thf(fact_9774_less__eq__integer_Orep__eq,axiom,
% 5.25/5.59 ( ord_le3102999989581377725nteger
% 5.25/5.59 = ( ^ [X2: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % less_eq_integer.rep_eq
% 5.25/5.59 thf(fact_9775_integer__less__eq__iff,axiom,
% 5.25/5.59 ( ord_le3102999989581377725nteger
% 5.25/5.59 = ( ^ [K3: code_integer,L: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % integer_less_eq_iff
% 5.25/5.59 thf(fact_9776_times__int_Oabs__eq,axiom,
% 5.25/5.59 ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 5.25/5.59 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 5.25/5.59 = ( abs_Integ
% 5.25/5.59 @ ( produc27273713700761075at_nat
% 5.25/5.59 @ ^ [X2: nat,Y6: nat] :
% 5.25/5.59 ( produc2626176000494625587at_nat
% 5.25/5.59 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y6 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y6 @ U2 ) ) ) )
% 5.25/5.59 @ Xa2
% 5.25/5.59 @ X3 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % times_int.abs_eq
% 5.25/5.59 thf(fact_9777_one__int__def,axiom,
% 5.25/5.59 ( one_one_int
% 5.25/5.59 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % one_int_def
% 5.25/5.59 thf(fact_9778_less__int_Oabs__eq,axiom,
% 5.25/5.59 ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 5.25/5.59 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 5.25/5.59 = ( produc8739625826339149834_nat_o
% 5.25/5.59 @ ^ [X2: nat,Y6: nat] :
% 5.25/5.59 ( produc6081775807080527818_nat_o
% 5.25/5.59 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) )
% 5.25/5.59 @ Xa2
% 5.25/5.59 @ X3 ) ) ).
% 5.25/5.59
% 5.25/5.59 % less_int.abs_eq
% 5.25/5.59 thf(fact_9779_less__eq__int_Oabs__eq,axiom,
% 5.25/5.59 ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 5.25/5.59 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 5.25/5.59 = ( produc8739625826339149834_nat_o
% 5.25/5.59 @ ^ [X2: nat,Y6: nat] :
% 5.25/5.59 ( produc6081775807080527818_nat_o
% 5.25/5.59 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) )
% 5.25/5.59 @ Xa2
% 5.25/5.59 @ X3 ) ) ).
% 5.25/5.59
% 5.25/5.59 % less_eq_int.abs_eq
% 5.25/5.59 thf(fact_9780_plus__int_Oabs__eq,axiom,
% 5.25/5.59 ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 5.25/5.59 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 5.25/5.59 = ( abs_Integ
% 5.25/5.59 @ ( produc27273713700761075at_nat
% 5.25/5.59 @ ^ [X2: nat,Y6: nat] :
% 5.25/5.59 ( produc2626176000494625587at_nat
% 5.25/5.59 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y6 @ V4 ) ) )
% 5.25/5.59 @ Xa2
% 5.25/5.59 @ X3 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % plus_int.abs_eq
% 5.25/5.59 thf(fact_9781_minus__int_Oabs__eq,axiom,
% 5.25/5.59 ! [Xa2: product_prod_nat_nat,X3: product_prod_nat_nat] :
% 5.25/5.59 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X3 ) )
% 5.25/5.59 = ( abs_Integ
% 5.25/5.59 @ ( produc27273713700761075at_nat
% 5.25/5.59 @ ^ [X2: nat,Y6: nat] :
% 5.25/5.59 ( produc2626176000494625587at_nat
% 5.25/5.59 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y6 @ U2 ) ) )
% 5.25/5.59 @ Xa2
% 5.25/5.59 @ X3 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % minus_int.abs_eq
% 5.25/5.59 thf(fact_9782_num__of__nat_Osimps_I2_J,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( num_of_nat @ ( suc @ N ) )
% 5.25/5.59 = ( inc @ ( num_of_nat @ N ) ) ) )
% 5.25/5.59 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( num_of_nat @ ( suc @ N ) )
% 5.25/5.59 = one ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % num_of_nat.simps(2)
% 5.25/5.59 thf(fact_9783_num__of__nat__numeral__eq,axiom,
% 5.25/5.59 ! [Q2: num] :
% 5.25/5.59 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 5.25/5.59 = Q2 ) ).
% 5.25/5.59
% 5.25/5.59 % num_of_nat_numeral_eq
% 5.25/5.59 thf(fact_9784_num__of__nat_Osimps_I1_J,axiom,
% 5.25/5.59 ( ( num_of_nat @ zero_zero_nat )
% 5.25/5.59 = one ) ).
% 5.25/5.59
% 5.25/5.59 % num_of_nat.simps(1)
% 5.25/5.59 thf(fact_9785_numeral__num__of__nat,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 5.25/5.59 = N ) ) ).
% 5.25/5.59
% 5.25/5.59 % numeral_num_of_nat
% 5.25/5.59 thf(fact_9786_num__of__nat__One,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 5.25/5.59 => ( ( num_of_nat @ N )
% 5.25/5.59 = one ) ) ).
% 5.25/5.59
% 5.25/5.59 % num_of_nat_One
% 5.25/5.59 thf(fact_9787_num__of__nat__double,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 5.25/5.59 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % num_of_nat_double
% 5.25/5.59 thf(fact_9788_num__of__nat__plus__distrib,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 5.25/5.59 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % num_of_nat_plus_distrib
% 5.25/5.59 thf(fact_9789_less__eq__int_Orep__eq,axiom,
% 5.25/5.59 ( ord_less_eq_int
% 5.25/5.59 = ( ^ [X2: int,Xa4: int] :
% 5.25/5.59 ( produc8739625826339149834_nat_o
% 5.25/5.59 @ ^ [Y6: nat,Z5: nat] :
% 5.25/5.59 ( produc6081775807080527818_nat_o
% 5.25/5.59 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y6 @ V4 ) @ ( plus_plus_nat @ U2 @ Z5 ) ) )
% 5.25/5.59 @ ( rep_Integ @ X2 )
% 5.25/5.59 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % less_eq_int.rep_eq
% 5.25/5.59 thf(fact_9790_less__int_Orep__eq,axiom,
% 5.25/5.59 ( ord_less_int
% 5.25/5.59 = ( ^ [X2: int,Xa4: int] :
% 5.25/5.59 ( produc8739625826339149834_nat_o
% 5.25/5.59 @ ^ [Y6: nat,Z5: nat] :
% 5.25/5.59 ( produc6081775807080527818_nat_o
% 5.25/5.59 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y6 @ V4 ) @ ( plus_plus_nat @ U2 @ Z5 ) ) )
% 5.25/5.59 @ ( rep_Integ @ X2 )
% 5.25/5.59 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % less_int.rep_eq
% 5.25/5.59 thf(fact_9791_pred__nat__def,axiom,
% 5.25/5.59 ( pred_nat
% 5.25/5.59 = ( collec3392354462482085612at_nat
% 5.25/5.59 @ ( produc6081775807080527818_nat_o
% 5.25/5.59 @ ^ [M6: nat,N2: nat] :
% 5.25/5.59 ( N2
% 5.25/5.59 = ( suc @ M6 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % pred_nat_def
% 5.25/5.59 thf(fact_9792_pow_Osimps_I3_J,axiom,
% 5.25/5.59 ! [X3: num,Y: num] :
% 5.25/5.59 ( ( pow @ X3 @ ( bit1 @ Y ) )
% 5.25/5.59 = ( times_times_num @ ( sqr @ ( pow @ X3 @ Y ) ) @ X3 ) ) ).
% 5.25/5.59
% 5.25/5.59 % pow.simps(3)
% 5.25/5.59 thf(fact_9793_image__minus__const__atLeastLessThan__nat,axiom,
% 5.25/5.59 ! [C: nat,Y: nat,X3: nat] :
% 5.25/5.59 ( ( ( ord_less_nat @ C @ Y )
% 5.25/5.59 => ( ( image_nat_nat
% 5.25/5.59 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 5.25/5.59 @ ( set_or4665077453230672383an_nat @ X3 @ Y ) )
% 5.25/5.59 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X3 @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 5.25/5.59 & ( ~ ( ord_less_nat @ C @ Y )
% 5.25/5.59 => ( ( ( ord_less_nat @ X3 @ Y )
% 5.25/5.59 => ( ( image_nat_nat
% 5.25/5.59 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 5.25/5.59 @ ( set_or4665077453230672383an_nat @ X3 @ Y ) )
% 5.25/5.59 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.25/5.59 & ( ~ ( ord_less_nat @ X3 @ Y )
% 5.25/5.59 => ( ( image_nat_nat
% 5.25/5.59 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 5.25/5.59 @ ( set_or4665077453230672383an_nat @ X3 @ Y ) )
% 5.25/5.59 = bot_bot_set_nat ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % image_minus_const_atLeastLessThan_nat
% 5.25/5.59 thf(fact_9794_bij__betw__Suc,axiom,
% 5.25/5.59 ! [M7: set_nat,N5: set_nat] :
% 5.25/5.59 ( ( bij_betw_nat_nat @ suc @ M7 @ N5 )
% 5.25/5.59 = ( ( image_nat_nat @ suc @ M7 )
% 5.25/5.59 = N5 ) ) ).
% 5.25/5.59
% 5.25/5.59 % bij_betw_Suc
% 5.25/5.59 thf(fact_9795_image__Suc__atLeastAtMost,axiom,
% 5.25/5.59 ! [I2: nat,J2: nat] :
% 5.25/5.59 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I2 @ J2 ) )
% 5.25/5.59 = ( set_or1269000886237332187st_nat @ ( suc @ I2 ) @ ( suc @ J2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % image_Suc_atLeastAtMost
% 5.25/5.59 thf(fact_9796_image__Suc__atLeastLessThan,axiom,
% 5.25/5.59 ! [I2: nat,J2: nat] :
% 5.25/5.59 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I2 @ J2 ) )
% 5.25/5.59 = ( set_or4665077453230672383an_nat @ ( suc @ I2 ) @ ( suc @ J2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % image_Suc_atLeastLessThan
% 5.25/5.59 thf(fact_9797_zero__notin__Suc__image,axiom,
% 5.25/5.59 ! [A2: set_nat] :
% 5.25/5.59 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % zero_notin_Suc_image
% 5.25/5.59 thf(fact_9798_sqr_Osimps_I2_J,axiom,
% 5.25/5.59 ! [N: num] :
% 5.25/5.59 ( ( sqr @ ( bit0 @ N ) )
% 5.25/5.59 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % sqr.simps(2)
% 5.25/5.59 thf(fact_9799_sqr_Osimps_I1_J,axiom,
% 5.25/5.59 ( ( sqr @ one )
% 5.25/5.59 = one ) ).
% 5.25/5.59
% 5.25/5.59 % sqr.simps(1)
% 5.25/5.59 thf(fact_9800_sqr__conv__mult,axiom,
% 5.25/5.59 ( sqr
% 5.25/5.59 = ( ^ [X2: num] : ( times_times_num @ X2 @ X2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % sqr_conv_mult
% 5.25/5.59 thf(fact_9801_image__Suc__lessThan,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.59 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % image_Suc_lessThan
% 5.25/5.59 thf(fact_9802_image__Suc__atMost,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 5.25/5.59 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % image_Suc_atMost
% 5.25/5.59 thf(fact_9803_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.25/5.59 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % atLeast0_atMost_Suc_eq_insert_0
% 5.25/5.59 thf(fact_9804_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.25/5.59 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % atLeast0_lessThan_Suc_eq_insert_0
% 5.25/5.59 thf(fact_9805_lessThan__Suc__eq__insert__0,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 5.25/5.59 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % lessThan_Suc_eq_insert_0
% 5.25/5.59 thf(fact_9806_atMost__Suc__eq__insert__0,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 5.25/5.59 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % atMost_Suc_eq_insert_0
% 5.25/5.59 thf(fact_9807_pow_Osimps_I2_J,axiom,
% 5.25/5.59 ! [X3: num,Y: num] :
% 5.25/5.59 ( ( pow @ X3 @ ( bit0 @ Y ) )
% 5.25/5.59 = ( sqr @ ( pow @ X3 @ Y ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % pow.simps(2)
% 5.25/5.59 thf(fact_9808_sqr_Osimps_I3_J,axiom,
% 5.25/5.59 ! [N: num] :
% 5.25/5.59 ( ( sqr @ ( bit1 @ N ) )
% 5.25/5.59 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % sqr.simps(3)
% 5.25/5.59 thf(fact_9809_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.25/5.59 ! [N: nat,J2: nat,I2: nat] :
% 5.25/5.59 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J2 @ ( suc @ I2 ) ) )
% 5.25/5.59 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J2 ) ) @ N )
% 5.25/5.59 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % nth_sorted_list_of_set_greaterThanLessThan
% 5.25/5.59 thf(fact_9810_Inf__real__def,axiom,
% 5.25/5.59 ( comple4887499456419720421f_real
% 5.25/5.59 = ( ^ [X4: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X4 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Inf_real_def
% 5.25/5.59 thf(fact_9811_UN__atMost__UNIV,axiom,
% 5.25/5.59 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 5.25/5.59 = top_top_set_nat ) ).
% 5.25/5.59
% 5.25/5.59 % UN_atMost_UNIV
% 5.25/5.59 thf(fact_9812_UN__lessThan__UNIV,axiom,
% 5.25/5.59 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 5.25/5.59 = top_top_set_nat ) ).
% 5.25/5.59
% 5.25/5.59 % UN_lessThan_UNIV
% 5.25/5.59 thf(fact_9813_finite__int__iff__bounded__le,axiom,
% 5.25/5.59 ( finite_finite_int
% 5.25/5.59 = ( ^ [S4: set_int] :
% 5.25/5.59 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S4 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % finite_int_iff_bounded_le
% 5.25/5.59 thf(fact_9814_finite__int__iff__bounded,axiom,
% 5.25/5.59 ( finite_finite_int
% 5.25/5.59 = ( ^ [S4: set_int] :
% 5.25/5.59 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S4 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % finite_int_iff_bounded
% 5.25/5.59 thf(fact_9815_image__int__atLeastAtMost,axiom,
% 5.25/5.59 ! [A: nat,B: nat] :
% 5.25/5.59 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.25/5.59 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % image_int_atLeastAtMost
% 5.25/5.59 thf(fact_9816_image__int__atLeastLessThan,axiom,
% 5.25/5.59 ! [A: nat,B: nat] :
% 5.25/5.59 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 5.25/5.59 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % image_int_atLeastLessThan
% 5.25/5.59 thf(fact_9817_suminf__eq__SUP__real,axiom,
% 5.25/5.59 ! [X8: nat > real] :
% 5.25/5.59 ( ( summable_real @ X8 )
% 5.25/5.59 => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I4 ) )
% 5.25/5.59 => ( ( suminf_real @ X8 )
% 5.25/5.59 = ( comple1385675409528146559p_real
% 5.25/5.59 @ ( image_nat_real
% 5.25/5.59 @ ^ [I3: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I3 ) )
% 5.25/5.59 @ top_top_set_nat ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % suminf_eq_SUP_real
% 5.25/5.59 thf(fact_9818_image__add__int__atLeastLessThan,axiom,
% 5.25/5.59 ! [L2: int,U: int] :
% 5.25/5.59 ( ( image_int_int
% 5.25/5.59 @ ^ [X2: int] : ( plus_plus_int @ X2 @ L2 )
% 5.25/5.59 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L2 ) ) )
% 5.25/5.59 = ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 5.25/5.59
% 5.25/5.59 % image_add_int_atLeastLessThan
% 5.25/5.59 thf(fact_9819_range__mod,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( image_nat_nat
% 5.25/5.59 @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N )
% 5.25/5.59 @ top_top_set_nat )
% 5.25/5.59 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % range_mod
% 5.25/5.59 thf(fact_9820_image__atLeastZeroLessThan__int,axiom,
% 5.25/5.59 ! [U: int] :
% 5.25/5.59 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.25/5.59 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 5.25/5.59 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % image_atLeastZeroLessThan_int
% 5.25/5.59 thf(fact_9821_UNIV__nat__eq,axiom,
% 5.25/5.59 ( top_top_set_nat
% 5.25/5.59 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % UNIV_nat_eq
% 5.25/5.59 thf(fact_9822_card__UNIV__unit,axiom,
% 5.25/5.59 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.25/5.59 = one_one_nat ) ).
% 5.25/5.59
% 5.25/5.59 % card_UNIV_unit
% 5.25/5.59 thf(fact_9823_card__UNIV__bool,axiom,
% 5.25/5.59 ( ( finite_card_o @ top_top_set_o )
% 5.25/5.59 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_UNIV_bool
% 5.25/5.59 thf(fact_9824_range__mult,axiom,
% 5.25/5.59 ! [A: real] :
% 5.25/5.59 ( ( ( A = zero_zero_real )
% 5.25/5.59 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.25/5.59 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.25/5.59 & ( ( A != zero_zero_real )
% 5.25/5.59 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.25/5.59 = top_top_set_real ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % range_mult
% 5.25/5.59 thf(fact_9825_root__def,axiom,
% 5.25/5.59 ( root
% 5.25/5.59 = ( ^ [N2: nat,X2: real] :
% 5.25/5.59 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 5.25/5.59 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.25/5.59 @ ^ [Y6: real] : ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N2 ) )
% 5.25/5.59 @ X2 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % root_def
% 5.25/5.59 thf(fact_9826_card__UNIV__char,axiom,
% 5.25/5.59 ( ( finite_card_char @ top_top_set_char )
% 5.25/5.59 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_UNIV_char
% 5.25/5.59 thf(fact_9827_UNIV__char__of__nat,axiom,
% 5.25/5.59 ( top_top_set_char
% 5.25/5.59 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % UNIV_char_of_nat
% 5.25/5.59 thf(fact_9828_nat__of__char__less__256,axiom,
% 5.25/5.59 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % nat_of_char_less_256
% 5.25/5.59 thf(fact_9829_range__nat__of__char,axiom,
% 5.25/5.59 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.25/5.59 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % range_nat_of_char
% 5.25/5.59 thf(fact_9830_integer__of__char__code,axiom,
% 5.25/5.59 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.25/5.59 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.25/5.59 = ( 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 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % integer_of_char_code
% 5.25/5.59 thf(fact_9831_String_Ochar__of__ascii__of,axiom,
% 5.25/5.59 ! [C: char] :
% 5.25/5.59 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.25/5.59 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % String.char_of_ascii_of
% 5.25/5.59 thf(fact_9832_sorted__list__of__set__lessThan__Suc,axiom,
% 5.25/5.59 ! [K: nat] :
% 5.25/5.59 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.25/5.59 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % sorted_list_of_set_lessThan_Suc
% 5.25/5.59 thf(fact_9833_sorted__list__of__set__atMost__Suc,axiom,
% 5.25/5.59 ! [K: nat] :
% 5.25/5.59 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.25/5.59 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % sorted_list_of_set_atMost_Suc
% 5.25/5.59 thf(fact_9834_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.25/5.59 ! [I2: nat,J2: nat] :
% 5.25/5.59 ( ( ord_less_nat @ ( suc @ I2 ) @ J2 )
% 5.25/5.59 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J2 ) )
% 5.25/5.59 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J2 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % sorted_list_of_set_greaterThanLessThan
% 5.25/5.59 thf(fact_9835_upto__aux__rec,axiom,
% 5.25/5.59 ( upto_aux
% 5.25/5.59 = ( ^ [I3: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I3 ) @ Js @ ( upto_aux @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_aux_rec
% 5.25/5.59 thf(fact_9836_sup__enat__def,axiom,
% 5.25/5.59 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 5.25/5.59
% 5.25/5.59 % sup_enat_def
% 5.25/5.59 thf(fact_9837_sup__nat__def,axiom,
% 5.25/5.59 sup_sup_nat = ord_max_nat ).
% 5.25/5.59
% 5.25/5.59 % sup_nat_def
% 5.25/5.59 thf(fact_9838_atLeastLessThan__add__Un,axiom,
% 5.25/5.59 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.59 => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J2 @ K ) )
% 5.25/5.59 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J2 ) @ ( set_or4665077453230672383an_nat @ J2 @ ( plus_plus_nat @ J2 @ K ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % atLeastLessThan_add_Un
% 5.25/5.59 thf(fact_9839_upto_Opelims,axiom,
% 5.25/5.59 ! [X3: int,Xa2: int,Y: list_int] :
% 5.25/5.59 ( ( ( upto @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X3 @ Xa2 ) )
% 5.25/5.59 => ~ ( ( ( ( ord_less_eq_int @ X3 @ Xa2 )
% 5.25/5.59 => ( Y
% 5.25/5.59 = ( cons_int @ X3 @ ( upto @ ( plus_plus_int @ X3 @ one_one_int ) @ Xa2 ) ) ) )
% 5.25/5.59 & ( ~ ( ord_less_eq_int @ X3 @ Xa2 )
% 5.25/5.59 => ( Y = nil_int ) ) )
% 5.25/5.59 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X3 @ Xa2 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto.pelims
% 5.25/5.59 thf(fact_9840_upto_Opsimps,axiom,
% 5.25/5.59 ! [I2: int,J2: int] :
% 5.25/5.59 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J2 ) )
% 5.25/5.59 => ( ( ( ord_less_eq_int @ I2 @ J2 )
% 5.25/5.59 => ( ( upto @ I2 @ J2 )
% 5.25/5.59 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) ) ) )
% 5.25/5.59 & ( ~ ( ord_less_eq_int @ I2 @ J2 )
% 5.25/5.59 => ( ( upto @ I2 @ J2 )
% 5.25/5.59 = nil_int ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto.psimps
% 5.25/5.59 thf(fact_9841_upto__Nil,axiom,
% 5.25/5.59 ! [I2: int,J2: int] :
% 5.25/5.59 ( ( ( upto @ I2 @ J2 )
% 5.25/5.59 = nil_int )
% 5.25/5.59 = ( ord_less_int @ J2 @ I2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_Nil
% 5.25/5.59 thf(fact_9842_upto__Nil2,axiom,
% 5.25/5.59 ! [I2: int,J2: int] :
% 5.25/5.59 ( ( nil_int
% 5.25/5.59 = ( upto @ I2 @ J2 ) )
% 5.25/5.59 = ( ord_less_int @ J2 @ I2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_Nil2
% 5.25/5.59 thf(fact_9843_upto__empty,axiom,
% 5.25/5.59 ! [J2: int,I2: int] :
% 5.25/5.59 ( ( ord_less_int @ J2 @ I2 )
% 5.25/5.59 => ( ( upto @ I2 @ J2 )
% 5.25/5.59 = nil_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_empty
% 5.25/5.59 thf(fact_9844_upto__single,axiom,
% 5.25/5.59 ! [I2: int] :
% 5.25/5.59 ( ( upto @ I2 @ I2 )
% 5.25/5.59 = ( cons_int @ I2 @ nil_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_single
% 5.25/5.59 thf(fact_9845_nth__upto,axiom,
% 5.25/5.59 ! [I2: int,K: nat,J2: int] :
% 5.25/5.59 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) @ J2 )
% 5.25/5.59 => ( ( nth_int @ ( upto @ I2 @ J2 ) @ K )
% 5.25/5.59 = ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % nth_upto
% 5.25/5.59 thf(fact_9846_length__upto,axiom,
% 5.25/5.59 ! [I2: int,J2: int] :
% 5.25/5.59 ( ( size_size_list_int @ ( upto @ I2 @ J2 ) )
% 5.25/5.59 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J2 @ I2 ) @ one_one_int ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % length_upto
% 5.25/5.59 thf(fact_9847_upto__rec__numeral_I1_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.59 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.59 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.25/5.59 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.59 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.59 = nil_int ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_rec_numeral(1)
% 5.25/5.59 thf(fact_9848_upto__rec__numeral_I2_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.25/5.59 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 = nil_int ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_rec_numeral(2)
% 5.25/5.59 thf(fact_9849_upto__rec__numeral_I3_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.59 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.59 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.25/5.59 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.59 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.59 = nil_int ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_rec_numeral(3)
% 5.25/5.59 thf(fact_9850_upto__rec__numeral_I4_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.25/5.59 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 = nil_int ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_rec_numeral(4)
% 5.25/5.59 thf(fact_9851_upto__aux__def,axiom,
% 5.25/5.59 ( upto_aux
% 5.25/5.59 = ( ^ [I3: int,J3: int] : ( append_int @ ( upto @ I3 @ J3 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_aux_def
% 5.25/5.59 thf(fact_9852_upto__code,axiom,
% 5.25/5.59 ( upto
% 5.25/5.59 = ( ^ [I3: int,J3: int] : ( upto_aux @ I3 @ J3 @ nil_int ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_code
% 5.25/5.59 thf(fact_9853_distinct__upto,axiom,
% 5.25/5.59 ! [I2: int,J2: int] : ( distinct_int @ ( upto @ I2 @ J2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % distinct_upto
% 5.25/5.59 thf(fact_9854_atLeastAtMost__upto,axiom,
% 5.25/5.59 ( set_or1266510415728281911st_int
% 5.25/5.59 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ J3 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % atLeastAtMost_upto
% 5.25/5.59 thf(fact_9855_upto__split2,axiom,
% 5.25/5.59 ! [I2: int,J2: int,K: int] :
% 5.25/5.59 ( ( ord_less_eq_int @ I2 @ J2 )
% 5.25/5.59 => ( ( ord_less_eq_int @ J2 @ K )
% 5.25/5.59 => ( ( upto @ I2 @ K )
% 5.25/5.59 = ( append_int @ ( upto @ I2 @ J2 ) @ ( upto @ ( plus_plus_int @ J2 @ one_one_int ) @ K ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_split2
% 5.25/5.59 thf(fact_9856_upto__split1,axiom,
% 5.25/5.59 ! [I2: int,J2: int,K: int] :
% 5.25/5.59 ( ( ord_less_eq_int @ I2 @ J2 )
% 5.25/5.59 => ( ( ord_less_eq_int @ J2 @ K )
% 5.25/5.59 => ( ( upto @ I2 @ K )
% 5.25/5.59 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J2 @ one_one_int ) ) @ ( upto @ J2 @ K ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_split1
% 5.25/5.59 thf(fact_9857_atLeastLessThan__upto,axiom,
% 5.25/5.59 ( set_or4662586982721622107an_int
% 5.25/5.59 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % atLeastLessThan_upto
% 5.25/5.59 thf(fact_9858_upto__rec1,axiom,
% 5.25/5.59 ! [I2: int,J2: int] :
% 5.25/5.59 ( ( ord_less_eq_int @ I2 @ J2 )
% 5.25/5.59 => ( ( upto @ I2 @ J2 )
% 5.25/5.59 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_rec1
% 5.25/5.59 thf(fact_9859_upto_Oelims,axiom,
% 5.25/5.59 ! [X3: int,Xa2: int,Y: list_int] :
% 5.25/5.59 ( ( ( upto @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( ( ord_less_eq_int @ X3 @ Xa2 )
% 5.25/5.59 => ( Y
% 5.25/5.59 = ( cons_int @ X3 @ ( upto @ ( plus_plus_int @ X3 @ one_one_int ) @ Xa2 ) ) ) )
% 5.25/5.59 & ( ~ ( ord_less_eq_int @ X3 @ Xa2 )
% 5.25/5.59 => ( Y = nil_int ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto.elims
% 5.25/5.59 thf(fact_9860_upto_Osimps,axiom,
% 5.25/5.59 ( upto
% 5.25/5.59 = ( ^ [I3: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I3 @ J3 ) @ ( cons_int @ I3 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto.simps
% 5.25/5.59 thf(fact_9861_upto__rec2,axiom,
% 5.25/5.59 ! [I2: int,J2: int] :
% 5.25/5.59 ( ( ord_less_eq_int @ I2 @ J2 )
% 5.25/5.59 => ( ( upto @ I2 @ J2 )
% 5.25/5.59 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J2 @ one_one_int ) ) @ ( cons_int @ J2 @ nil_int ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_rec2
% 5.25/5.59 thf(fact_9862_greaterThanLessThan__upto,axiom,
% 5.25/5.59 ( set_or5832277885323065728an_int
% 5.25/5.59 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % greaterThanLessThan_upto
% 5.25/5.59 thf(fact_9863_upto__split3,axiom,
% 5.25/5.59 ! [I2: int,J2: int,K: int] :
% 5.25/5.59 ( ( ord_less_eq_int @ I2 @ J2 )
% 5.25/5.59 => ( ( ord_less_eq_int @ J2 @ K )
% 5.25/5.59 => ( ( upto @ I2 @ K )
% 5.25/5.59 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J2 @ one_one_int ) ) @ ( cons_int @ J2 @ ( upto @ ( plus_plus_int @ J2 @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upto_split3
% 5.25/5.59 thf(fact_9864_DERIV__even__real__root,axiom,
% 5.25/5.59 ! [N: nat,X3: real] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.59 => ( ( ord_less_real @ X3 @ zero_zero_real )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_even_real_root
% 5.25/5.59 thf(fact_9865_DERIV__pos__imp__increasing,axiom,
% 5.25/5.59 ! [A: real,B: real,F: real > real] :
% 5.25/5.59 ( ( ord_less_real @ A @ B )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ A @ X5 )
% 5.25/5.59 => ( ( ord_less_eq_real @ X5 @ B )
% 5.25/5.59 => ? [Y4: real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.25/5.59 & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 5.25/5.59 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_pos_imp_increasing
% 5.25/5.59 thf(fact_9866_DERIV__neg__imp__decreasing,axiom,
% 5.25/5.59 ! [A: real,B: real,F: real > real] :
% 5.25/5.59 ( ( ord_less_real @ A @ B )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ A @ X5 )
% 5.25/5.59 => ( ( ord_less_eq_real @ X5 @ B )
% 5.25/5.59 => ? [Y4: real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.25/5.59 & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 5.25/5.59 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_neg_imp_decreasing
% 5.25/5.59 thf(fact_9867_DERIV__nonpos__imp__nonincreasing,axiom,
% 5.25/5.59 ! [A: real,B: real,F: real > real] :
% 5.25/5.59 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ A @ X5 )
% 5.25/5.59 => ( ( ord_less_eq_real @ X5 @ B )
% 5.25/5.59 => ? [Y4: real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.25/5.59 & ( ord_less_eq_real @ Y4 @ zero_zero_real ) ) ) )
% 5.25/5.59 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_nonpos_imp_nonincreasing
% 5.25/5.59 thf(fact_9868_DERIV__nonneg__imp__nondecreasing,axiom,
% 5.25/5.59 ! [A: real,B: real,F: real > real] :
% 5.25/5.59 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ A @ X5 )
% 5.25/5.59 => ( ( ord_less_eq_real @ X5 @ B )
% 5.25/5.59 => ? [Y4: real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.25/5.59 & ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) )
% 5.25/5.59 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_nonneg_imp_nondecreasing
% 5.25/5.59 thf(fact_9869_deriv__nonneg__imp__mono,axiom,
% 5.25/5.59 ! [A: real,B: real,G: real > real,G2: real > real] :
% 5.25/5.59 ( ! [X5: real] :
% 5.25/5.59 ( ( member_real @ X5 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( member_real @ X5 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.25/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X5 ) ) )
% 5.25/5.59 => ( ( ord_less_eq_real @ A @ B )
% 5.25/5.59 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % deriv_nonneg_imp_mono
% 5.25/5.59 thf(fact_9870_DERIV__const__ratio__const,axiom,
% 5.25/5.59 ! [A: real,B: real,F: real > real,K: real] :
% 5.25/5.59 ( ( A != B )
% 5.25/5.59 => ( ! [X5: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.25/5.59 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.25/5.59 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_const_ratio_const
% 5.25/5.59 thf(fact_9871_has__real__derivative__pos__inc__right,axiom,
% 5.25/5.59 ! [F: real > real,L2: real,X3: real,S3: set_real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X3 @ S3 ) )
% 5.25/5.59 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.25/5.59 => ? [D3: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.25/5.59 & ! [H4: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.25/5.59 => ( ( member_real @ ( plus_plus_real @ X3 @ H4 ) @ S3 )
% 5.25/5.59 => ( ( ord_less_real @ H4 @ D3 )
% 5.25/5.59 => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % has_real_derivative_pos_inc_right
% 5.25/5.59 thf(fact_9872_has__real__derivative__neg__dec__right,axiom,
% 5.25/5.59 ! [F: real > real,L2: real,X3: real,S3: set_real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X3 @ S3 ) )
% 5.25/5.59 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.25/5.59 => ? [D3: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.25/5.59 & ! [H4: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.25/5.59 => ( ( member_real @ ( plus_plus_real @ X3 @ H4 ) @ S3 )
% 5.25/5.59 => ( ( ord_less_real @ H4 @ D3 )
% 5.25/5.59 => ( ord_less_real @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % has_real_derivative_neg_dec_right
% 5.25/5.59 thf(fact_9873_DERIV__pos__inc__right,axiom,
% 5.25/5.59 ! [F: real > real,L2: real,X3: real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.25/5.59 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.25/5.59 => ? [D3: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.25/5.59 & ! [H4: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.25/5.59 => ( ( ord_less_real @ H4 @ D3 )
% 5.25/5.59 => ( ord_less_real @ ( F @ X3 ) @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_pos_inc_right
% 5.25/5.59 thf(fact_9874_DERIV__neg__dec__right,axiom,
% 5.25/5.59 ! [F: real > real,L2: real,X3: real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.25/5.59 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.25/5.59 => ? [D3: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.25/5.59 & ! [H4: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.25/5.59 => ( ( ord_less_real @ H4 @ D3 )
% 5.25/5.59 => ( ord_less_real @ ( F @ ( plus_plus_real @ X3 @ H4 ) ) @ ( F @ X3 ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_neg_dec_right
% 5.25/5.59 thf(fact_9875_MVT2,axiom,
% 5.25/5.59 ! [A: real,B: real,F: real > real,F4: real > real] :
% 5.25/5.59 ( ( ord_less_real @ A @ B )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ A @ X5 )
% 5.25/5.59 => ( ( ord_less_eq_real @ X5 @ B )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.25/5.59 => ? [Z2: real] :
% 5.25/5.59 ( ( ord_less_real @ A @ Z2 )
% 5.25/5.59 & ( ord_less_real @ Z2 @ B )
% 5.25/5.59 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.25/5.59 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F4 @ Z2 ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % MVT2
% 5.25/5.59 thf(fact_9876_DERIV__const__average,axiom,
% 5.25/5.59 ! [A: real,B: real,V: real > real,K: real] :
% 5.25/5.59 ( ( A != B )
% 5.25/5.59 => ( ! [X5: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.25/5.59 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.59 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_const_average
% 5.25/5.59 thf(fact_9877_DERIV__local__min,axiom,
% 5.25/5.59 ! [F: real > real,L2: real,X3: real,D: real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.25/5.59 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.25/5.59 => ( ! [Y3: real] :
% 5.25/5.59 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) @ D )
% 5.25/5.59 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.25/5.59 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_local_min
% 5.25/5.59 thf(fact_9878_DERIV__local__max,axiom,
% 5.25/5.59 ! [F: real > real,L2: real,X3: real,D: real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.25/5.59 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.25/5.59 => ( ! [Y3: real] :
% 5.25/5.59 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) @ D )
% 5.25/5.59 => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X3 ) ) )
% 5.25/5.59 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_local_max
% 5.25/5.59 thf(fact_9879_DERIV__ln__divide,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_ln_divide
% 5.25/5.59 thf(fact_9880_DERIV__pow,axiom,
% 5.25/5.59 ! [N: nat,X3: real,S: set_real] :
% 5.25/5.59 ( has_fi5821293074295781190e_real
% 5.25/5.59 @ ^ [X2: real] : ( power_power_real @ X2 @ N )
% 5.25/5.59 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.25/5.59 @ ( topolo2177554685111907308n_real @ X3 @ S ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_pow
% 5.25/5.59 thf(fact_9881_DERIV__fun__pow,axiom,
% 5.25/5.59 ! [G: real > real,M: real,X3: real,N: nat] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real
% 5.25/5.59 @ ^ [X2: real] : ( power_power_real @ ( G @ X2 ) @ N )
% 5.25/5.59 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X3 ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 5.25/5.59 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_fun_pow
% 5.25/5.59 thf(fact_9882_has__real__derivative__powr,axiom,
% 5.25/5.59 ! [Z: real,R2: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.25/5.59 => ( has_fi5821293074295781190e_real
% 5.25/5.59 @ ^ [Z5: real] : ( powr_real @ Z5 @ R2 )
% 5.25/5.59 @ ( times_times_real @ R2 @ ( powr_real @ Z @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 5.25/5.59 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % has_real_derivative_powr
% 5.25/5.59 thf(fact_9883_DERIV__log,axiom,
% 5.25/5.59 ! [X3: real,B: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X3 ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_log
% 5.25/5.59 thf(fact_9884_DERIV__fun__powr,axiom,
% 5.25/5.59 ! [G: real > real,M: real,X3: real,R2: real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.25/5.59 => ( ( ord_less_real @ zero_zero_real @ ( G @ X3 ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real
% 5.25/5.59 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ R2 )
% 5.25/5.59 @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X3 ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.25/5.59 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_fun_powr
% 5.25/5.59 thf(fact_9885_DERIV__powr,axiom,
% 5.25/5.59 ! [G: real > real,M: real,X3: real,F: real > real,R2: real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.25/5.59 => ( ( ord_less_real @ zero_zero_real @ ( G @ X3 ) )
% 5.25/5.59 => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real
% 5.25/5.59 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) )
% 5.25/5.59 @ ( times_times_real @ ( powr_real @ ( G @ X3 ) @ ( F @ X3 ) ) @ ( plus_plus_real @ ( times_times_real @ R2 @ ( ln_ln_real @ ( G @ X3 ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X3 ) ) @ ( G @ X3 ) ) ) )
% 5.25/5.59 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_powr
% 5.25/5.59 thf(fact_9886_DERIV__real__sqrt,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_real_sqrt
% 5.25/5.59 thf(fact_9887_DERIV__series_H,axiom,
% 5.25/5.59 ! [F: real > nat > real,F4: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 5.25/5.59 ( ! [N3: nat] :
% 5.25/5.59 ( has_fi5821293074295781190e_real
% 5.25/5.59 @ ^ [X2: real] : ( F @ X2 @ N3 )
% 5.25/5.59 @ ( F4 @ X0 @ N3 )
% 5.25/5.59 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.25/5.59 => ( summable_real @ ( F @ X5 ) ) )
% 5.25/5.59 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.25/5.59 => ( ( summable_real @ ( F4 @ X0 ) )
% 5.25/5.59 => ( ( summable_real @ L5 )
% 5.25/5.59 => ( ! [N3: nat,X5: real,Y3: real] :
% 5.25/5.59 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.25/5.59 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.25/5.59 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X5 @ N3 ) @ ( F @ Y3 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X5 @ Y3 ) ) ) ) ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real
% 5.25/5.59 @ ^ [X2: real] : ( suminf_real @ ( F @ X2 ) )
% 5.25/5.59 @ ( suminf_real @ ( F4 @ X0 ) )
% 5.25/5.59 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_series'
% 5.25/5.59 thf(fact_9888_DERIV__arctan,axiom,
% 5.25/5.59 ! [X3: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_arctan
% 5.25/5.59 thf(fact_9889_arsinh__real__has__field__derivative,axiom,
% 5.25/5.59 ! [X3: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ A2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % arsinh_real_has_field_derivative
% 5.25/5.59 thf(fact_9890_DERIV__real__sqrt__generic,axiom,
% 5.25/5.59 ! [X3: real,D4: real] :
% 5.25/5.59 ( ( X3 != zero_zero_real )
% 5.25/5.59 => ( ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.59 => ( D4
% 5.25/5.59 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 => ( ( ( ord_less_real @ X3 @ zero_zero_real )
% 5.25/5.59 => ( D4
% 5.25/5.59 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_real_sqrt_generic
% 5.25/5.59 thf(fact_9891_arcosh__real__has__field__derivative,axiom,
% 5.25/5.59 ! [X3: real,A2: set_real] :
% 5.25/5.59 ( ( ord_less_real @ one_one_real @ X3 )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ A2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % arcosh_real_has_field_derivative
% 5.25/5.59 thf(fact_9892_artanh__real__has__field__derivative,axiom,
% 5.25/5.59 ! [X3: real,A2: set_real] :
% 5.25/5.59 ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ A2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % artanh_real_has_field_derivative
% 5.25/5.59 thf(fact_9893_DERIV__power__series_H,axiom,
% 5.25/5.59 ! [R: real,F: nat > real,X0: real] :
% 5.25/5.59 ( ! [X5: real] :
% 5.25/5.59 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.25/5.59 => ( summable_real
% 5.25/5.59 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X5 @ N2 ) ) ) )
% 5.25/5.59 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.25/5.59 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.25/5.59 => ( has_fi5821293074295781190e_real
% 5.25/5.59 @ ^ [X2: real] :
% 5.25/5.59 ( suminf_real
% 5.25/5.59 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X2 @ ( suc @ N2 ) ) ) )
% 5.25/5.59 @ ( suminf_real
% 5.25/5.59 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X0 @ N2 ) ) )
% 5.25/5.59 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_power_series'
% 5.25/5.59 thf(fact_9894_DERIV__real__root,axiom,
% 5.25/5.59 ! [N: nat,X3: real] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_real_root
% 5.25/5.59 thf(fact_9895_DERIV__arccos,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.59 => ( ( ord_less_real @ X3 @ one_one_real )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_arccos
% 5.25/5.59 thf(fact_9896_DERIV__arcsin,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.59 => ( ( ord_less_real @ X3 @ one_one_real )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_arcsin
% 5.25/5.59 thf(fact_9897_Maclaurin__all__le__objl,axiom,
% 5.25/5.59 ! [Diff: nat > real > real,F: real > real,X3: real,N: nat] :
% 5.25/5.59 ( ( ( ( Diff @ zero_zero_nat )
% 5.25/5.59 = F )
% 5.25/5.59 & ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.25/5.59 => ? [T3: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 5.25/5.59 & ( ( F @ X3 )
% 5.25/5.59 = ( plus_plus_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.59 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Maclaurin_all_le_objl
% 5.25/5.59 thf(fact_9898_Maclaurin__all__le,axiom,
% 5.25/5.59 ! [Diff: nat > real > real,F: real > real,X3: real,N: nat] :
% 5.25/5.59 ( ( ( Diff @ zero_zero_nat )
% 5.25/5.59 = F )
% 5.25/5.59 => ( ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.25/5.59 => ? [T3: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 5.25/5.59 & ( ( F @ X3 )
% 5.25/5.59 = ( plus_plus_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.59 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Maclaurin_all_le
% 5.25/5.59 thf(fact_9899_DERIV__odd__real__root,axiom,
% 5.25/5.59 ! [N: nat,X3: real] :
% 5.25/5.59 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.59 => ( ( X3 != zero_zero_real )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_odd_real_root
% 5.25/5.59 thf(fact_9900_Maclaurin,axiom,
% 5.25/5.59 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.25/5.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( ( Diff @ zero_zero_nat )
% 5.25/5.59 = F )
% 5.25/5.59 => ( ! [M5: nat,T3: real] :
% 5.25/5.59 ( ( ( ord_less_nat @ M5 @ N )
% 5.25/5.59 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.25/5.59 & ( ord_less_eq_real @ T3 @ H2 ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.25/5.59 => ? [T3: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.25/5.59 & ( ord_less_real @ T3 @ H2 )
% 5.25/5.59 & ( ( F @ H2 )
% 5.25/5.59 = ( plus_plus_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.59 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Maclaurin
% 5.25/5.59 thf(fact_9901_Maclaurin2,axiom,
% 5.25/5.59 ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.25/5.59 => ( ( ( Diff @ zero_zero_nat )
% 5.25/5.59 = F )
% 5.25/5.59 => ( ! [M5: nat,T3: real] :
% 5.25/5.59 ( ( ( ord_less_nat @ M5 @ N )
% 5.25/5.59 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.25/5.59 & ( ord_less_eq_real @ T3 @ H2 ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.25/5.59 => ? [T3: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.25/5.59 & ( ord_less_eq_real @ T3 @ H2 )
% 5.25/5.59 & ( ( F @ H2 )
% 5.25/5.59 = ( plus_plus_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.59 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Maclaurin2
% 5.25/5.59 thf(fact_9902_Maclaurin__minus,axiom,
% 5.25/5.59 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.25/5.59 ( ( ord_less_real @ H2 @ zero_zero_real )
% 5.25/5.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( ( Diff @ zero_zero_nat )
% 5.25/5.59 = F )
% 5.25/5.59 => ( ! [M5: nat,T3: real] :
% 5.25/5.59 ( ( ( ord_less_nat @ M5 @ N )
% 5.25/5.59 & ( ord_less_eq_real @ H2 @ T3 )
% 5.25/5.59 & ( ord_less_eq_real @ T3 @ zero_zero_real ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.25/5.59 => ? [T3: real] :
% 5.25/5.59 ( ( ord_less_real @ H2 @ T3 )
% 5.25/5.59 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.25/5.59 & ( ( F @ H2 )
% 5.25/5.59 = ( plus_plus_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.59 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Maclaurin_minus
% 5.25/5.59 thf(fact_9903_Maclaurin__all__lt,axiom,
% 5.25/5.59 ! [Diff: nat > real > real,F: real > real,N: nat,X3: real] :
% 5.25/5.59 ( ( ( Diff @ zero_zero_nat )
% 5.25/5.59 = F )
% 5.25/5.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( X3 != zero_zero_real )
% 5.25/5.59 => ( ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.25/5.59 => ? [T3: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.25/5.59 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 5.25/5.59 & ( ( F @ X3 )
% 5.25/5.59 = ( plus_plus_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.59 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Maclaurin_all_lt
% 5.25/5.59 thf(fact_9904_Maclaurin__bi__le,axiom,
% 5.25/5.59 ! [Diff: nat > real > real,F: real > real,N: nat,X3: real] :
% 5.25/5.59 ( ( ( Diff @ zero_zero_nat )
% 5.25/5.59 = F )
% 5.25/5.59 => ( ! [M5: nat,T3: real] :
% 5.25/5.59 ( ( ( ord_less_nat @ M5 @ N )
% 5.25/5.59 & ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.25/5.59 => ? [T3: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X3 ) )
% 5.25/5.59 & ( ( F @ X3 )
% 5.25/5.59 = ( plus_plus_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X3 @ M6 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.59 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X3 @ N ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Maclaurin_bi_le
% 5.25/5.59 thf(fact_9905_Taylor,axiom,
% 5.25/5.59 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X3: real] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( ( Diff @ zero_zero_nat )
% 5.25/5.59 = F )
% 5.25/5.59 => ( ! [M5: nat,T3: real] :
% 5.25/5.59 ( ( ( ord_less_nat @ M5 @ N )
% 5.25/5.59 & ( ord_less_eq_real @ A @ T3 )
% 5.25/5.59 & ( ord_less_eq_real @ T3 @ B ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.25/5.59 => ( ( ord_less_eq_real @ A @ C )
% 5.25/5.59 => ( ( ord_less_eq_real @ C @ B )
% 5.25/5.59 => ( ( ord_less_eq_real @ A @ X3 )
% 5.25/5.59 => ( ( ord_less_eq_real @ X3 @ B )
% 5.25/5.59 => ( ( X3 != C )
% 5.25/5.59 => ? [T3: real] :
% 5.25/5.59 ( ( ( ord_less_real @ X3 @ C )
% 5.25/5.59 => ( ( ord_less_real @ X3 @ T3 )
% 5.25/5.59 & ( ord_less_real @ T3 @ C ) ) )
% 5.25/5.59 & ( ~ ( ord_less_real @ X3 @ C )
% 5.25/5.59 => ( ( ord_less_real @ C @ T3 )
% 5.25/5.59 & ( ord_less_real @ T3 @ X3 ) ) )
% 5.25/5.59 & ( ( F @ X3 )
% 5.25/5.59 = ( plus_plus_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ C ) @ M6 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.59 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X3 @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Taylor
% 5.25/5.59 thf(fact_9906_Taylor__up,axiom,
% 5.25/5.59 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( ( Diff @ zero_zero_nat )
% 5.25/5.59 = F )
% 5.25/5.59 => ( ! [M5: nat,T3: real] :
% 5.25/5.59 ( ( ( ord_less_nat @ M5 @ N )
% 5.25/5.59 & ( ord_less_eq_real @ A @ T3 )
% 5.25/5.59 & ( ord_less_eq_real @ T3 @ B ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.25/5.59 => ( ( ord_less_eq_real @ A @ C )
% 5.25/5.59 => ( ( ord_less_real @ C @ B )
% 5.25/5.59 => ? [T3: real] :
% 5.25/5.59 ( ( ord_less_real @ C @ T3 )
% 5.25/5.59 & ( ord_less_real @ T3 @ B )
% 5.25/5.59 & ( ( F @ B )
% 5.25/5.59 = ( plus_plus_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M6 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.59 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Taylor_up
% 5.25/5.59 thf(fact_9907_Taylor__down,axiom,
% 5.25/5.59 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( ( Diff @ zero_zero_nat )
% 5.25/5.59 = F )
% 5.25/5.59 => ( ! [M5: nat,T3: real] :
% 5.25/5.59 ( ( ( ord_less_nat @ M5 @ N )
% 5.25/5.59 & ( ord_less_eq_real @ A @ T3 )
% 5.25/5.59 & ( ord_less_eq_real @ T3 @ B ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.25/5.59 => ( ( ord_less_real @ A @ C )
% 5.25/5.59 => ( ( ord_less_eq_real @ C @ B )
% 5.25/5.59 => ? [T3: real] :
% 5.25/5.59 ( ( ord_less_real @ A @ T3 )
% 5.25/5.59 & ( ord_less_real @ T3 @ C )
% 5.25/5.59 & ( ( F @ A )
% 5.25/5.59 = ( plus_plus_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M6 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ N ) )
% 5.25/5.59 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Taylor_down
% 5.25/5.59 thf(fact_9908_Maclaurin__lemma2,axiom,
% 5.25/5.59 ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B3: real] :
% 5.25/5.59 ( ! [M5: nat,T3: real] :
% 5.25/5.59 ( ( ( ord_less_nat @ M5 @ N )
% 5.25/5.59 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.25/5.59 & ( ord_less_eq_real @ T3 @ H2 ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.25/5.59 => ( ( N
% 5.25/5.59 = ( suc @ K ) )
% 5.25/5.59 => ! [M2: nat,T4: real] :
% 5.25/5.59 ( ( ( ord_less_nat @ M2 @ N )
% 5.25/5.59 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.25/5.59 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real
% 5.25/5.59 @ ^ [U2: real] :
% 5.25/5.59 ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 5.25/5.59 @ ( plus_plus_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [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 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M2 ) ) )
% 5.25/5.59 @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) )
% 5.25/5.59 @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T4 )
% 5.25/5.59 @ ( plus_plus_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [P4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P4 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ T4 @ P4 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) )
% 5.25/5.59 @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ T4 @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) ) ) ) )
% 5.25/5.59 @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Maclaurin_lemma2
% 5.25/5.59 thf(fact_9909_DERIV__arctan__series,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( ( ord_less_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.59 => ( has_fi5821293074295781190e_real
% 5.25/5.59 @ ^ [X9: real] :
% 5.25/5.59 ( suminf_real
% 5.25/5.59 @ ^ [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 ) ) ) ) )
% 5.25/5.59 @ ( suminf_real
% 5.25/5.59 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X3 @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_arctan_series
% 5.25/5.59 thf(fact_9910_DERIV__real__root__generic,axiom,
% 5.25/5.59 ! [N: nat,X3: real,D4: real] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( X3 != zero_zero_real )
% 5.25/5.59 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.59 => ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.25/5.59 => ( D4
% 5.25/5.59 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.25/5.59 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.59 => ( ( ord_less_real @ X3 @ zero_zero_real )
% 5.25/5.59 => ( D4
% 5.25/5.59 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.25/5.59 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.59 => ( D4
% 5.25/5.59 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X3 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_real_root_generic
% 5.25/5.59 thf(fact_9911_isCont__Lb__Ub,axiom,
% 5.25/5.59 ! [A: real,B: real,F: real > real] :
% 5.25/5.59 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.25/5.59 & ( ord_less_eq_real @ X5 @ B ) )
% 5.25/5.59 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 5.25/5.59 => ? [L6: real,M8: real] :
% 5.25/5.59 ( ! [X: real] :
% 5.25/5.59 ( ( ( ord_less_eq_real @ A @ X )
% 5.25/5.59 & ( ord_less_eq_real @ X @ B ) )
% 5.25/5.59 => ( ( ord_less_eq_real @ L6 @ ( F @ X ) )
% 5.25/5.59 & ( ord_less_eq_real @ ( F @ X ) @ M8 ) ) )
% 5.25/5.59 & ! [Y4: real] :
% 5.25/5.59 ( ( ( ord_less_eq_real @ L6 @ Y4 )
% 5.25/5.59 & ( ord_less_eq_real @ Y4 @ M8 ) )
% 5.25/5.59 => ? [X5: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ A @ X5 )
% 5.25/5.59 & ( ord_less_eq_real @ X5 @ B )
% 5.25/5.59 & ( ( F @ X5 )
% 5.25/5.59 = Y4 ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % isCont_Lb_Ub
% 5.25/5.59 thf(fact_9912_isCont__real__sqrt,axiom,
% 5.25/5.59 ! [X3: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ sqrt ) ).
% 5.25/5.59
% 5.25/5.59 % isCont_real_sqrt
% 5.25/5.59 thf(fact_9913_isCont__real__root,axiom,
% 5.25/5.59 ! [X3: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ ( root @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % isCont_real_root
% 5.25/5.59 thf(fact_9914_isCont__inverse__function2,axiom,
% 5.25/5.59 ! [A: real,X3: real,B: real,G: real > real,F: real > real] :
% 5.25/5.59 ( ( ord_less_real @ A @ X3 )
% 5.25/5.59 => ( ( ord_less_real @ X3 @ B )
% 5.25/5.59 => ( ! [Z2: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ A @ Z2 )
% 5.25/5.59 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.25/5.59 => ( ( G @ ( F @ Z2 ) )
% 5.25/5.59 = Z2 ) ) )
% 5.25/5.59 => ( ! [Z2: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ A @ Z2 )
% 5.25/5.59 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.25/5.59 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 5.25/5.59 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X3 ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % isCont_inverse_function2
% 5.25/5.59 thf(fact_9915_isCont__arcosh,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( ( ord_less_real @ one_one_real @ X3 )
% 5.25/5.59 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.25/5.59
% 5.25/5.59 % isCont_arcosh
% 5.25/5.59 thf(fact_9916_LIM__cos__div__sin,axiom,
% 5.25/5.59 ( filterlim_real_real
% 5.25/5.59 @ ^ [X2: real] : ( divide_divide_real @ ( cos_real @ X2 ) @ ( sin_real @ X2 ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.25/5.59 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.25/5.59
% 5.25/5.59 % LIM_cos_div_sin
% 5.25/5.59 thf(fact_9917_isCont__arccos,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.59 => ( ( ord_less_real @ X3 @ one_one_real )
% 5.25/5.59 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arccos ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % isCont_arccos
% 5.25/5.59 thf(fact_9918_isCont__arcsin,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.59 => ( ( ord_less_real @ X3 @ one_one_real )
% 5.25/5.59 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % isCont_arcsin
% 5.25/5.59 thf(fact_9919_LIM__less__bound,axiom,
% 5.25/5.59 ! [B: real,X3: real,F: real > real] :
% 5.25/5.59 ( ( ord_less_real @ B @ X3 )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ B @ X3 ) )
% 5.25/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.25/5.59 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F )
% 5.25/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % LIM_less_bound
% 5.25/5.59 thf(fact_9920_isCont__artanh,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X3 )
% 5.25/5.59 => ( ( ord_less_real @ X3 @ one_one_real )
% 5.25/5.59 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % isCont_artanh
% 5.25/5.59 thf(fact_9921_isCont__inverse__function,axiom,
% 5.25/5.59 ! [D: real,X3: real,G: real > real,F: real > real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ D )
% 5.25/5.59 => ( ! [Z2: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X3 ) ) @ D )
% 5.25/5.59 => ( ( G @ ( F @ Z2 ) )
% 5.25/5.59 = Z2 ) )
% 5.25/5.59 => ( ! [Z2: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X3 ) ) @ D )
% 5.25/5.59 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) )
% 5.25/5.59 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X3 ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % isCont_inverse_function
% 5.25/5.59 thf(fact_9922_GMVT_H,axiom,
% 5.25/5.59 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F4: real > real] :
% 5.25/5.59 ( ( ord_less_real @ A @ B )
% 5.25/5.59 => ( ! [Z2: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ A @ Z2 )
% 5.25/5.59 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.25/5.59 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 5.25/5.59 => ( ! [Z2: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ A @ Z2 )
% 5.25/5.59 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.25/5.59 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ G ) ) )
% 5.25/5.59 => ( ! [Z2: real] :
% 5.25/5.59 ( ( ord_less_real @ A @ Z2 )
% 5.25/5.59 => ( ( ord_less_real @ Z2 @ B )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 5.25/5.59 => ( ! [Z2: real] :
% 5.25/5.59 ( ( ord_less_real @ A @ Z2 )
% 5.25/5.59 => ( ( ord_less_real @ Z2 @ B )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 5.25/5.59 => ? [C3: real] :
% 5.25/5.59 ( ( ord_less_real @ A @ C3 )
% 5.25/5.59 & ( ord_less_real @ C3 @ B )
% 5.25/5.59 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 5.25/5.59 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F4 @ C3 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % GMVT'
% 5.25/5.59 thf(fact_9923_summable__Leibniz_I2_J,axiom,
% 5.25/5.59 ! [A: nat > real] :
% 5.25/5.59 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.25/5.59 => ( ( topolo6980174941875973593q_real @ A )
% 5.25/5.59 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.25/5.59 => ! [N8: nat] :
% 5.25/5.59 ( member_real
% 5.25/5.59 @ ( suminf_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 5.25/5.59 @ ( set_or1222579329274155063t_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) )
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % summable_Leibniz(2)
% 5.25/5.59 thf(fact_9924_summable__Leibniz_I3_J,axiom,
% 5.25/5.59 ! [A: nat > real] :
% 5.25/5.59 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.25/5.59 => ( ( topolo6980174941875973593q_real @ A )
% 5.25/5.59 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.25/5.59 => ! [N8: nat] :
% 5.25/5.59 ( member_real
% 5.25/5.59 @ ( suminf_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 5.25/5.59 @ ( set_or1222579329274155063t_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) )
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % summable_Leibniz(3)
% 5.25/5.59 thf(fact_9925_filterlim__Suc,axiom,
% 5.25/5.59 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.25/5.59
% 5.25/5.59 % filterlim_Suc
% 5.25/5.59 thf(fact_9926_mult__nat__right__at__top,axiom,
% 5.25/5.59 ! [C: nat] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.25/5.59 => ( filterlim_nat_nat
% 5.25/5.59 @ ^ [X2: nat] : ( times_times_nat @ X2 @ C )
% 5.25/5.59 @ at_top_nat
% 5.25/5.59 @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % mult_nat_right_at_top
% 5.25/5.59 thf(fact_9927_mult__nat__left__at__top,axiom,
% 5.25/5.59 ! [C: nat] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.25/5.59 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % mult_nat_left_at_top
% 5.25/5.59 thf(fact_9928_monoseq__convergent,axiom,
% 5.25/5.59 ! [X8: nat > real,B3: real] :
% 5.25/5.59 ( ( topolo6980174941875973593q_real @ X8 )
% 5.25/5.59 => ( ! [I4: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I4 ) ) @ B3 )
% 5.25/5.59 => ~ ! [L6: real] :
% 5.25/5.59 ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % monoseq_convergent
% 5.25/5.59 thf(fact_9929_LIMSEQ__root,axiom,
% 5.25/5.59 ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] : ( root @ N2 @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.25/5.59 @ at_top_nat ) ).
% 5.25/5.59
% 5.25/5.59 % LIMSEQ_root
% 5.25/5.59 thf(fact_9930_nested__sequence__unique,axiom,
% 5.25/5.59 ! [F: nat > real,G: nat > real] :
% 5.25/5.59 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.59 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 5.25/5.59 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.25/5.59 => ( ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.25/5.59 @ at_top_nat )
% 5.25/5.59 => ? [L4: real] :
% 5.25/5.59 ( ! [N8: nat] : ( ord_less_eq_real @ ( F @ N8 ) @ L4 )
% 5.25/5.59 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 5.25/5.59 & ! [N8: nat] : ( ord_less_eq_real @ L4 @ ( G @ N8 ) )
% 5.25/5.59 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % nested_sequence_unique
% 5.25/5.59 thf(fact_9931_LIMSEQ__inverse__zero,axiom,
% 5.25/5.59 ! [X8: nat > real] :
% 5.25/5.59 ( ! [R3: real] :
% 5.25/5.59 ? [N6: nat] :
% 5.25/5.59 ! [N3: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ N6 @ N3 )
% 5.25/5.59 => ( ord_less_real @ R3 @ ( X8 @ N3 ) ) )
% 5.25/5.59 => ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] : ( inverse_inverse_real @ ( X8 @ N2 ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.25/5.59 @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % LIMSEQ_inverse_zero
% 5.25/5.59 thf(fact_9932_lim__inverse__n_H,axiom,
% 5.25/5.59 ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.25/5.59 @ at_top_nat ) ).
% 5.25/5.59
% 5.25/5.59 % lim_inverse_n'
% 5.25/5.59 thf(fact_9933_LIMSEQ__root__const,axiom,
% 5.25/5.59 ! [C: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.59 => ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] : ( root @ N2 @ C )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.25/5.59 @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % LIMSEQ_root_const
% 5.25/5.59 thf(fact_9934_LIMSEQ__inverse__real__of__nat,axiom,
% 5.25/5.59 ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.25/5.59 @ at_top_nat ) ).
% 5.25/5.59
% 5.25/5.59 % LIMSEQ_inverse_real_of_nat
% 5.25/5.59 thf(fact_9935_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.25/5.59 ! [R2: real] :
% 5.25/5.59 ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ R2 )
% 5.25/5.59 @ at_top_nat ) ).
% 5.25/5.59
% 5.25/5.59 % LIMSEQ_inverse_real_of_nat_add
% 5.25/5.59 thf(fact_9936_increasing__LIMSEQ,axiom,
% 5.25/5.59 ! [F: nat > real,L2: real] :
% 5.25/5.59 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.59 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L2 )
% 5.25/5.59 => ( ! [E2: real] :
% 5.25/5.59 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.25/5.59 => ? [N8: nat] : ( ord_less_eq_real @ L2 @ ( plus_plus_real @ ( F @ N8 ) @ E2 ) ) )
% 5.25/5.59 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % increasing_LIMSEQ
% 5.25/5.59 thf(fact_9937_LIMSEQ__realpow__zero,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.59 => ( ( ord_less_real @ X3 @ one_one_real )
% 5.25/5.59 => ( filterlim_nat_real @ ( power_power_real @ X3 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % LIMSEQ_realpow_zero
% 5.25/5.59 thf(fact_9938_LIMSEQ__divide__realpow__zero,axiom,
% 5.25/5.59 ! [X3: real,A: real] :
% 5.25/5.59 ( ( ord_less_real @ one_one_real @ X3 )
% 5.25/5.59 => ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] : ( divide_divide_real @ A @ ( power_power_real @ X3 @ N2 ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.25/5.59 @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % LIMSEQ_divide_realpow_zero
% 5.25/5.59 thf(fact_9939_LIMSEQ__abs__realpow__zero,axiom,
% 5.25/5.59 ! [C: real] :
% 5.25/5.59 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.25/5.59 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % LIMSEQ_abs_realpow_zero
% 5.25/5.59 thf(fact_9940_LIMSEQ__abs__realpow__zero2,axiom,
% 5.25/5.59 ! [C: real] :
% 5.25/5.59 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.25/5.59 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % LIMSEQ_abs_realpow_zero2
% 5.25/5.59 thf(fact_9941_LIMSEQ__inverse__realpow__zero,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( ( ord_less_real @ one_one_real @ X3 )
% 5.25/5.59 => ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] : ( inverse_inverse_real @ ( power_power_real @ X3 @ N2 ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.25/5.59 @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % LIMSEQ_inverse_realpow_zero
% 5.25/5.59 thf(fact_9942_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.25/5.59 ! [R2: real] :
% 5.25/5.59 ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ R2 )
% 5.25/5.59 @ at_top_nat ) ).
% 5.25/5.59
% 5.25/5.59 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.25/5.59 thf(fact_9943_tendsto__exp__limit__sequentially,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X3 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ ( exp_real @ X3 ) )
% 5.25/5.59 @ at_top_nat ) ).
% 5.25/5.59
% 5.25/5.59 % tendsto_exp_limit_sequentially
% 5.25/5.59 thf(fact_9944_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.25/5.59 ! [R2: real] :
% 5.25/5.59 ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ R2 )
% 5.25/5.59 @ at_top_nat ) ).
% 5.25/5.59
% 5.25/5.59 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.25/5.59 thf(fact_9945_summable__Leibniz_I1_J,axiom,
% 5.25/5.59 ! [A: nat > real] :
% 5.25/5.59 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.25/5.59 => ( ( topolo6980174941875973593q_real @ A )
% 5.25/5.59 => ( summable_real
% 5.25/5.59 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % summable_Leibniz(1)
% 5.25/5.59 thf(fact_9946_summable,axiom,
% 5.25/5.59 ! [A: nat > real] :
% 5.25/5.59 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.25/5.59 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.25/5.59 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.25/5.59 => ( summable_real
% 5.25/5.59 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % summable
% 5.25/5.59 thf(fact_9947_cos__diff__limit__1,axiom,
% 5.25/5.59 ! [Theta: nat > real,Theta2: real] :
% 5.25/5.59 ( ( filterlim_nat_real
% 5.25/5.59 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.25/5.59 @ at_top_nat )
% 5.25/5.59 => ~ ! [K2: nat > int] :
% 5.25/5.59 ~ ( filterlim_nat_real
% 5.25/5.59 @ ^ [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 ) ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.25/5.59 @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % cos_diff_limit_1
% 5.25/5.59 thf(fact_9948_cos__limit__1,axiom,
% 5.25/5.59 ! [Theta: nat > real] :
% 5.25/5.59 ( ( filterlim_nat_real
% 5.25/5.59 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.25/5.59 @ at_top_nat )
% 5.25/5.59 => ? [K2: nat > int] :
% 5.25/5.59 ( filterlim_nat_real
% 5.25/5.59 @ ^ [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 ) ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.25/5.59 @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % cos_limit_1
% 5.25/5.59 thf(fact_9949_summable__Leibniz_I4_J,axiom,
% 5.25/5.59 ! [A: nat > real] :
% 5.25/5.59 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.25/5.59 => ( ( topolo6980174941875973593q_real @ A )
% 5.25/5.59 => ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] :
% 5.25/5.59 ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real
% 5.25/5.59 @ ( suminf_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.25/5.59 @ at_top_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % summable_Leibniz(4)
% 5.25/5.59 thf(fact_9950_zeroseq__arctan__series,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ X3 ) @ one_one_real )
% 5.25/5.59 => ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X3 @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.25/5.59 @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % zeroseq_arctan_series
% 5.25/5.59 thf(fact_9951_summable__Leibniz_H_I3_J,axiom,
% 5.25/5.59 ! [A: nat > real] :
% 5.25/5.59 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.25/5.59 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.25/5.59 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.25/5.59 => ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] :
% 5.25/5.59 ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real
% 5.25/5.59 @ ( suminf_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.25/5.59 @ at_top_nat ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % summable_Leibniz'(3)
% 5.25/5.59 thf(fact_9952_summable__Leibniz_H_I2_J,axiom,
% 5.25/5.59 ! [A: nat > real,N: nat] :
% 5.25/5.59 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.25/5.59 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.25/5.59 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.25/5.59 => ( ord_less_eq_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.25/5.59 @ ( suminf_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % summable_Leibniz'(2)
% 5.25/5.59 thf(fact_9953_sums__alternating__upper__lower,axiom,
% 5.25/5.59 ! [A: nat > real] :
% 5.25/5.59 ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.25/5.59 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.25/5.59 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.25/5.59 => ? [L4: real] :
% 5.25/5.59 ( ! [N8: nat] :
% 5.25/5.59 ( ord_less_eq_real
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) )
% 5.25/5.59 @ L4 )
% 5.25/5.59 & ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] :
% 5.25/5.59 ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ L4 )
% 5.25/5.59 @ at_top_nat )
% 5.25/5.59 & ! [N8: nat] :
% 5.25/5.59 ( ord_less_eq_real @ L4
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) ) )
% 5.25/5.59 & ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] :
% 5.25/5.59 ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ L4 )
% 5.25/5.59 @ at_top_nat ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % sums_alternating_upper_lower
% 5.25/5.59 thf(fact_9954_summable__Leibniz_I5_J,axiom,
% 5.25/5.59 ! [A: nat > real] :
% 5.25/5.59 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.25/5.59 => ( ( topolo6980174941875973593q_real @ A )
% 5.25/5.59 => ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] :
% 5.25/5.59 ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real
% 5.25/5.59 @ ( suminf_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.25/5.59 @ at_top_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % summable_Leibniz(5)
% 5.25/5.59 thf(fact_9955_summable__Leibniz_H_I4_J,axiom,
% 5.25/5.59 ! [A: nat > real,N: nat] :
% 5.25/5.59 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.25/5.59 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.25/5.59 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.25/5.59 => ( ord_less_eq_real
% 5.25/5.59 @ ( suminf_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 5.25/5.59 @ ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % summable_Leibniz'(4)
% 5.25/5.59 thf(fact_9956_summable__Leibniz_H_I5_J,axiom,
% 5.25/5.59 ! [A: nat > real] :
% 5.25/5.59 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.25/5.59 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.25/5.59 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.25/5.59 => ( filterlim_nat_real
% 5.25/5.59 @ ^ [N2: nat] :
% 5.25/5.59 ( groups6591440286371151544t_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.25/5.59 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real
% 5.25/5.59 @ ( suminf_real
% 5.25/5.59 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.25/5.59 @ at_top_nat ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % summable_Leibniz'(5)
% 5.25/5.59 thf(fact_9957_real__bounded__linear,axiom,
% 5.25/5.59 ( real_V5970128139526366754l_real
% 5.25/5.59 = ( ^ [F3: real > real] :
% 5.25/5.59 ? [C2: real] :
% 5.25/5.59 ( F3
% 5.25/5.59 = ( ^ [X2: real] : ( times_times_real @ X2 @ C2 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % real_bounded_linear
% 5.25/5.59 thf(fact_9958_tendsto__exp__limit__at__right,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( filterlim_real_real
% 5.25/5.59 @ ^ [Y6: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X3 @ Y6 ) ) @ ( divide_divide_real @ one_one_real @ Y6 ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ ( exp_real @ X3 ) )
% 5.25/5.59 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % tendsto_exp_limit_at_right
% 5.25/5.59 thf(fact_9959_tendsto__arcosh__at__left__1,axiom,
% 5.25/5.59 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 5.25/5.59
% 5.25/5.59 % tendsto_arcosh_at_left_1
% 5.25/5.59 thf(fact_9960_filterlim__tan__at__right,axiom,
% 5.25/5.59 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 ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % filterlim_tan_at_right
% 5.25/5.59 thf(fact_9961_tendsto__arctan__at__bot,axiom,
% 5.25/5.59 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.25/5.59
% 5.25/5.59 % tendsto_arctan_at_bot
% 5.25/5.59 thf(fact_9962_INT__greaterThan__UNIV,axiom,
% 5.25/5.59 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 5.25/5.59 = bot_bot_set_nat ) ).
% 5.25/5.59
% 5.25/5.59 % INT_greaterThan_UNIV
% 5.25/5.59 thf(fact_9963_greaterThan__0,axiom,
% 5.25/5.59 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.25/5.59 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % greaterThan_0
% 5.25/5.59 thf(fact_9964_greaterThan__Suc,axiom,
% 5.25/5.59 ! [K: nat] :
% 5.25/5.59 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.25/5.59 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % greaterThan_Suc
% 5.25/5.59 thf(fact_9965_tanh__real__at__bot,axiom,
% 5.25/5.59 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 5.25/5.59
% 5.25/5.59 % tanh_real_at_bot
% 5.25/5.59 thf(fact_9966_artanh__real__at__right__1,axiom,
% 5.25/5.59 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 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % artanh_real_at_right_1
% 5.25/5.59 thf(fact_9967_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.25/5.59 ! [B: real,F: real > real,Flim: real] :
% 5.25/5.59 ( ! [X5: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ X5 @ B )
% 5.25/5.59 => ? [Y4: real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.25/5.59 & ( ord_less_real @ zero_zero_real @ Y4 ) ) )
% 5.25/5.59 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.25/5.59 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_pos_imp_increasing_at_bot
% 5.25/5.59 thf(fact_9968_filterlim__pow__at__bot__odd,axiom,
% 5.25/5.59 ! [N: nat,F: real > real,F5: filter_real] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.25/5.59 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.59 => ( filterlim_real_real
% 5.25/5.59 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N )
% 5.25/5.59 @ at_bot_real
% 5.25/5.59 @ F5 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % filterlim_pow_at_bot_odd
% 5.25/5.59 thf(fact_9969_filterlim__pow__at__bot__even,axiom,
% 5.25/5.59 ! [N: nat,F: real > real,F5: filter_real] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.25/5.59 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.25/5.59 => ( filterlim_real_real
% 5.25/5.59 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N )
% 5.25/5.59 @ at_top_real
% 5.25/5.59 @ F5 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % filterlim_pow_at_bot_even
% 5.25/5.59 thf(fact_9970_at__bot__le__at__infinity,axiom,
% 5.25/5.59 ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 5.25/5.59
% 5.25/5.59 % at_bot_le_at_infinity
% 5.25/5.59 thf(fact_9971_at__top__le__at__infinity,axiom,
% 5.25/5.59 ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 5.25/5.59
% 5.25/5.59 % at_top_le_at_infinity
% 5.25/5.59 thf(fact_9972_sqrt__at__top,axiom,
% 5.25/5.59 filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 5.25/5.59
% 5.25/5.59 % sqrt_at_top
% 5.25/5.59 thf(fact_9973_tanh__real__at__top,axiom,
% 5.25/5.59 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 5.25/5.59
% 5.25/5.59 % tanh_real_at_top
% 5.25/5.59 thf(fact_9974_artanh__real__at__left__1,axiom,
% 5.25/5.59 filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 5.25/5.59
% 5.25/5.59 % artanh_real_at_left_1
% 5.25/5.59 thf(fact_9975_tendsto__power__div__exp__0,axiom,
% 5.25/5.59 ! [K: nat] :
% 5.25/5.59 ( filterlim_real_real
% 5.25/5.59 @ ^ [X2: real] : ( divide_divide_real @ ( power_power_real @ X2 @ K ) @ ( exp_real @ X2 ) )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.25/5.59 @ at_top_real ) ).
% 5.25/5.59
% 5.25/5.59 % tendsto_power_div_exp_0
% 5.25/5.59 thf(fact_9976_tendsto__exp__limit__at__top,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( filterlim_real_real
% 5.25/5.59 @ ^ [Y6: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X3 @ Y6 ) ) @ Y6 )
% 5.25/5.59 @ ( topolo2815343760600316023s_real @ ( exp_real @ X3 ) )
% 5.25/5.59 @ at_top_real ) ).
% 5.25/5.59
% 5.25/5.59 % tendsto_exp_limit_at_top
% 5.25/5.59 thf(fact_9977_filterlim__tan__at__left,axiom,
% 5.25/5.59 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 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % filterlim_tan_at_left
% 5.25/5.59 thf(fact_9978_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.25/5.59 ! [B: real,F: real > real,Flim: real] :
% 5.25/5.59 ( ! [X5: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ B @ X5 )
% 5.25/5.59 => ? [Y4: real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.25/5.59 & ( ord_less_real @ Y4 @ zero_zero_real ) ) )
% 5.25/5.59 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.25/5.59 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_neg_imp_decreasing_at_top
% 5.25/5.59 thf(fact_9979_tendsto__arctan__at__top,axiom,
% 5.25/5.59 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.25/5.59
% 5.25/5.59 % tendsto_arctan_at_top
% 5.25/5.59 thf(fact_9980_GMVT,axiom,
% 5.25/5.59 ! [A: real,B: real,F: real > real,G: real > real] :
% 5.25/5.59 ( ( ord_less_real @ A @ B )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.25/5.59 & ( ord_less_eq_real @ X5 @ B ) )
% 5.25/5.59 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( ( ord_less_real @ A @ X5 )
% 5.25/5.59 & ( ord_less_real @ X5 @ B ) )
% 5.25/5.59 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.25/5.59 & ( ord_less_eq_real @ X5 @ B ) )
% 5.25/5.59 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ G ) )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( ( ord_less_real @ A @ X5 )
% 5.25/5.59 & ( ord_less_real @ X5 @ B ) )
% 5.25/5.59 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.25/5.59 => ? [G_c: real,F_c: real,C3: real] :
% 5.25/5.59 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.25/5.59 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.25/5.59 & ( ord_less_real @ A @ C3 )
% 5.25/5.59 & ( ord_less_real @ C3 @ B )
% 5.25/5.59 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 5.25/5.59 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % GMVT
% 5.25/5.59 thf(fact_9981_eventually__sequentially__Suc,axiom,
% 5.25/5.59 ! [P: nat > $o] :
% 5.25/5.59 ( ( eventually_nat
% 5.25/5.59 @ ^ [I3: nat] : ( P @ ( suc @ I3 ) )
% 5.25/5.59 @ at_top_nat )
% 5.25/5.59 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % eventually_sequentially_Suc
% 5.25/5.59 thf(fact_9982_eventually__sequentially__seg,axiom,
% 5.25/5.59 ! [P: nat > $o,K: nat] :
% 5.25/5.59 ( ( eventually_nat
% 5.25/5.59 @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K ) )
% 5.25/5.59 @ at_top_nat )
% 5.25/5.59 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % eventually_sequentially_seg
% 5.25/5.59 thf(fact_9983_sequentially__offset,axiom,
% 5.25/5.59 ! [P: nat > $o,K: nat] :
% 5.25/5.59 ( ( eventually_nat @ P @ at_top_nat )
% 5.25/5.59 => ( eventually_nat
% 5.25/5.59 @ ^ [I3: nat] : ( P @ ( plus_plus_nat @ I3 @ K ) )
% 5.25/5.59 @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % sequentially_offset
% 5.25/5.59 thf(fact_9984_le__sequentially,axiom,
% 5.25/5.59 ! [F5: filter_nat] :
% 5.25/5.59 ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 5.25/5.59 = ( ! [N9: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N9 ) @ F5 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % le_sequentially
% 5.25/5.59 thf(fact_9985_eventually__sequentiallyI,axiom,
% 5.25/5.59 ! [C: nat,P: nat > $o] :
% 5.25/5.59 ( ! [X5: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ C @ X5 )
% 5.25/5.59 => ( P @ X5 ) )
% 5.25/5.59 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % eventually_sequentiallyI
% 5.25/5.59 thf(fact_9986_eventually__sequentially,axiom,
% 5.25/5.59 ! [P: nat > $o] :
% 5.25/5.59 ( ( eventually_nat @ P @ at_top_nat )
% 5.25/5.59 = ( ? [N9: nat] :
% 5.25/5.59 ! [N2: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ N9 @ N2 )
% 5.25/5.59 => ( P @ N2 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % eventually_sequentially
% 5.25/5.59 thf(fact_9987_eventually__at__right__to__0,axiom,
% 5.25/5.59 ! [P: real > $o,A: real] :
% 5.25/5.59 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.25/5.59 = ( eventually_real
% 5.25/5.59 @ ^ [X2: real] : ( P @ ( plus_plus_real @ X2 @ A ) )
% 5.25/5.59 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % eventually_at_right_to_0
% 5.25/5.59 thf(fact_9988_Bseq__eq__bounded,axiom,
% 5.25/5.59 ! [F: nat > real,A: real,B: real] :
% 5.25/5.59 ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.25/5.59 => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % Bseq_eq_bounded
% 5.25/5.59 thf(fact_9989_Bseq__realpow,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.59 => ( ( ord_less_eq_real @ X3 @ one_one_real )
% 5.25/5.59 => ( bfun_nat_real @ ( power_power_real @ X3 ) @ at_top_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Bseq_realpow
% 5.25/5.59 thf(fact_9990_finite__greaterThanAtMost,axiom,
% 5.25/5.59 ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 5.25/5.59
% 5.25/5.59 % finite_greaterThanAtMost
% 5.25/5.59 thf(fact_9991_card__greaterThanAtMost,axiom,
% 5.25/5.59 ! [L2: nat,U: nat] :
% 5.25/5.59 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L2 @ U ) )
% 5.25/5.59 = ( minus_minus_nat @ U @ L2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_greaterThanAtMost
% 5.25/5.59 thf(fact_9992_GreatestI__ex__nat,axiom,
% 5.25/5.59 ! [P: nat > $o,B: nat] :
% 5.25/5.59 ( ? [X_1: nat] : ( P @ X_1 )
% 5.25/5.59 => ( ! [Y3: nat] :
% 5.25/5.59 ( ( P @ Y3 )
% 5.25/5.59 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.25/5.59 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % GreatestI_ex_nat
% 5.25/5.59 thf(fact_9993_Greatest__le__nat,axiom,
% 5.25/5.59 ! [P: nat > $o,K: nat,B: nat] :
% 5.25/5.59 ( ( P @ K )
% 5.25/5.59 => ( ! [Y3: nat] :
% 5.25/5.59 ( ( P @ Y3 )
% 5.25/5.59 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.25/5.59 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Greatest_le_nat
% 5.25/5.59 thf(fact_9994_GreatestI__nat,axiom,
% 5.25/5.59 ! [P: nat > $o,K: nat,B: nat] :
% 5.25/5.59 ( ( P @ K )
% 5.25/5.59 => ( ! [Y3: nat] :
% 5.25/5.59 ( ( P @ Y3 )
% 5.25/5.59 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.25/5.59 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % GreatestI_nat
% 5.25/5.59 thf(fact_9995_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.25/5.59 ! [L2: nat,U: nat] :
% 5.25/5.59 ( ( set_or1269000886237332187st_nat @ ( suc @ L2 ) @ U )
% 5.25/5.59 = ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 5.25/5.59
% 5.25/5.59 % atLeastSucAtMost_greaterThanAtMost
% 5.25/5.59 thf(fact_9996_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.25/5.59 ! [I2: nat,J2: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J2 )
% 5.25/5.59 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J2 ) )
% 5.25/5.59 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J2 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % sorted_list_of_set_greaterThanAtMost
% 5.25/5.59 thf(fact_9997_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.25/5.59 ! [N: nat,J2: nat,I2: nat] :
% 5.25/5.59 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J2 @ I2 ) )
% 5.25/5.59 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J2 ) ) @ N )
% 5.25/5.59 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % nth_sorted_list_of_set_greaterThanAtMost
% 5.25/5.59 thf(fact_9998_finite__greaterThanAtMost__int,axiom,
% 5.25/5.59 ! [L2: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L2 @ U ) ) ).
% 5.25/5.59
% 5.25/5.59 % finite_greaterThanAtMost_int
% 5.25/5.59 thf(fact_9999_atLeast__0,axiom,
% 5.25/5.59 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 5.25/5.59 = top_top_set_nat ) ).
% 5.25/5.59
% 5.25/5.59 % atLeast_0
% 5.25/5.59 thf(fact_10000_card__greaterThanAtMost__int,axiom,
% 5.25/5.59 ! [L2: int,U: int] :
% 5.25/5.59 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L2 @ U ) )
% 5.25/5.59 = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_greaterThanAtMost_int
% 5.25/5.59 thf(fact_10001_atLeast__Suc__greaterThan,axiom,
% 5.25/5.59 ! [K: nat] :
% 5.25/5.59 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.25/5.59 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.25/5.59
% 5.25/5.59 % atLeast_Suc_greaterThan
% 5.25/5.59 thf(fact_10002_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 5.25/5.59 ! [L2: int,U: int] :
% 5.25/5.59 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 5.25/5.59 = ( set_or6656581121297822940st_int @ L2 @ U ) ) ).
% 5.25/5.59
% 5.25/5.59 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 5.25/5.59 thf(fact_10003_decseq__bounded,axiom,
% 5.25/5.59 ! [X8: nat > real,B3: real] :
% 5.25/5.59 ( ( order_9091379641038594480t_real @ X8 )
% 5.25/5.59 => ( ! [I4: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I4 ) )
% 5.25/5.59 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % decseq_bounded
% 5.25/5.59 thf(fact_10004_greaterThanAtMost__upto,axiom,
% 5.25/5.59 ( set_or6656581121297822940st_int
% 5.25/5.59 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % greaterThanAtMost_upto
% 5.25/5.59 thf(fact_10005_decseq__convergent,axiom,
% 5.25/5.59 ! [X8: nat > real,B3: real] :
% 5.25/5.59 ( ( order_9091379641038594480t_real @ X8 )
% 5.25/5.59 => ( ! [I4: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I4 ) )
% 5.25/5.59 => ~ ! [L6: real] :
% 5.25/5.59 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.25/5.59 => ~ ! [I: nat] : ( ord_less_eq_real @ L6 @ ( X8 @ I ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % decseq_convergent
% 5.25/5.59 thf(fact_10006_UN__atLeast__UNIV,axiom,
% 5.25/5.59 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 5.25/5.59 = top_top_set_nat ) ).
% 5.25/5.59
% 5.25/5.59 % UN_atLeast_UNIV
% 5.25/5.59 thf(fact_10007_atLeast__Suc,axiom,
% 5.25/5.59 ! [K: nat] :
% 5.25/5.59 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.25/5.59 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % atLeast_Suc
% 5.25/5.59 thf(fact_10008_MVT,axiom,
% 5.25/5.59 ! [A: real,B: real,F: real > real] :
% 5.25/5.59 ( ( ord_less_real @ A @ B )
% 5.25/5.59 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( ord_less_real @ A @ X5 )
% 5.25/5.59 => ( ( ord_less_real @ X5 @ B )
% 5.25/5.59 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.25/5.59 => ? [L4: real,Z2: real] :
% 5.25/5.59 ( ( ord_less_real @ A @ Z2 )
% 5.25/5.59 & ( ord_less_real @ Z2 @ B )
% 5.25/5.59 & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) )
% 5.25/5.59 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.25/5.59 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % MVT
% 5.25/5.59 thf(fact_10009_continuous__on__arcosh_H,axiom,
% 5.25/5.59 ! [A2: set_real,F: real > real] :
% 5.25/5.59 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( member_real @ X5 @ A2 )
% 5.25/5.59 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.25/5.59 => ( topolo5044208981011980120l_real @ A2
% 5.25/5.59 @ ^ [X2: real] : ( arcosh_real @ ( F @ X2 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % continuous_on_arcosh'
% 5.25/5.59 thf(fact_10010_continuous__image__closed__interval,axiom,
% 5.25/5.59 ! [A: real,B: real,F: real > real] :
% 5.25/5.59 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.59 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.25/5.59 => ? [C3: real,D3: real] :
% 5.25/5.59 ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.25/5.59 = ( set_or1222579329274155063t_real @ C3 @ D3 ) )
% 5.25/5.59 & ( ord_less_eq_real @ C3 @ D3 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % continuous_image_closed_interval
% 5.25/5.59 thf(fact_10011_continuous__on__arcosh,axiom,
% 5.25/5.59 ! [A2: set_real] :
% 5.25/5.59 ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.25/5.59 => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 5.25/5.59
% 5.25/5.59 % continuous_on_arcosh
% 5.25/5.59 thf(fact_10012_continuous__on__arccos_H,axiom,
% 5.25/5.59 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 5.25/5.59
% 5.25/5.59 % continuous_on_arccos'
% 5.25/5.59 thf(fact_10013_continuous__on__arcsin_H,axiom,
% 5.25/5.59 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 5.25/5.59
% 5.25/5.59 % continuous_on_arcsin'
% 5.25/5.59 thf(fact_10014_continuous__on__artanh_H,axiom,
% 5.25/5.59 ! [A2: set_real,F: real > real] :
% 5.25/5.59 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( member_real @ X5 @ A2 )
% 5.25/5.59 => ( member_real @ ( F @ X5 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 5.25/5.59 => ( topolo5044208981011980120l_real @ A2
% 5.25/5.59 @ ^ [X2: real] : ( artanh_real @ ( F @ X2 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % continuous_on_artanh'
% 5.25/5.59 thf(fact_10015_continuous__on__artanh,axiom,
% 5.25/5.59 ! [A2: set_real] :
% 5.25/5.59 ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.25/5.59 => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 5.25/5.59
% 5.25/5.59 % continuous_on_artanh
% 5.25/5.59 thf(fact_10016_DERIV__isconst2,axiom,
% 5.25/5.59 ! [A: real,B: real,F: real > real,X3: real] :
% 5.25/5.59 ( ( ord_less_real @ A @ B )
% 5.25/5.59 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.25/5.59 => ( ! [X5: real] :
% 5.25/5.59 ( ( ord_less_real @ A @ X5 )
% 5.25/5.59 => ( ( ord_less_real @ X5 @ B )
% 5.25/5.59 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.25/5.59 => ( ( ord_less_eq_real @ A @ X3 )
% 5.25/5.59 => ( ( ord_less_eq_real @ X3 @ B )
% 5.25/5.59 => ( ( F @ X3 )
% 5.25/5.59 = ( F @ A ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % DERIV_isconst2
% 5.25/5.59 thf(fact_10017_mono__times__nat,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % mono_times_nat
% 5.25/5.59 thf(fact_10018_mono__Suc,axiom,
% 5.25/5.59 order_mono_nat_nat @ suc ).
% 5.25/5.59
% 5.25/5.59 % mono_Suc
% 5.25/5.59 thf(fact_10019_incseq__bounded,axiom,
% 5.25/5.59 ! [X8: nat > real,B3: real] :
% 5.25/5.59 ( ( order_mono_nat_real @ X8 )
% 5.25/5.59 => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B3 )
% 5.25/5.59 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % incseq_bounded
% 5.25/5.59 thf(fact_10020_incseq__convergent,axiom,
% 5.25/5.59 ! [X8: nat > real,B3: real] :
% 5.25/5.59 ( ( order_mono_nat_real @ X8 )
% 5.25/5.59 => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B3 )
% 5.25/5.59 => ~ ! [L6: real] :
% 5.25/5.59 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.25/5.59 => ~ ! [I: nat] : ( ord_less_eq_real @ ( X8 @ I ) @ L6 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % incseq_convergent
% 5.25/5.59 thf(fact_10021_mono__ge2__power__minus__self,axiom,
% 5.25/5.59 ! [K: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.25/5.59 => ( order_mono_nat_nat
% 5.25/5.59 @ ^ [M6: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M6 ) @ M6 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % mono_ge2_power_minus_self
% 5.25/5.59 thf(fact_10022_nonneg__incseq__Bseq__subseq__iff,axiom,
% 5.25/5.59 ! [F: nat > real,G: nat > nat] :
% 5.25/5.59 ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.25/5.59 => ( ( order_mono_nat_real @ F )
% 5.25/5.59 => ( ( order_5726023648592871131at_nat @ G )
% 5.25/5.59 => ( ( bfun_nat_real
% 5.25/5.59 @ ^ [X2: nat] : ( F @ ( G @ X2 ) )
% 5.25/5.59 @ at_top_nat )
% 5.25/5.59 = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % nonneg_incseq_Bseq_subseq_iff
% 5.25/5.59 thf(fact_10023_strict__mono__imp__increasing,axiom,
% 5.25/5.59 ! [F: nat > nat,N: nat] :
% 5.25/5.59 ( ( order_5726023648592871131at_nat @ F )
% 5.25/5.59 => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % strict_mono_imp_increasing
% 5.25/5.59 thf(fact_10024_inj__sgn__power,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( inj_on_real_real
% 5.25/5.59 @ ^ [Y6: real] : ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N ) )
% 5.25/5.59 @ top_top_set_real ) ) ).
% 5.25/5.59
% 5.25/5.59 % inj_sgn_power
% 5.25/5.59 thf(fact_10025_log__inj,axiom,
% 5.25/5.59 ! [B: real] :
% 5.25/5.59 ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.59 => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % log_inj
% 5.25/5.59 thf(fact_10026_inj__Suc,axiom,
% 5.25/5.59 ! [N5: set_nat] : ( inj_on_nat_nat @ suc @ N5 ) ).
% 5.25/5.59
% 5.25/5.59 % inj_Suc
% 5.25/5.59 thf(fact_10027_inj__on__diff__nat,axiom,
% 5.25/5.59 ! [N5: set_nat,K: nat] :
% 5.25/5.59 ( ! [N3: nat] :
% 5.25/5.59 ( ( member_nat @ N3 @ N5 )
% 5.25/5.59 => ( ord_less_eq_nat @ K @ N3 ) )
% 5.25/5.59 => ( inj_on_nat_nat
% 5.25/5.59 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ K )
% 5.25/5.59 @ N5 ) ) ).
% 5.25/5.59
% 5.25/5.59 % inj_on_diff_nat
% 5.25/5.59 thf(fact_10028_summable__reindex,axiom,
% 5.25/5.59 ! [F: nat > real,G: nat > nat] :
% 5.25/5.59 ( ( summable_real @ F )
% 5.25/5.59 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.25/5.59 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.25/5.59 => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % summable_reindex
% 5.25/5.59 thf(fact_10029_suminf__reindex__mono,axiom,
% 5.25/5.59 ! [F: nat > real,G: nat > nat] :
% 5.25/5.59 ( ( summable_real @ F )
% 5.25/5.59 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.25/5.59 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.25/5.59 => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % suminf_reindex_mono
% 5.25/5.59 thf(fact_10030_inj__on__char__of__nat,axiom,
% 5.25/5.59 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % inj_on_char_of_nat
% 5.25/5.59 thf(fact_10031_suminf__reindex,axiom,
% 5.25/5.59 ! [F: nat > real,G: nat > nat] :
% 5.25/5.59 ( ( summable_real @ F )
% 5.25/5.59 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.25/5.59 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.25/5.59 => ( ! [X5: nat] :
% 5.25/5.59 ( ~ ( member_nat @ X5 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 5.25/5.59 => ( ( F @ X5 )
% 5.25/5.59 = zero_zero_real ) )
% 5.25/5.59 => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 5.25/5.59 = ( suminf_real @ F ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % suminf_reindex
% 5.25/5.59 thf(fact_10032_powr__real__of__int_H,axiom,
% 5.25/5.59 ! [X3: real,N: int] :
% 5.25/5.59 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.25/5.59 => ( ( ( X3 != zero_zero_real )
% 5.25/5.59 | ( ord_less_int @ zero_zero_int @ N ) )
% 5.25/5.59 => ( ( powr_real @ X3 @ ( ring_1_of_int_real @ N ) )
% 5.25/5.59 = ( power_int_real @ X3 @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % powr_real_of_int'
% 5.25/5.59 thf(fact_10033_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.25/5.59 ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.25/5.59 ( ( ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( ? [Uu: $o,Uv: $o] :
% 5.25/5.59 ( X3
% 5.25/5.59 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 = ( Xa2 != one_one_nat ) ) )
% 5.25/5.59 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 = ( ~ ( ( Deg2 = Xa2 )
% 5.25/5.59 & ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.25/5.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 & ( case_o184042715313410164at_nat
% 5.25/5.59 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.25/5.59 & ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.59 @ ( produc6081775807080527818_nat_o
% 5.25/5.59 @ ^ [Mi3: nat,Ma3: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.25/5.59 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.25/5.59 & ! [I3: nat] :
% 5.25/5.59 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 5.25/5.59 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.25/5.59 & ( ( Mi3 = Ma3 )
% 5.25/5.59 => ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.59 & ( ( Mi3 != Ma3 )
% 5.25/5.59 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.25/5.59 & ! [X2: nat] :
% 5.25/5.59 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.25/5.59 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.25/5.59 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.25/5.59 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.25/5.59 @ Mima ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % VEBT_internal.valid'.elims(1)
% 5.25/5.59 thf(fact_10034_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.25/5.59 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 5.25/5.59 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList @ Summary ) @ Deg4 )
% 5.25/5.59 = ( ( Deg = Deg4 )
% 5.25/5.59 & ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.59 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.25/5.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 & ( case_o184042715313410164at_nat
% 5.25/5.59 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X4 )
% 5.25/5.59 & ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.59 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.59 @ ( produc6081775807080527818_nat_o
% 5.25/5.59 @ ^ [Mi3: nat,Ma3: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.25/5.59 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.25/5.59 & ! [I3: nat] :
% 5.25/5.59 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X4 ) )
% 5.25/5.59 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.25/5.59 & ( ( Mi3 = Ma3 )
% 5.25/5.59 => ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.59 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.59 & ( ( Mi3 != Ma3 )
% 5.25/5.59 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.25/5.59 & ! [X2: nat] :
% 5.25/5.59 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.25/5.59 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X2 )
% 5.25/5.59 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.25/5.59 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.25/5.59 @ Mima2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % VEBT_internal.valid'.simps(2)
% 5.25/5.59 thf(fact_10035_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.25/5.59 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.59 ( ~ ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 5.25/5.59 => ( ( ? [Uu: $o,Uv: $o] :
% 5.25/5.59 ( X3
% 5.25/5.59 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.25/5.59 => ( Xa2 = one_one_nat ) )
% 5.25/5.59 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.25/5.59 => ( ( Deg2 = Xa2 )
% 5.25/5.59 & ! [X5: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.25/5.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 & ( case_o184042715313410164at_nat
% 5.25/5.59 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.25/5.59 & ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.59 @ ( produc6081775807080527818_nat_o
% 5.25/5.59 @ ^ [Mi3: nat,Ma3: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.25/5.59 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.25/5.59 & ! [I3: nat] :
% 5.25/5.59 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 5.25/5.59 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.25/5.59 & ( ( Mi3 = Ma3 )
% 5.25/5.59 => ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.59 & ( ( Mi3 != Ma3 )
% 5.25/5.59 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.25/5.59 & ! [X2: nat] :
% 5.25/5.59 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.25/5.59 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.25/5.59 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.25/5.59 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.25/5.59 @ Mima ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % VEBT_internal.valid'.elims(3)
% 5.25/5.59 thf(fact_10036_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.25/5.59 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.59 ( ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 5.25/5.59 => ( ( ? [Uu: $o,Uv: $o] :
% 5.25/5.59 ( X3
% 5.25/5.59 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.25/5.59 => ( Xa2 != one_one_nat ) )
% 5.25/5.59 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.25/5.59 => ~ ( ( Deg2 = Xa2 )
% 5.25/5.59 & ! [X: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.25/5.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 & ( case_o184042715313410164at_nat
% 5.25/5.59 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.25/5.59 & ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.59 @ ( produc6081775807080527818_nat_o
% 5.25/5.59 @ ^ [Mi3: nat,Ma3: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.25/5.59 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.25/5.59 & ! [I3: nat] :
% 5.25/5.59 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 5.25/5.59 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.25/5.59 & ( ( Mi3 = Ma3 )
% 5.25/5.59 => ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.59 & ( ( Mi3 != Ma3 )
% 5.25/5.59 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.25/5.59 & ! [X2: nat] :
% 5.25/5.59 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.25/5.59 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.25/5.59 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.25/5.59 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.25/5.59 @ Mima ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % VEBT_internal.valid'.elims(2)
% 5.25/5.59 thf(fact_10037_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.25/5.59 ! [X3: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.25/5.59 ( ( ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 5.25/5.59 => ( ! [Uu: $o,Uv: $o] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( Xa2 = one_one_nat ) )
% 5.25/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) ) )
% 5.25/5.59 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( ( Deg2 = Xa2 )
% 5.25/5.59 & ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.25/5.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 & ( case_o184042715313410164at_nat
% 5.25/5.59 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.25/5.59 & ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.59 @ ( produc6081775807080527818_nat_o
% 5.25/5.59 @ ^ [Mi3: nat,Ma3: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.25/5.59 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.25/5.59 & ! [I3: nat] :
% 5.25/5.59 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 5.25/5.59 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.25/5.59 & ( ( Mi3 = Ma3 )
% 5.25/5.59 => ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.59 & ( ( Mi3 != Ma3 )
% 5.25/5.59 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.25/5.59 & ! [X2: nat] :
% 5.25/5.59 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.25/5.59 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.25/5.59 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.25/5.59 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.25/5.59 @ Mima ) ) )
% 5.25/5.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % VEBT_internal.valid'.pelims(1)
% 5.25/5.59 thf(fact_10038_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.25/5.59 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.59 ( ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 5.25/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 5.25/5.59 => ( ! [Uu: $o,Uv: $o] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.25/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) )
% 5.25/5.59 => ( Xa2 != one_one_nat ) ) )
% 5.25/5.59 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.25/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.25/5.59 => ~ ( ( Deg2 = Xa2 )
% 5.25/5.59 & ! [X: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.25/5.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 & ( case_o184042715313410164at_nat
% 5.25/5.59 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.25/5.59 & ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.59 @ ( produc6081775807080527818_nat_o
% 5.25/5.59 @ ^ [Mi3: nat,Ma3: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.25/5.59 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.25/5.59 & ! [I3: nat] :
% 5.25/5.59 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 5.25/5.59 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.25/5.59 & ( ( Mi3 = Ma3 )
% 5.25/5.59 => ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.59 & ( ( Mi3 != Ma3 )
% 5.25/5.59 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.25/5.59 & ! [X2: nat] :
% 5.25/5.59 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.25/5.59 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.25/5.59 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.25/5.59 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.25/5.59 @ Mima ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % VEBT_internal.valid'.pelims(2)
% 5.25/5.59 thf(fact_10039_Sup__int__def,axiom,
% 5.25/5.59 ( complete_Sup_Sup_int
% 5.25/5.59 = ( ^ [X4: set_int] :
% 5.25/5.59 ( the_int
% 5.25/5.59 @ ^ [X2: int] :
% 5.25/5.59 ( ( member_int @ X2 @ X4 )
% 5.25/5.59 & ! [Y6: int] :
% 5.25/5.59 ( ( member_int @ Y6 @ X4 )
% 5.25/5.59 => ( ord_less_eq_int @ Y6 @ X2 ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Sup_int_def
% 5.25/5.59 thf(fact_10040_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.25/5.59 ! [X3: vEBT_VEBT,Xa2: nat] :
% 5.25/5.59 ( ~ ( vEBT_VEBT_valid @ X3 @ Xa2 )
% 5.25/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X3 @ Xa2 ) )
% 5.25/5.59 => ( ! [Uu: $o,Uv: $o] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.25/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) )
% 5.25/5.59 => ( Xa2 = one_one_nat ) ) )
% 5.25/5.59 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.25/5.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.25/5.59 => ( ( Deg2 = Xa2 )
% 5.25/5.59 & ! [X5: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.59 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.25/5.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 & ( case_o184042715313410164at_nat
% 5.25/5.59 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.25/5.59 & ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.59 @ ( produc6081775807080527818_nat_o
% 5.25/5.59 @ ^ [Mi3: nat,Ma3: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.25/5.59 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.25/5.59 & ! [I3: nat] :
% 5.25/5.59 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.25/5.59 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 5.25/5.59 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.25/5.59 & ( ( Mi3 = Ma3 )
% 5.25/5.59 => ! [X2: vEBT_VEBT] :
% 5.25/5.59 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.59 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.25/5.59 & ( ( Mi3 != Ma3 )
% 5.25/5.59 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.25/5.59 & ! [X2: nat] :
% 5.25/5.59 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.25/5.59 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.25/5.59 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.25/5.59 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.25/5.59 @ Mima ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % VEBT_internal.valid'.pelims(3)
% 5.25/5.59 thf(fact_10041_less__eq,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 5.25/5.59 = ( ord_less_nat @ M @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % less_eq
% 5.25/5.59 thf(fact_10042_pred__nat__trancl__eq__le,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 5.25/5.59 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % pred_nat_trancl_eq_le
% 5.25/5.59 thf(fact_10043_Rats__eq__int__div__nat,axiom,
% 5.25/5.59 ( field_5140801741446780682s_real
% 5.25/5.59 = ( collect_real
% 5.25/5.59 @ ^ [Uu3: real] :
% 5.25/5.59 ? [I3: int,N2: nat] :
% 5.25/5.59 ( ( Uu3
% 5.25/5.59 = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.25/5.59 & ( N2 != zero_zero_nat ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Rats_eq_int_div_nat
% 5.25/5.59 thf(fact_10044_rat__floor__lemma,axiom,
% 5.25/5.59 ! [A: int,B: int] :
% 5.25/5.59 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 5.25/5.59 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_floor_lemma
% 5.25/5.59 thf(fact_10045_Rats__abs__iff,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ( ( member_real @ ( abs_abs_real @ X3 ) @ field_5140801741446780682s_real )
% 5.25/5.59 = ( member_real @ X3 @ field_5140801741446780682s_real ) ) ).
% 5.25/5.59
% 5.25/5.59 % Rats_abs_iff
% 5.25/5.59 thf(fact_10046_mult__rat,axiom,
% 5.25/5.59 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.59 ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.25/5.59 = ( fract @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % mult_rat
% 5.25/5.59 thf(fact_10047_divide__rat,axiom,
% 5.25/5.59 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.59 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.25/5.59 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % divide_rat
% 5.25/5.59 thf(fact_10048_less__rat,axiom,
% 5.25/5.59 ! [B: int,D: int,A: int,C: int] :
% 5.25/5.59 ( ( B != zero_zero_int )
% 5.25/5.59 => ( ( D != zero_zero_int )
% 5.25/5.59 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.25/5.59 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % less_rat
% 5.25/5.59 thf(fact_10049_add__rat,axiom,
% 5.25/5.59 ! [B: int,D: int,A: int,C: int] :
% 5.25/5.59 ( ( B != zero_zero_int )
% 5.25/5.59 => ( ( D != zero_zero_int )
% 5.25/5.59 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.25/5.59 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % add_rat
% 5.25/5.59 thf(fact_10050_le__rat,axiom,
% 5.25/5.59 ! [B: int,D: int,A: int,C: int] :
% 5.25/5.59 ( ( B != zero_zero_int )
% 5.25/5.59 => ( ( D != zero_zero_int )
% 5.25/5.59 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.25/5.59 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % le_rat
% 5.25/5.59 thf(fact_10051_diff__rat,axiom,
% 5.25/5.59 ! [B: int,D: int,A: int,C: int] :
% 5.25/5.59 ( ( B != zero_zero_int )
% 5.25/5.59 => ( ( D != zero_zero_int )
% 5.25/5.59 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.25/5.59 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % diff_rat
% 5.25/5.59 thf(fact_10052_sgn__rat,axiom,
% 5.25/5.59 ! [A: int,B: int] :
% 5.25/5.59 ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 5.25/5.59 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % sgn_rat
% 5.25/5.59 thf(fact_10053_Rats__no__top__le,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ? [X5: real] :
% 5.25/5.59 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.25/5.59 & ( ord_less_eq_real @ X3 @ X5 ) ) ).
% 5.25/5.59
% 5.25/5.59 % Rats_no_top_le
% 5.25/5.59 thf(fact_10054_Fract__of__int__eq,axiom,
% 5.25/5.59 ! [K: int] :
% 5.25/5.59 ( ( fract @ K @ one_one_int )
% 5.25/5.59 = ( ring_1_of_int_rat @ K ) ) ).
% 5.25/5.59
% 5.25/5.59 % Fract_of_int_eq
% 5.25/5.59 thf(fact_10055_Fract__of__nat__eq,axiom,
% 5.25/5.59 ! [K: nat] :
% 5.25/5.59 ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 5.25/5.59 = ( semiri681578069525770553at_rat @ K ) ) ).
% 5.25/5.59
% 5.25/5.59 % Fract_of_nat_eq
% 5.25/5.59 thf(fact_10056_mult__rat__cancel,axiom,
% 5.25/5.59 ! [C: int,A: int,B: int] :
% 5.25/5.59 ( ( C != zero_zero_int )
% 5.25/5.59 => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.59 = ( fract @ A @ B ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % mult_rat_cancel
% 5.25/5.59 thf(fact_10057_eq__rat_I1_J,axiom,
% 5.25/5.59 ! [B: int,D: int,A: int,C: int] :
% 5.25/5.59 ( ( B != zero_zero_int )
% 5.25/5.59 => ( ( D != zero_zero_int )
% 5.25/5.59 => ( ( ( fract @ A @ B )
% 5.25/5.59 = ( fract @ C @ D ) )
% 5.25/5.59 = ( ( times_times_int @ A @ D )
% 5.25/5.59 = ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % eq_rat(1)
% 5.25/5.59 thf(fact_10058_eq__rat_I2_J,axiom,
% 5.25/5.59 ! [A: int] :
% 5.25/5.59 ( ( fract @ A @ zero_zero_int )
% 5.25/5.59 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % eq_rat(2)
% 5.25/5.59 thf(fact_10059_Rats__no__bot__less,axiom,
% 5.25/5.59 ! [X3: real] :
% 5.25/5.59 ? [X5: real] :
% 5.25/5.59 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.25/5.59 & ( ord_less_real @ X5 @ X3 ) ) ).
% 5.25/5.59
% 5.25/5.59 % Rats_no_bot_less
% 5.25/5.59 thf(fact_10060_Rats__dense__in__real,axiom,
% 5.25/5.59 ! [X3: real,Y: real] :
% 5.25/5.59 ( ( ord_less_real @ X3 @ Y )
% 5.25/5.59 => ? [X5: real] :
% 5.25/5.59 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.25/5.59 & ( ord_less_real @ X3 @ X5 )
% 5.25/5.59 & ( ord_less_real @ X5 @ Y ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Rats_dense_in_real
% 5.25/5.59 thf(fact_10061_One__rat__def,axiom,
% 5.25/5.59 ( one_one_rat
% 5.25/5.59 = ( fract @ one_one_int @ one_one_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % One_rat_def
% 5.25/5.59 thf(fact_10062_Zero__rat__def,axiom,
% 5.25/5.59 ( zero_zero_rat
% 5.25/5.59 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % Zero_rat_def
% 5.25/5.59 thf(fact_10063_rat__number__expand_I3_J,axiom,
% 5.25/5.59 ( numeral_numeral_rat
% 5.25/5.59 = ( ^ [K3: num] : ( fract @ ( numeral_numeral_int @ K3 ) @ one_one_int ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_number_expand(3)
% 5.25/5.59 thf(fact_10064_rat__number__collapse_I3_J,axiom,
% 5.25/5.59 ! [W: num] :
% 5.25/5.59 ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 5.25/5.59 = ( numeral_numeral_rat @ W ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_number_collapse(3)
% 5.25/5.59 thf(fact_10065_Fract__less__one__iff,axiom,
% 5.25/5.59 ! [B: int,A: int] :
% 5.25/5.59 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.59 => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.25/5.59 = ( ord_less_int @ A @ B ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Fract_less_one_iff
% 5.25/5.59 thf(fact_10066_one__less__Fract__iff,axiom,
% 5.25/5.59 ! [B: int,A: int] :
% 5.25/5.59 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.59 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.25/5.59 = ( ord_less_int @ B @ A ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % one_less_Fract_iff
% 5.25/5.59 thf(fact_10067_Rats__eq__int__div__int,axiom,
% 5.25/5.59 ( field_5140801741446780682s_real
% 5.25/5.59 = ( collect_real
% 5.25/5.59 @ ^ [Uu3: real] :
% 5.25/5.59 ? [I3: int,J3: int] :
% 5.25/5.59 ( ( Uu3
% 5.25/5.59 = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 5.25/5.59 & ( J3 != zero_zero_int ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Rats_eq_int_div_int
% 5.25/5.59 thf(fact_10068_rat__number__collapse_I5_J,axiom,
% 5.25/5.59 ( ( fract @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.25/5.59 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_number_collapse(5)
% 5.25/5.59 thf(fact_10069_Fract__add__one,axiom,
% 5.25/5.59 ! [N: int,M: int] :
% 5.25/5.59 ( ( N != zero_zero_int )
% 5.25/5.59 => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 5.25/5.59 = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Fract_add_one
% 5.25/5.59 thf(fact_10070_Fract__le__zero__iff,axiom,
% 5.25/5.59 ! [B: int,A: int] :
% 5.25/5.59 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.59 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.25/5.59 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Fract_le_zero_iff
% 5.25/5.59 thf(fact_10071_zero__le__Fract__iff,axiom,
% 5.25/5.59 ! [B: int,A: int] :
% 5.25/5.59 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.59 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.25/5.59 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % zero_le_Fract_iff
% 5.25/5.59 thf(fact_10072_one__le__Fract__iff,axiom,
% 5.25/5.59 ! [B: int,A: int] :
% 5.25/5.59 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.59 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.25/5.59 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % one_le_Fract_iff
% 5.25/5.59 thf(fact_10073_Fract__le__one__iff,axiom,
% 5.25/5.59 ! [B: int,A: int] :
% 5.25/5.59 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.59 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.25/5.59 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Fract_le_one_iff
% 5.25/5.59 thf(fact_10074_rat__number__collapse_I4_J,axiom,
% 5.25/5.59 ! [W: num] :
% 5.25/5.59 ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 5.25/5.59 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_number_collapse(4)
% 5.25/5.59 thf(fact_10075_rat__number__expand_I5_J,axiom,
% 5.25/5.59 ! [K: num] :
% 5.25/5.59 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 5.25/5.59 = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % rat_number_expand(5)
% 5.25/5.59 thf(fact_10076_take__bit__numeral__minus__numeral__int,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 = ( case_option_int_num @ zero_zero_int
% 5.25/5.59 @ ^ [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 ) ) )
% 5.25/5.59 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % take_bit_numeral_minus_numeral_int
% 5.25/5.59 thf(fact_10077_take__bit__num__simps_I1_J,axiom,
% 5.25/5.59 ! [M: num] :
% 5.25/5.59 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.25/5.59 = none_num ) ).
% 5.25/5.59
% 5.25/5.59 % take_bit_num_simps(1)
% 5.25/5.59 thf(fact_10078_take__bit__num__simps_I2_J,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 5.25/5.59 = ( some_num @ one ) ) ).
% 5.25/5.59
% 5.25/5.59 % take_bit_num_simps(2)
% 5.25/5.59 thf(fact_10079_take__bit__num__simps_I5_J,axiom,
% 5.25/5.59 ! [R2: num] :
% 5.25/5.59 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ one )
% 5.25/5.59 = ( some_num @ one ) ) ).
% 5.25/5.59
% 5.25/5.59 % take_bit_num_simps(5)
% 5.25/5.59 thf(fact_10080_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( bit_take_bit_num @ N @ one )
% 5.25/5.59 = ( case_nat_option_num @ none_num
% 5.25/5.59 @ ^ [N2: nat] : ( some_num @ one )
% 5.25/5.59 @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.25/5.59 thf(fact_10081_take__bit__num__def,axiom,
% 5.25/5.59 ( bit_take_bit_num
% 5.25/5.59 = ( ^ [N2: nat,M6: num] :
% 5.25/5.59 ( if_option_num
% 5.25/5.59 @ ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M6 ) )
% 5.25/5.59 = zero_zero_nat )
% 5.25/5.59 @ none_num
% 5.25/5.59 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % take_bit_num_def
% 5.25/5.59 thf(fact_10082_and__minus__numerals_I7_J,axiom,
% 5.25/5.59 ! [N: num,M: num] :
% 5.25/5.59 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.25/5.59 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_minus_numerals(7)
% 5.25/5.59 thf(fact_10083_and__minus__numerals_I3_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.25/5.59 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_minus_numerals(3)
% 5.25/5.59 thf(fact_10084_take__bit__num__simps_I4_J,axiom,
% 5.25/5.59 ! [N: nat,M: num] :
% 5.25/5.59 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 5.25/5.59 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % take_bit_num_simps(4)
% 5.25/5.59 thf(fact_10085_take__bit__num__simps_I3_J,axiom,
% 5.25/5.59 ! [N: nat,M: num] :
% 5.25/5.59 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 5.25/5.59 = ( case_o6005452278849405969um_num @ none_num
% 5.25/5.59 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.25/5.59 @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % take_bit_num_simps(3)
% 5.25/5.59 thf(fact_10086_take__bit__num__simps_I7_J,axiom,
% 5.25/5.59 ! [R2: num,M: num] :
% 5.25/5.59 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M ) )
% 5.25/5.59 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % take_bit_num_simps(7)
% 5.25/5.59 thf(fact_10087_take__bit__num__simps_I6_J,axiom,
% 5.25/5.59 ! [R2: num,M: num] :
% 5.25/5.59 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M ) )
% 5.25/5.59 = ( case_o6005452278849405969um_num @ none_num
% 5.25/5.59 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.25/5.59 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % take_bit_num_simps(6)
% 5.25/5.59 thf(fact_10088_and__minus__numerals_I4_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.25/5.59 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_minus_numerals(4)
% 5.25/5.59 thf(fact_10089_and__minus__numerals_I8_J,axiom,
% 5.25/5.59 ! [N: num,M: num] :
% 5.25/5.59 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.25/5.59 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_minus_numerals(8)
% 5.25/5.59 thf(fact_10090_and__not__num_Osimps_I8_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.25/5.59 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.25/5.59 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.25/5.59 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_not_num.simps(8)
% 5.25/5.59 thf(fact_10091_and__not__num_Osimps_I1_J,axiom,
% 5.25/5.59 ( ( bit_and_not_num @ one @ one )
% 5.25/5.59 = none_num ) ).
% 5.25/5.59
% 5.25/5.59 % and_not_num.simps(1)
% 5.25/5.59 thf(fact_10092_and__not__num_Osimps_I4_J,axiom,
% 5.25/5.59 ! [M: num] :
% 5.25/5.59 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.25/5.59 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_not_num.simps(4)
% 5.25/5.59 thf(fact_10093_and__not__num_Osimps_I2_J,axiom,
% 5.25/5.59 ! [N: num] :
% 5.25/5.59 ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 5.25/5.59 = ( some_num @ one ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_not_num.simps(2)
% 5.25/5.59 thf(fact_10094_and__not__num_Osimps_I3_J,axiom,
% 5.25/5.59 ! [N: num] :
% 5.25/5.59 ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 5.25/5.59 = none_num ) ).
% 5.25/5.59
% 5.25/5.59 % and_not_num.simps(3)
% 5.25/5.59 thf(fact_10095_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.25/5.59 ! [N: nat,M: num] :
% 5.25/5.59 ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 5.25/5.59 = ( case_nat_option_num @ none_num
% 5.25/5.59 @ ^ [N2: nat] :
% 5.25/5.59 ( case_o6005452278849405969um_num @ none_num
% 5.25/5.59 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.25/5.59 @ ( bit_take_bit_num @ N2 @ M ) )
% 5.25/5.59 @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.25/5.59 thf(fact_10096_and__not__num_Osimps_I7_J,axiom,
% 5.25/5.59 ! [M: num] :
% 5.25/5.59 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.25/5.59 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_not_num.simps(7)
% 5.25/5.59 thf(fact_10097_and__not__num__eq__Some__iff,axiom,
% 5.25/5.59 ! [M: num,N: num,Q2: num] :
% 5.25/5.59 ( ( ( bit_and_not_num @ M @ N )
% 5.25/5.59 = ( some_num @ Q2 ) )
% 5.25/5.59 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 = ( numeral_numeral_int @ Q2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_not_num_eq_Some_iff
% 5.25/5.59 thf(fact_10098_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.25/5.59 ! [N: nat,M: num] :
% 5.25/5.59 ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 5.25/5.59 = ( case_nat_option_num @ none_num
% 5.25/5.59 @ ^ [N2: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) )
% 5.25/5.59 @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.25/5.59 thf(fact_10099_and__not__num__eq__None__iff,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( ( bit_and_not_num @ M @ N )
% 5.25/5.59 = none_num )
% 5.25/5.59 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 = zero_zero_int ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_not_num_eq_None_iff
% 5.25/5.59 thf(fact_10100_int__numeral__and__not__num,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.25/5.59 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % int_numeral_and_not_num
% 5.25/5.59 thf(fact_10101_int__numeral__not__and__num,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.25/5.59 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % int_numeral_not_and_num
% 5.25/5.59 thf(fact_10102_positive__rat,axiom,
% 5.25/5.59 ! [A: int,B: int] :
% 5.25/5.59 ( ( positive @ ( fract @ A @ B ) )
% 5.25/5.59 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % positive_rat
% 5.25/5.59 thf(fact_10103_Rat_Opositive__add,axiom,
% 5.25/5.59 ! [X3: rat,Y: rat] :
% 5.25/5.59 ( ( positive @ X3 )
% 5.25/5.59 => ( ( positive @ Y )
% 5.25/5.59 => ( positive @ ( plus_plus_rat @ X3 @ Y ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Rat.positive_add
% 5.25/5.59 thf(fact_10104_Rat_Opositive__mult,axiom,
% 5.25/5.59 ! [X3: rat,Y: rat] :
% 5.25/5.59 ( ( positive @ X3 )
% 5.25/5.59 => ( ( positive @ Y )
% 5.25/5.59 => ( positive @ ( times_times_rat @ X3 @ Y ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Rat.positive_mult
% 5.25/5.59 thf(fact_10105_Rat_Opositive_Orep__eq,axiom,
% 5.25/5.59 ( positive
% 5.25/5.59 = ( ^ [X2: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X2 ) ) @ ( product_snd_int_int @ ( rep_Rat @ X2 ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Rat.positive.rep_eq
% 5.25/5.59 thf(fact_10106_and__not__num_Oelims,axiom,
% 5.25/5.59 ! [X3: num,Xa2: num,Y: option_num] :
% 5.25/5.59 ( ( ( bit_and_not_num @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( Y != none_num ) ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ( ? [N3: num] :
% 5.25/5.59 ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( some_num @ one ) ) ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ( ? [N3: num] :
% 5.25/5.59 ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( Y != none_num ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.25/5.59 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.25/5.59 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 5.25/5.59 => ~ ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_not_num.elims
% 5.25/5.59 thf(fact_10107_and__not__num_Osimps_I6_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_not_num.simps(6)
% 5.25/5.59 thf(fact_10108_and__not__num_Osimps_I9_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_not_num.simps(9)
% 5.25/5.59 thf(fact_10109_and__not__num_Osimps_I5_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_not_num.simps(5)
% 5.25/5.59 thf(fact_10110_and__not__num_Opelims,axiom,
% 5.25/5.59 ! [X3: num,Xa2: num,Y: option_num] :
% 5.25/5.59 ( ( ( bit_and_not_num @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X3 @ Xa2 ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( ( Y = none_num )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( some_num @ one ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( ( Y = none_num )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( some_num @ ( bit0 @ M5 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( some_num @ ( bit0 @ M5 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.25/5.59 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.25/5.59 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ~ ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_not_num.pelims
% 5.25/5.59 thf(fact_10111_and__num_Oelims,axiom,
% 5.25/5.59 ! [X3: num,Xa2: num,Y: option_num] :
% 5.25/5.59 ( ( ( bit_un7362597486090784418nd_num @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( some_num @ one ) ) ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ( ? [N3: num] :
% 5.25/5.59 ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( Y != none_num ) ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ( ? [N3: num] :
% 5.25/5.59 ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( some_num @ one ) ) ) )
% 5.25/5.59 => ( ( ? [M5: num] :
% 5.25/5.59 ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( Y != none_num ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 5.25/5.59 => ( ( ? [M5: num] :
% 5.25/5.59 ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( some_num @ one ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 5.25/5.59 => ~ ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.25/5.59 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.25/5.59 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_num.elims
% 5.25/5.59 thf(fact_10112_and__num_Osimps_I1_J,axiom,
% 5.25/5.59 ( ( bit_un7362597486090784418nd_num @ one @ one )
% 5.25/5.59 = ( some_num @ one ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_num.simps(1)
% 5.25/5.59 thf(fact_10113_and__num_Osimps_I5_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_num.simps(5)
% 5.25/5.59 thf(fact_10114_and__num_Osimps_I7_J,axiom,
% 5.25/5.59 ! [M: num] :
% 5.25/5.59 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 5.25/5.59 = ( some_num @ one ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_num.simps(7)
% 5.25/5.59 thf(fact_10115_and__num_Osimps_I3_J,axiom,
% 5.25/5.59 ! [N: num] :
% 5.25/5.59 ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N ) )
% 5.25/5.59 = ( some_num @ one ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_num.simps(3)
% 5.25/5.59 thf(fact_10116_and__num_Osimps_I2_J,axiom,
% 5.25/5.59 ! [N: num] :
% 5.25/5.59 ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N ) )
% 5.25/5.59 = none_num ) ).
% 5.25/5.59
% 5.25/5.59 % and_num.simps(2)
% 5.25/5.59 thf(fact_10117_and__num_Osimps_I4_J,axiom,
% 5.25/5.59 ! [M: num] :
% 5.25/5.59 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 5.25/5.59 = none_num ) ).
% 5.25/5.59
% 5.25/5.59 % and_num.simps(4)
% 5.25/5.59 thf(fact_10118_and__num_Osimps_I6_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_num.simps(6)
% 5.25/5.59 thf(fact_10119_and__num_Osimps_I8_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_num.simps(8)
% 5.25/5.59 thf(fact_10120_and__num_Osimps_I9_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.25/5.59 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.25/5.59 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.25/5.59 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_num.simps(9)
% 5.25/5.59 thf(fact_10121_and__num_Opelims,axiom,
% 5.25/5.59 ! [X3: num,Xa2: num,Y: option_num] :
% 5.25/5.59 ( ( ( bit_un7362597486090784418nd_num @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X3 @ Xa2 ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( some_num @ one ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( ( Y = none_num )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( some_num @ one ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( ( Y = none_num )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( some_num @ one ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ~ ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.25/5.59 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.25/5.59 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % and_num.pelims
% 5.25/5.59 thf(fact_10122_xor__num_Oelims,axiom,
% 5.25/5.59 ! [X3: num,Xa2: num,Y: option_num] :
% 5.25/5.59 ( ( ( bit_un2480387367778600638or_num @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( Y != none_num ) ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( some_num @ ( bit1 @ N3 ) ) ) ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( some_num @ ( bit0 @ N3 ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( some_num @ ( bit1 @ M5 ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ~ ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % xor_num.elims
% 5.25/5.59 thf(fact_10123_xor__num_Osimps_I1_J,axiom,
% 5.25/5.59 ( ( bit_un2480387367778600638or_num @ one @ one )
% 5.25/5.59 = none_num ) ).
% 5.25/5.59
% 5.25/5.59 % xor_num.simps(1)
% 5.25/5.59 thf(fact_10124_xor__num_Osimps_I5_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % xor_num.simps(5)
% 5.25/5.59 thf(fact_10125_xor__num_Osimps_I9_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % xor_num.simps(9)
% 5.25/5.59 thf(fact_10126_xor__num_Osimps_I7_J,axiom,
% 5.25/5.59 ! [M: num] :
% 5.25/5.59 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 5.25/5.59 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % xor_num.simps(7)
% 5.25/5.59 thf(fact_10127_xor__num_Osimps_I4_J,axiom,
% 5.25/5.59 ! [M: num] :
% 5.25/5.59 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 5.25/5.59 = ( some_num @ ( bit1 @ M ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % xor_num.simps(4)
% 5.25/5.59 thf(fact_10128_xor__num_Osimps_I3_J,axiom,
% 5.25/5.59 ! [N: num] :
% 5.25/5.59 ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N ) )
% 5.25/5.59 = ( some_num @ ( bit0 @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % xor_num.simps(3)
% 5.25/5.59 thf(fact_10129_xor__num_Osimps_I2_J,axiom,
% 5.25/5.59 ! [N: num] :
% 5.25/5.59 ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N ) )
% 5.25/5.59 = ( some_num @ ( bit1 @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % xor_num.simps(2)
% 5.25/5.59 thf(fact_10130_xor__num_Osimps_I8_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.25/5.59 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % xor_num.simps(8)
% 5.25/5.59 thf(fact_10131_xor__num_Osimps_I6_J,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.25/5.59 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % xor_num.simps(6)
% 5.25/5.59 thf(fact_10132_xor__num_Opelims,axiom,
% 5.25/5.59 ! [X3: num,Xa2: num,Y: option_num] :
% 5.25/5.59 ( ( ( bit_un2480387367778600638or_num @ X3 @ Xa2 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X3 @ Xa2 ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( ( Y = none_num )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( some_num @ ( bit1 @ N3 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ( ( ( X3 = one )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( some_num @ ( bit0 @ N3 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( some_num @ ( bit1 @ M5 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit0 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ( ( Xa2 = one )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( some_num @ ( bit0 @ M5 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 5.25/5.59 => ( ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit0 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.25/5.59 => ~ ! [M5: num] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( bit1 @ M5 ) )
% 5.25/5.59 => ! [N3: num] :
% 5.25/5.59 ( ( Xa2
% 5.25/5.59 = ( bit1 @ N3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) )
% 5.25/5.59 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % xor_num.pelims
% 5.25/5.59 thf(fact_10133_and__num__rel__dict,axiom,
% 5.25/5.59 bit_un4731106466462545111um_rel = bit_un5425074673868309765um_rel ).
% 5.25/5.59
% 5.25/5.59 % and_num_rel_dict
% 5.25/5.59 thf(fact_10134_xor__num__rel__dict,axiom,
% 5.25/5.59 bit_un2901131394128224187um_rel = bit_un3595099601533988841um_rel ).
% 5.25/5.59
% 5.25/5.59 % xor_num_rel_dict
% 5.25/5.59 thf(fact_10135_and__num__dict,axiom,
% 5.25/5.59 bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 5.25/5.59
% 5.25/5.59 % and_num_dict
% 5.25/5.59 thf(fact_10136_xor__num__dict,axiom,
% 5.25/5.59 bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 5.25/5.59
% 5.25/5.59 % xor_num_dict
% 5.25/5.59 thf(fact_10137_Bit__Operations_Otake__bit__num__code,axiom,
% 5.25/5.59 ( bit_take_bit_num
% 5.25/5.59 = ( ^ [N2: nat,M6: num] :
% 5.25/5.59 ( produc478579273971653890on_num
% 5.25/5.59 @ ^ [A3: nat,X2: num] :
% 5.25/5.59 ( case_nat_option_num @ none_num
% 5.25/5.59 @ ^ [O: nat] :
% 5.25/5.59 ( case_num_option_num @ ( some_num @ one )
% 5.25/5.59 @ ^ [P4: num] :
% 5.25/5.59 ( case_o6005452278849405969um_num @ none_num
% 5.25/5.59 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.25/5.59 @ ( bit_take_bit_num @ O @ P4 ) )
% 5.25/5.59 @ ^ [P4: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P4 ) ) )
% 5.25/5.59 @ X2 )
% 5.25/5.59 @ A3 )
% 5.25/5.59 @ ( product_Pair_nat_num @ N2 @ M6 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Bit_Operations.take_bit_num_code
% 5.25/5.59 thf(fact_10138_num__of__integer__code,axiom,
% 5.25/5.59 ( code_num_of_integer
% 5.25/5.59 = ( ^ [K3: code_integer] :
% 5.25/5.59 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 5.25/5.59 @ ( produc7336495610019696514er_num
% 5.25/5.59 @ ^ [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 ) )
% 5.25/5.59 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % num_of_integer_code
% 5.25/5.59 thf(fact_10139_min__Suc__Suc,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.25/5.59 = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % min_Suc_Suc
% 5.25/5.59 thf(fact_10140_min__0L,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( ord_min_nat @ zero_zero_nat @ N )
% 5.25/5.59 = zero_zero_nat ) ).
% 5.25/5.59
% 5.25/5.59 % min_0L
% 5.25/5.59 thf(fact_10141_min__0R,axiom,
% 5.25/5.59 ! [N: nat] :
% 5.25/5.59 ( ( ord_min_nat @ N @ zero_zero_nat )
% 5.25/5.59 = zero_zero_nat ) ).
% 5.25/5.59
% 5.25/5.59 % min_0R
% 5.25/5.59 thf(fact_10142_min__numeral__Suc,axiom,
% 5.25/5.59 ! [K: num,N: nat] :
% 5.25/5.59 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.25/5.59 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % min_numeral_Suc
% 5.25/5.59 thf(fact_10143_min__Suc__numeral,axiom,
% 5.25/5.59 ! [N: nat,K: num] :
% 5.25/5.59 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.25/5.59 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % min_Suc_numeral
% 5.25/5.59 thf(fact_10144_concat__bit__assoc__sym,axiom,
% 5.25/5.59 ! [M: nat,N: nat,K: int,L2: int,R2: int] :
% 5.25/5.59 ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N @ K @ L2 ) @ R2 )
% 5.25/5.59 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N ) @ L2 @ R2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % concat_bit_assoc_sym
% 5.25/5.59 thf(fact_10145_inf__nat__def,axiom,
% 5.25/5.59 inf_inf_nat = ord_min_nat ).
% 5.25/5.59
% 5.25/5.59 % inf_nat_def
% 5.25/5.59 thf(fact_10146_nat__mult__min__right,axiom,
% 5.25/5.59 ! [M: nat,N: nat,Q2: nat] :
% 5.25/5.59 ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q2 ) )
% 5.25/5.59 = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % nat_mult_min_right
% 5.25/5.59 thf(fact_10147_nat__mult__min__left,axiom,
% 5.25/5.59 ! [M: nat,N: nat,Q2: nat] :
% 5.25/5.59 ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q2 )
% 5.25/5.59 = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % nat_mult_min_left
% 5.25/5.59 thf(fact_10148_min__diff,axiom,
% 5.25/5.59 ! [M: nat,I2: nat,N: nat] :
% 5.25/5.59 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I2 ) @ ( minus_minus_nat @ N @ I2 ) )
% 5.25/5.59 = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % min_diff
% 5.25/5.59 thf(fact_10149_take__bit__concat__bit__eq,axiom,
% 5.25/5.59 ! [M: nat,N: nat,K: int,L2: int] :
% 5.25/5.59 ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N @ K @ L2 ) )
% 5.25/5.59 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ L2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % take_bit_concat_bit_eq
% 5.25/5.59 thf(fact_10150_min__Suc1,axiom,
% 5.25/5.59 ! [N: nat,M: nat] :
% 5.25/5.59 ( ( ord_min_nat @ ( suc @ N ) @ M )
% 5.25/5.59 = ( case_nat_nat @ zero_zero_nat
% 5.25/5.59 @ ^ [M3: nat] : ( suc @ ( ord_min_nat @ N @ M3 ) )
% 5.25/5.59 @ M ) ) ).
% 5.25/5.59
% 5.25/5.59 % min_Suc1
% 5.25/5.59 thf(fact_10151_min__Suc2,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( ord_min_nat @ M @ ( suc @ N ) )
% 5.25/5.59 = ( case_nat_nat @ zero_zero_nat
% 5.25/5.59 @ ^ [M3: nat] : ( suc @ ( ord_min_nat @ M3 @ N ) )
% 5.25/5.59 @ M ) ) ).
% 5.25/5.59
% 5.25/5.59 % min_Suc2
% 5.25/5.59 thf(fact_10152_min__enat__simps_I3_J,axiom,
% 5.25/5.59 ! [Q2: extended_enat] :
% 5.25/5.59 ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.25/5.59 = zero_z5237406670263579293d_enat ) ).
% 5.25/5.59
% 5.25/5.59 % min_enat_simps(3)
% 5.25/5.59 thf(fact_10153_min__enat__simps_I2_J,axiom,
% 5.25/5.59 ! [Q2: extended_enat] :
% 5.25/5.59 ( ( ord_mi8085742599997312461d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.25/5.59 = zero_z5237406670263579293d_enat ) ).
% 5.25/5.59
% 5.25/5.59 % min_enat_simps(2)
% 5.25/5.59 thf(fact_10154_inf__enat__def,axiom,
% 5.25/5.59 inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 5.25/5.59
% 5.25/5.59 % inf_enat_def
% 5.25/5.59 thf(fact_10155_upt__rec__numeral,axiom,
% 5.25/5.59 ! [M: num,N: num] :
% 5.25/5.59 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.59 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.59 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 5.25/5.59 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.59 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.25/5.59 = nil_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upt_rec_numeral
% 5.25/5.59 thf(fact_10156_remdups__upt,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( remdups_nat @ ( upt @ M @ N ) )
% 5.25/5.59 = ( upt @ M @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % remdups_upt
% 5.25/5.59 thf(fact_10157_hd__upt,axiom,
% 5.25/5.59 ! [I2: nat,J2: nat] :
% 5.25/5.59 ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.59 => ( ( hd_nat @ ( upt @ I2 @ J2 ) )
% 5.25/5.59 = I2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % hd_upt
% 5.25/5.59 thf(fact_10158_drop__upt,axiom,
% 5.25/5.59 ! [M: nat,I2: nat,J2: nat] :
% 5.25/5.59 ( ( drop_nat @ M @ ( upt @ I2 @ J2 ) )
% 5.25/5.59 = ( upt @ ( plus_plus_nat @ I2 @ M ) @ J2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % drop_upt
% 5.25/5.59 thf(fact_10159_length__upt,axiom,
% 5.25/5.59 ! [I2: nat,J2: nat] :
% 5.25/5.59 ( ( size_size_list_nat @ ( upt @ I2 @ J2 ) )
% 5.25/5.59 = ( minus_minus_nat @ J2 @ I2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % length_upt
% 5.25/5.59 thf(fact_10160_take__upt,axiom,
% 5.25/5.59 ! [I2: nat,M: nat,N: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M ) @ N )
% 5.25/5.59 => ( ( take_nat @ M @ ( upt @ I2 @ N ) )
% 5.25/5.59 = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % take_upt
% 5.25/5.59 thf(fact_10161_upt__conv__Nil,axiom,
% 5.25/5.59 ! [J2: nat,I2: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ J2 @ I2 )
% 5.25/5.59 => ( ( upt @ I2 @ J2 )
% 5.25/5.59 = nil_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % upt_conv_Nil
% 5.25/5.59 thf(fact_10162_sorted__list__of__set__range,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.25/5.59 = ( upt @ M @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % sorted_list_of_set_range
% 5.25/5.59 thf(fact_10163_upt__eq__Nil__conv,axiom,
% 5.25/5.59 ! [I2: nat,J2: nat] :
% 5.25/5.59 ( ( ( upt @ I2 @ J2 )
% 5.25/5.59 = nil_nat )
% 5.25/5.59 = ( ( J2 = zero_zero_nat )
% 5.25/5.59 | ( ord_less_eq_nat @ J2 @ I2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upt_eq_Nil_conv
% 5.25/5.59 thf(fact_10164_nth__upt,axiom,
% 5.25/5.59 ! [I2: nat,K: nat,J2: nat] :
% 5.25/5.59 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J2 )
% 5.25/5.59 => ( ( nth_nat @ ( upt @ I2 @ J2 ) @ K )
% 5.25/5.59 = ( plus_plus_nat @ I2 @ K ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % nth_upt
% 5.25/5.59 thf(fact_10165_upt__0,axiom,
% 5.25/5.59 ! [I2: nat] :
% 5.25/5.59 ( ( upt @ I2 @ zero_zero_nat )
% 5.25/5.59 = nil_nat ) ).
% 5.25/5.59
% 5.25/5.59 % upt_0
% 5.25/5.59 thf(fact_10166_distinct__upt,axiom,
% 5.25/5.59 ! [I2: nat,J2: nat] : ( distinct_nat @ ( upt @ I2 @ J2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % distinct_upt
% 5.25/5.59 thf(fact_10167_upt__conv__Cons__Cons,axiom,
% 5.25/5.59 ! [M: nat,N: nat,Ns: list_nat,Q2: nat] :
% 5.25/5.59 ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 5.25/5.59 = ( upt @ M @ Q2 ) )
% 5.25/5.59 = ( ( cons_nat @ N @ Ns )
% 5.25/5.59 = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upt_conv_Cons_Cons
% 5.25/5.59 thf(fact_10168_greaterThanAtMost__upt,axiom,
% 5.25/5.59 ( set_or6659071591806873216st_nat
% 5.25/5.59 = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ ( suc @ M6 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % greaterThanAtMost_upt
% 5.25/5.59 thf(fact_10169_atLeast__upt,axiom,
% 5.25/5.59 ( set_ord_lessThan_nat
% 5.25/5.59 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % atLeast_upt
% 5.25/5.59 thf(fact_10170_greaterThanLessThan__upt,axiom,
% 5.25/5.59 ( set_or5834768355832116004an_nat
% 5.25/5.59 = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ M6 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % greaterThanLessThan_upt
% 5.25/5.59 thf(fact_10171_atLeastAtMost__upt,axiom,
% 5.25/5.59 ( set_or1269000886237332187st_nat
% 5.25/5.59 = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ N2 @ ( suc @ M6 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % atLeastAtMost_upt
% 5.25/5.59 thf(fact_10172_atLeastLessThan__upt,axiom,
% 5.25/5.59 ( set_or4665077453230672383an_nat
% 5.25/5.59 = ( ^ [I3: nat,J3: nat] : ( set_nat2 @ ( upt @ I3 @ J3 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % atLeastLessThan_upt
% 5.25/5.59 thf(fact_10173_atMost__upto,axiom,
% 5.25/5.59 ( set_ord_atMost_nat
% 5.25/5.59 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % atMost_upto
% 5.25/5.59 thf(fact_10174_upt__conv__Cons,axiom,
% 5.25/5.59 ! [I2: nat,J2: nat] :
% 5.25/5.59 ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.59 => ( ( upt @ I2 @ J2 )
% 5.25/5.59 = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J2 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upt_conv_Cons
% 5.25/5.59 thf(fact_10175_upt__add__eq__append,axiom,
% 5.25/5.59 ! [I2: nat,J2: nat,K: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.59 => ( ( upt @ I2 @ ( plus_plus_nat @ J2 @ K ) )
% 5.25/5.59 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( upt @ J2 @ ( plus_plus_nat @ J2 @ K ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upt_add_eq_append
% 5.25/5.59 thf(fact_10176_upt__eq__Cons__conv,axiom,
% 5.25/5.59 ! [I2: nat,J2: nat,X3: nat,Xs: list_nat] :
% 5.25/5.59 ( ( ( upt @ I2 @ J2 )
% 5.25/5.59 = ( cons_nat @ X3 @ Xs ) )
% 5.25/5.59 = ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.59 & ( I2 = X3 )
% 5.25/5.59 & ( ( upt @ ( plus_plus_nat @ I2 @ one_one_nat ) @ J2 )
% 5.25/5.59 = Xs ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upt_eq_Cons_conv
% 5.25/5.59 thf(fact_10177_upt__rec,axiom,
% 5.25/5.59 ( upt
% 5.25/5.59 = ( ^ [I3: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I3 @ J3 ) @ ( cons_nat @ I3 @ ( upt @ ( suc @ I3 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upt_rec
% 5.25/5.59 thf(fact_10178_upt__Suc,axiom,
% 5.25/5.59 ! [I2: nat,J2: nat] :
% 5.25/5.59 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.59 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 5.25/5.59 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( cons_nat @ J2 @ nil_nat ) ) ) )
% 5.25/5.59 & ( ~ ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.59 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 5.25/5.59 = nil_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upt_Suc
% 5.25/5.59 thf(fact_10179_upt__Suc__append,axiom,
% 5.25/5.59 ! [I2: nat,J2: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.25/5.59 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 5.25/5.59 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( cons_nat @ J2 @ nil_nat ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % upt_Suc_append
% 5.25/5.59 thf(fact_10180_map__Suc__upt,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 5.25/5.59 = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % map_Suc_upt
% 5.25/5.59 thf(fact_10181_map__add__upt,axiom,
% 5.25/5.59 ! [N: nat,M: nat] :
% 5.25/5.59 ( ( map_nat_nat
% 5.25/5.59 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ N )
% 5.25/5.59 @ ( upt @ zero_zero_nat @ M ) )
% 5.25/5.59 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % map_add_upt
% 5.25/5.59 thf(fact_10182_map__decr__upt,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( map_nat_nat
% 5.25/5.59 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.25/5.59 @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.25/5.59 = ( upt @ M @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % map_decr_upt
% 5.25/5.59 thf(fact_10183_Divides_Oadjust__div__def,axiom,
% 5.25/5.59 ( adjust_div
% 5.25/5.59 = ( produc8211389475949308722nt_int
% 5.25/5.59 @ ^ [Q4: int,R5: int] : ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Divides.adjust_div_def
% 5.25/5.59 thf(fact_10184_sum__list__upt,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ M @ N )
% 5.25/5.59 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 5.25/5.59 = ( groups3542108847815614940at_nat
% 5.25/5.59 @ ^ [X2: nat] : X2
% 5.25/5.59 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % sum_list_upt
% 5.25/5.59 thf(fact_10185_card__length__sum__list__rec,axiom,
% 5.25/5.59 ! [M: nat,N5: nat] :
% 5.25/5.59 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.25/5.59 => ( ( finite_card_list_nat
% 5.25/5.59 @ ( collect_list_nat
% 5.25/5.59 @ ^ [L: list_nat] :
% 5.25/5.59 ( ( ( size_size_list_nat @ L )
% 5.25/5.59 = M )
% 5.25/5.59 & ( ( groups4561878855575611511st_nat @ L )
% 5.25/5.59 = N5 ) ) ) )
% 5.25/5.59 = ( plus_plus_nat
% 5.25/5.59 @ ( finite_card_list_nat
% 5.25/5.59 @ ( collect_list_nat
% 5.25/5.59 @ ^ [L: list_nat] :
% 5.25/5.59 ( ( ( size_size_list_nat @ L )
% 5.25/5.59 = ( minus_minus_nat @ M @ one_one_nat ) )
% 5.25/5.59 & ( ( groups4561878855575611511st_nat @ L )
% 5.25/5.59 = N5 ) ) ) )
% 5.25/5.59 @ ( finite_card_list_nat
% 5.25/5.59 @ ( collect_list_nat
% 5.25/5.59 @ ^ [L: list_nat] :
% 5.25/5.59 ( ( ( size_size_list_nat @ L )
% 5.25/5.59 = M )
% 5.25/5.59 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L ) @ one_one_nat )
% 5.25/5.59 = N5 ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_length_sum_list_rec
% 5.25/5.59 thf(fact_10186_card__length__sum__list,axiom,
% 5.25/5.59 ! [M: nat,N5: nat] :
% 5.25/5.59 ( ( finite_card_list_nat
% 5.25/5.59 @ ( collect_list_nat
% 5.25/5.59 @ ^ [L: list_nat] :
% 5.25/5.59 ( ( ( size_size_list_nat @ L )
% 5.25/5.59 = M )
% 5.25/5.59 & ( ( groups4561878855575611511st_nat @ L )
% 5.25/5.59 = N5 ) ) ) )
% 5.25/5.59 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N5 @ M ) @ one_one_nat ) @ N5 ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_length_sum_list
% 5.25/5.59 thf(fact_10187_sorted__wrt__upt,axiom,
% 5.25/5.59 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % sorted_wrt_upt
% 5.25/5.59 thf(fact_10188_sorted__upt,axiom,
% 5.25/5.59 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % sorted_upt
% 5.25/5.59 thf(fact_10189_sorted__wrt__less__idx,axiom,
% 5.25/5.59 ! [Ns: list_nat,I2: nat] :
% 5.25/5.59 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.25/5.59 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 5.25/5.59 => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % sorted_wrt_less_idx
% 5.25/5.59 thf(fact_10190_sorted__upto,axiom,
% 5.25/5.59 ! [M: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % sorted_upto
% 5.25/5.59 thf(fact_10191_sorted__wrt__upto,axiom,
% 5.25/5.59 ! [I2: int,J2: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I2 @ J2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % sorted_wrt_upto
% 5.25/5.59 thf(fact_10192_tl__upt,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( tl_nat @ ( upt @ M @ N ) )
% 5.25/5.59 = ( upt @ ( suc @ M ) @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % tl_upt
% 5.25/5.59 thf(fact_10193_VEBT_Osize_I3_J,axiom,
% 5.25/5.59 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.25/5.59 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.25/5.59 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % VEBT.size(3)
% 5.25/5.59 thf(fact_10194_VEBT_Osize__gen_I1_J,axiom,
% 5.25/5.59 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.25/5.59 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.25/5.59 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % VEBT.size_gen(1)
% 5.25/5.59 thf(fact_10195_pairs__le__eq__Sigma,axiom,
% 5.25/5.59 ! [M: nat] :
% 5.25/5.59 ( ( collec3392354462482085612at_nat
% 5.25/5.59 @ ( produc6081775807080527818_nat_o
% 5.25/5.59 @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ M ) ) )
% 5.25/5.59 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 5.25/5.59 @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % pairs_le_eq_Sigma
% 5.25/5.59 thf(fact_10196_card__le__Suc__Max,axiom,
% 5.25/5.59 ! [S3: set_nat] :
% 5.25/5.59 ( ( finite_finite_nat @ S3 )
% 5.25/5.59 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % card_le_Suc_Max
% 5.25/5.59 thf(fact_10197_divide__nat__def,axiom,
% 5.25/5.59 ( divide_divide_nat
% 5.25/5.59 = ( ^ [M6: nat,N2: nat] :
% 5.25/5.59 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 5.25/5.59 @ ( lattic8265883725875713057ax_nat
% 5.25/5.59 @ ( collect_nat
% 5.25/5.59 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N2 ) @ M6 ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % divide_nat_def
% 5.25/5.59 thf(fact_10198_gcd__is__Max__divisors__nat,axiom,
% 5.25/5.59 ! [N: nat,M: nat] :
% 5.25/5.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.25/5.59 => ( ( gcd_gcd_nat @ M @ N )
% 5.25/5.59 = ( lattic8265883725875713057ax_nat
% 5.25/5.59 @ ( collect_nat
% 5.25/5.59 @ ^ [D2: nat] :
% 5.25/5.59 ( ( dvd_dvd_nat @ D2 @ M )
% 5.25/5.59 & ( dvd_dvd_nat @ D2 @ N ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % gcd_is_Max_divisors_nat
% 5.25/5.59 thf(fact_10199_prod__encode__prod__decode__aux,axiom,
% 5.25/5.59 ! [K: nat,M: nat] :
% 5.25/5.59 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.25/5.59 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.25/5.59
% 5.25/5.59 % prod_encode_prod_decode_aux
% 5.25/5.59 thf(fact_10200_le__prod__encode__1,axiom,
% 5.25/5.59 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % le_prod_encode_1
% 5.25/5.59 thf(fact_10201_le__prod__encode__2,axiom,
% 5.25/5.59 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % le_prod_encode_2
% 5.25/5.59 thf(fact_10202_prod__encode__def,axiom,
% 5.25/5.59 ( nat_prod_encode
% 5.25/5.59 = ( produc6842872674320459806at_nat
% 5.25/5.59 @ ^ [M6: nat,N2: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N2 ) ) @ M6 ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % prod_encode_def
% 5.25/5.59 thf(fact_10203_list__encode_Oelims,axiom,
% 5.25/5.59 ! [X3: list_nat,Y: nat] :
% 5.25/5.59 ( ( ( nat_list_encode @ X3 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( ( X3 = nil_nat )
% 5.25/5.59 => ( Y != zero_zero_nat ) )
% 5.25/5.59 => ~ ! [X5: nat,Xs3: list_nat] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( cons_nat @ X5 @ Xs3 ) )
% 5.25/5.59 => ( Y
% 5.25/5.59 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % list_encode.elims
% 5.25/5.59 thf(fact_10204_list__encode_Osimps_I2_J,axiom,
% 5.25/5.59 ! [X3: nat,Xs: list_nat] :
% 5.25/5.59 ( ( nat_list_encode @ ( cons_nat @ X3 @ Xs ) )
% 5.25/5.59 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % list_encode.simps(2)
% 5.25/5.59 thf(fact_10205_list__encode_Opelims,axiom,
% 5.25/5.59 ! [X3: list_nat,Y: nat] :
% 5.25/5.59 ( ( ( nat_list_encode @ X3 )
% 5.25/5.59 = Y )
% 5.25/5.59 => ( ( accp_list_nat @ nat_list_encode_rel @ X3 )
% 5.25/5.59 => ( ( ( X3 = nil_nat )
% 5.25/5.59 => ( ( Y = zero_zero_nat )
% 5.25/5.59 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.25/5.59 => ~ ! [X5: nat,Xs3: list_nat] :
% 5.25/5.59 ( ( X3
% 5.25/5.59 = ( cons_nat @ X5 @ Xs3 ) )
% 5.25/5.59 => ( ( Y
% 5.25/5.59 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 5.25/5.59 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X5 @ Xs3 ) ) ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % list_encode.pelims
% 5.25/5.59 thf(fact_10206_Gcd__nat__eq__one,axiom,
% 5.25/5.59 ! [N5: set_nat] :
% 5.25/5.59 ( ( member_nat @ one_one_nat @ N5 )
% 5.25/5.59 => ( ( gcd_Gcd_nat @ N5 )
% 5.25/5.59 = one_one_nat ) ) ).
% 5.25/5.59
% 5.25/5.59 % Gcd_nat_eq_one
% 5.25/5.59 thf(fact_10207_Gcd__int__greater__eq__0,axiom,
% 5.25/5.59 ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 5.25/5.59
% 5.25/5.59 % Gcd_int_greater_eq_0
% 5.25/5.59 thf(fact_10208_of__nat__eq__id,axiom,
% 5.25/5.59 semiri1316708129612266289at_nat = id_nat ).
% 5.25/5.59
% 5.25/5.59 % of_nat_eq_id
% 5.25/5.59 thf(fact_10209_Rat_Opositive__def,axiom,
% 5.25/5.59 ( positive
% 5.25/5.59 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 5.25/5.59 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ).
% 5.25/5.59
% 5.25/5.59 % Rat.positive_def
% 5.25/5.59 thf(fact_10210_sort__upt,axiom,
% 5.25/5.59 ! [M: nat,N: nat] :
% 5.25/5.59 ( ( linord738340561235409698at_nat
% 5.25/5.59 @ ^ [X2: nat] : X2
% 5.25/5.59 @ ( upt @ M @ N ) )
% 5.25/5.59 = ( upt @ M @ N ) ) ).
% 5.25/5.59
% 5.25/5.59 % sort_upt
% 5.25/5.59 thf(fact_10211_sort__upto,axiom,
% 5.25/5.59 ! [I2: int,J2: int] :
% 5.25/5.59 ( ( linord1735203802627413978nt_int
% 5.25/5.59 @ ^ [X2: int] : X2
% 5.25/5.59 @ ( upto @ I2 @ J2 ) )
% 5.25/5.59 = ( upto @ I2 @ J2 ) ) ).
% 5.25/5.59
% 5.25/5.59 % sort_upto
% 5.25/5.59
% 5.25/5.59 % Helper facts (42)
% 5.25/5.59 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.25/5.59 ! [X3: int,Y: int] :
% 5.25/5.59 ( ( if_int @ $false @ X3 @ Y )
% 5.25/5.59 = Y ) ).
% 5.25/5.59
% 5.25/5.59 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.25/5.59 ! [X3: int,Y: int] :
% 5.25/5.59 ( ( if_int @ $true @ X3 @ Y )
% 5.25/5.59 = X3 ) ).
% 5.25/5.59
% 5.25/5.59 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.25/5.59 ! [X3: nat,Y: nat] :
% 5.25/5.59 ( ( if_nat @ $false @ X3 @ Y )
% 5.25/5.59 = Y ) ).
% 5.25/5.59
% 5.25/5.59 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.25/5.59 ! [X3: nat,Y: nat] :
% 5.25/5.59 ( ( if_nat @ $true @ X3 @ Y )
% 5.25/5.59 = X3 ) ).
% 5.25/5.59
% 5.25/5.59 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.25/5.59 ! [X3: num,Y: num] :
% 5.25/5.59 ( ( if_num @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.25/5.60 ! [X3: num,Y: num] :
% 5.25/5.60 ( ( if_num @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.25/5.60 ! [X3: rat,Y: rat] :
% 5.25/5.60 ( ( if_rat @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.25/5.60 ! [X3: rat,Y: rat] :
% 5.25/5.60 ( ( if_rat @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.25/5.60 ! [X3: real,Y: real] :
% 5.25/5.60 ( ( if_real @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.25/5.60 ! [X3: real,Y: real] :
% 5.25/5.60 ( ( if_real @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.25/5.60 ! [P: real > $o] :
% 5.25/5.60 ( ( P @ ( fChoice_real @ P ) )
% 5.25/5.60 = ( ? [X4: real] : ( P @ X4 ) ) ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.25/5.60 ! [X3: complex,Y: complex] :
% 5.25/5.60 ( ( if_complex @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.25/5.60 ! [X3: complex,Y: complex] :
% 5.25/5.60 ( ( if_complex @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.25/5.60 ! [X3: extended_enat,Y: extended_enat] :
% 5.25/5.60 ( ( if_Extended_enat @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.25/5.60 ! [X3: extended_enat,Y: extended_enat] :
% 5.25/5.60 ( ( if_Extended_enat @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.25/5.60 ! [X3: code_integer,Y: code_integer] :
% 5.25/5.60 ( ( if_Code_integer @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.25/5.60 ! [X3: code_integer,Y: code_integer] :
% 5.25/5.60 ( ( if_Code_integer @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.25/5.60 ! [X3: set_int,Y: set_int] :
% 5.25/5.60 ( ( if_set_int @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.25/5.60 ! [X3: set_int,Y: set_int] :
% 5.25/5.60 ( ( if_set_int @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.25/5.60 ! [X3: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.25/5.60 ( ( if_VEBT_VEBT @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.25/5.60 ! [X3: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.25/5.60 ( ( if_VEBT_VEBT @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.25/5.60 ! [X3: list_int,Y: list_int] :
% 5.25/5.60 ( ( if_list_int @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.25/5.60 ! [X3: list_int,Y: list_int] :
% 5.25/5.60 ( ( if_list_int @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.25/5.60 ! [X3: list_nat,Y: list_nat] :
% 5.25/5.60 ( ( if_list_nat @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.25/5.60 ! [X3: list_nat,Y: list_nat] :
% 5.25/5.60 ( ( if_list_nat @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.25/5.60 ! [X3: int > int,Y: int > int] :
% 5.25/5.60 ( ( if_int_int @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.25/5.60 ! [X3: int > int,Y: int > int] :
% 5.25/5.60 ( ( if_int_int @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.25/5.60 ! [X3: option_num,Y: option_num] :
% 5.25/5.60 ( ( if_option_num @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.25/5.60 ! [X3: option_num,Y: option_num] :
% 5.25/5.60 ( ( if_option_num @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.25/5.60 ! [X3: product_prod_int_int,Y: product_prod_int_int] :
% 5.25/5.60 ( ( if_Pro3027730157355071871nt_int @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.25/5.60 ! [X3: product_prod_int_int,Y: product_prod_int_int] :
% 5.25/5.60 ( ( if_Pro3027730157355071871nt_int @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.25/5.60 ! [X3: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.25/5.60 ( ( if_Pro6206227464963214023at_nat @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.25/5.60 ! [X3: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.25/5.60 ( ( if_Pro6206227464963214023at_nat @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 5.25/5.60 ! [X3: nat > int > int,Y: nat > int > int] :
% 5.25/5.60 ( ( if_nat_int_int @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 5.25/5.60 ! [X3: nat > int > int,Y: nat > int > int] :
% 5.25/5.60 ( ( if_nat_int_int @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 5.25/5.60 ! [X3: nat > nat > nat,Y: nat > nat > nat] :
% 5.25/5.60 ( ( if_nat_nat_nat @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 5.25/5.60 ! [X3: nat > nat > nat,Y: nat > nat > nat] :
% 5.25/5.60 ( ( if_nat_nat_nat @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.25/5.60 ! [X3: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 5.25/5.60 ( ( if_Pro5737122678794959658eger_o @ $false @ X3 @ Y )
% 5.25/5.60 = Y ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.25/5.60 ! [X3: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 5.25/5.60 ( ( if_Pro5737122678794959658eger_o @ $true @ X3 @ Y )
% 5.25/5.60 = X3 ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.25/5.60 ! [P: $o] :
% 5.25/5.60 ( ( P = $true )
% 5.25/5.60 | ( P = $false ) ) ).
% 5.25/5.60
% 5.25/5.60 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.25/5.60 ! [X3: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.44/6.76 ( ( if_Pro6119634080678213985nteger @ $false @ X3 @ Y )
% 6.44/6.76 = Y ) ).
% 6.44/6.76
% 6.44/6.76 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.44/6.76 ! [X3: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.44/6.76 ( ( if_Pro6119634080678213985nteger @ $true @ X3 @ Y )
% 6.44/6.76 = X3 ) ).
% 6.44/6.76
% 6.44/6.76 % Conjectures (1)
% 6.44/6.76 thf(conj_0,conjecture,
% 6.44/6.76 ( ( xa != mi )
% 6.44/6.76 & ( xa != ma ) ) ).
% 6.44/6.76
% 6.44/6.76 %------------------------------------------------------------------------------
% 6.44/6.76 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.z3qdlqM5yJ/cvc5---1.0.5_8919.p...
% 6.44/6.76 (declare-sort $$unsorted 0)
% 6.44/6.76 (declare-sort tptp.produc3368934014287244435at_num 0)
% 6.44/6.76 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 6.44/6.76 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 6.44/6.76 (declare-sort tptp.produc2963631642982155120at_num 0)
% 6.44/6.76 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 6.44/6.76 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 6.44/6.76 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 6.44/6.76 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 6.44/6.76 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 6.44/6.76 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.44/6.76 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 6.44/6.76 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 6.44/6.76 (declare-sort tptp.list_P8526636022914148096eger_o 0)
% 6.44/6.76 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.44/6.76 (declare-sort tptp.list_P3744719386663036955um_num 0)
% 6.44/6.76 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 6.44/6.76 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.44/6.76 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 6.44/6.76 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 6.44/6.76 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 6.44/6.76 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.44/6.76 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 6.44/6.76 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 6.44/6.76 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 6.44/6.76 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 6.44/6.76 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.44/6.76 (declare-sort tptp.product_prod_num_num 0)
% 6.44/6.76 (declare-sort tptp.product_prod_nat_num 0)
% 6.44/6.76 (declare-sort tptp.product_prod_nat_nat 0)
% 6.44/6.76 (declare-sort tptp.product_prod_int_int 0)
% 6.44/6.76 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.44/6.76 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.44/6.76 (declare-sort tptp.set_list_nat 0)
% 6.44/6.76 (declare-sort tptp.product_prod_o_nat 0)
% 6.44/6.76 (declare-sort tptp.product_prod_o_int 0)
% 6.44/6.76 (declare-sort tptp.list_Code_integer 0)
% 6.44/6.76 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.44/6.76 (declare-sort tptp.set_set_nat 0)
% 6.44/6.76 (declare-sort tptp.set_set_int 0)
% 6.44/6.76 (declare-sort tptp.set_Code_integer 0)
% 6.44/6.76 (declare-sort tptp.set_Product_unit 0)
% 6.44/6.76 (declare-sort tptp.set_Extended_enat 0)
% 6.44/6.76 (declare-sort tptp.list_complex 0)
% 6.44/6.76 (declare-sort tptp.product_prod_o_o 0)
% 6.44/6.76 (declare-sort tptp.set_complex 0)
% 6.44/6.76 (declare-sort tptp.filter_real 0)
% 6.44/6.76 (declare-sort tptp.option_num 0)
% 6.44/6.76 (declare-sort tptp.filter_nat 0)
% 6.44/6.76 (declare-sort tptp.set_char 0)
% 6.44/6.76 (declare-sort tptp.list_real 0)
% 6.44/6.76 (declare-sort tptp.set_real 0)
% 6.44/6.76 (declare-sort tptp.list_num 0)
% 6.44/6.76 (declare-sort tptp.list_nat 0)
% 6.44/6.76 (declare-sort tptp.list_int 0)
% 6.44/6.76 (declare-sort tptp.vEBT_VEBT 0)
% 6.44/6.76 (declare-sort tptp.set_rat 0)
% 6.44/6.76 (declare-sort tptp.set_num 0)
% 6.44/6.76 (declare-sort tptp.set_nat 0)
% 6.44/6.76 (declare-sort tptp.set_int 0)
% 6.44/6.76 (declare-sort tptp.code_integer 0)
% 6.44/6.76 (declare-sort tptp.extended_enat 0)
% 6.44/6.76 (declare-sort tptp.list_o 0)
% 6.44/6.76 (declare-sort tptp.complex 0)
% 6.44/6.76 (declare-sort tptp.set_o 0)
% 6.44/6.76 (declare-sort tptp.char 0)
% 6.44/6.76 (declare-sort tptp.real 0)
% 6.44/6.76 (declare-sort tptp.rat 0)
% 6.44/6.76 (declare-sort tptp.num 0)
% 6.44/6.76 (declare-sort tptp.nat 0)
% 6.44/6.76 (declare-sort tptp.int 0)
% 6.44/6.76 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.44/6.76 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 6.44/6.76 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.44/6.76 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 6.44/6.76 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 6.44/6.76 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 6.44/6.76 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 6.44/6.76 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 6.44/6.76 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 6.44/6.76 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.44/6.76 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.44/6.76 (declare-fun tptp.bit_and_not_num_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.44/6.76 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 6.44/6.76 (declare-fun tptp.bit_or3848514188828904588eg_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.44/6.76 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.44/6.76 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.bit_se9216721137139052372nteger (tptp.code_integer tptp.nat) Bool)
% 6.44/6.76 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.44/6.76 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.44/6.76 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.44/6.76 (declare-fun tptp.bit_un1837492267222099188nd_num (tptp.num tptp.num) tptp.option_num)
% 6.44/6.76 (declare-fun tptp.bit_un5425074673868309765um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.44/6.76 (declare-fun tptp.bit_un6178654185764691216or_num (tptp.num tptp.num) tptp.option_num)
% 6.44/6.76 (declare-fun tptp.bit_un3595099601533988841um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.44/6.76 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 6.44/6.76 (declare-fun tptp.bit_un4731106466462545111um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.44/6.76 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 6.44/6.76 (declare-fun tptp.bit_un2901131394128224187um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.44/6.76 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.44/6.76 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.44/6.76 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.44/6.76 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.44/6.76 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.44/6.76 (declare-fun tptp.code_negative (tptp.num) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.44/6.76 (declare-fun tptp.code_positive (tptp.num) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.code_Target_negative (tptp.num) tptp.int)
% 6.44/6.76 (declare-fun tptp.code_Target_positive (tptp.num) tptp.int)
% 6.44/6.76 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 6.44/6.76 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.44/6.76 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 6.44/6.76 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 6.44/6.76 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.44/6.76 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.44/6.76 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.44/6.76 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.44/6.76 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.44/6.76 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.44/6.76 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.44/6.76 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.44/6.76 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.44/6.76 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.44/6.76 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.44/6.76 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.44/6.76 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.44/6.76 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.44/6.76 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 6.44/6.76 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.44/6.76 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.44/6.76 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.44/6.76 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.44/6.76 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.44/6.76 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.44/6.76 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.44/6.76 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.44/6.76 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 6.44/6.76 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.44/6.76 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 6.44/6.76 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 6.44/6.76 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.44/6.76 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.44/6.76 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 6.44/6.76 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.44/6.76 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.44/6.76 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.44/6.76 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.44/6.76 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.44/6.76 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.44/6.76 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.44/6.76 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.44/6.76 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 6.44/6.76 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.44/6.76 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.44/6.76 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.44/6.76 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.44/6.76 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.44/6.76 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 6.44/6.76 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 6.44/6.76 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 6.44/6.76 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.44/6.76 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.44/6.76 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.44/6.76 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.44/6.76 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.44/6.76 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.44/6.76 (declare-fun tptp.comp_C8797469213163452608nteger ((-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.44/6.76 (declare-fun tptp.comp_C1593894019821074884nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.44/6.76 (declare-fun tptp.comp_C3531382070062128313er_num ((-> tptp.code_integer tptp.code_integer) (-> tptp.num tptp.code_integer) tptp.num) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.comp_int_int_num ((-> tptp.int tptp.int) (-> tptp.num tptp.int) tptp.num) tptp.int)
% 6.44/6.76 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.comp_nat_real_nat ((-> tptp.nat tptp.real) (-> tptp.nat tptp.nat) tptp.nat) tptp.real)
% 6.44/6.76 (declare-fun tptp.id_o (Bool) Bool)
% 6.44/6.76 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.44/6.76 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 6.44/6.76 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 6.44/6.76 (declare-fun tptp.map_fu898904425404107465nt_o_o ((-> tptp.rat tptp.product_prod_int_int) (-> Bool Bool) (-> tptp.product_prod_int_int Bool) tptp.rat) Bool)
% 6.44/6.76 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.44/6.76 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.44/6.76 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 6.44/6.76 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.44/6.76 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.44/6.76 (declare-fun tptp.gcd_gcd_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.44/6.76 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.44/6.76 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.44/6.76 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.44/6.76 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.44/6.76 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.44/6.76 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.44/6.76 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.44/6.76 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.44/6.76 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.44/6.76 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.44/6.76 (declare-fun tptp.minus_1356011639430497352at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.44/6.76 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.44/6.76 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.44/6.76 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.44/6.76 (declare-fun tptp.one_one_int () tptp.int)
% 6.44/6.76 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.44/6.76 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.44/6.76 (declare-fun tptp.one_one_real () tptp.real)
% 6.44/6.76 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.44/6.76 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.44/6.76 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.44/6.76 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.44/6.76 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.44/6.76 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 6.44/6.76 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.44/6.76 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.44/6.76 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.44/6.76 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.44/6.76 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.76 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.44/6.76 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.44/6.76 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.44/6.76 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.44/6.76 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.44/6.76 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.44/6.76 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.44/6.76 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.44/6.76 (declare-fun tptp.uminus8566677241136511917omplex (tptp.set_complex) tptp.set_complex)
% 6.44/6.76 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 6.44/6.76 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.44/6.76 (declare-fun tptp.uminus6524753893492686040at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.44/6.77 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 6.44/6.77 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.44/6.77 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.44/6.77 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.44/6.77 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.44/6.77 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.44/6.77 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.44/6.77 (declare-fun tptp.groups6621422865394947399nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.44/6.77 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.44/6.77 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.44/6.77 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.44/6.77 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.44/6.77 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.44/6.77 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.44/6.77 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.44/6.77 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.44/6.77 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.44/6.77 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.44/6.77 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.44/6.77 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.44/6.77 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.44/6.77 (declare-fun tptp.groups6381953495645901045omplex ((-> tptp.product_prod_nat_nat tptp.complex) tptp.set_Pr1261947904930325089at_nat) tptp.complex)
% 6.44/6.77 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.groups4567486121110086003t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 6.44/6.77 (declare-fun tptp.groups7713935264441627589nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.44/6.77 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.44/6.77 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.44/6.77 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.44/6.77 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.44/6.77 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.44/6.77 (declare-fun tptp.groups225925009352817453ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.44/6.77 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.44/6.77 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.44/6.77 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.44/6.77 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.44/6.77 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.44/6.77 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.44/6.77 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.44/6.77 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.44/6.77 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.44/6.77 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.44/6.77 (declare-fun tptp.groups8110221916422527690omplex ((-> tptp.product_prod_nat_nat tptp.complex) tptp.set_Pr1261947904930325089at_nat) tptp.complex)
% 6.44/6.77 (declare-fun tptp.groups4075276357253098568at_int ((-> tptp.product_prod_nat_nat tptp.int) tptp.set_Pr1261947904930325089at_nat) tptp.int)
% 6.44/6.77 (declare-fun tptp.groups4077766827762148844at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.groups6036352826371341000t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 6.44/6.77 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.44/6.77 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.44/6.77 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.44/6.77 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.44/6.77 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.44/6.77 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.44/6.77 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.44/6.77 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 6.44/6.77 (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)
% 6.44/6.77 (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)
% 6.44/6.77 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.44/6.77 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.44/6.77 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.44/6.77 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.44/6.77 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.44/6.77 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.44/6.77 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.44/6.77 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.44/6.77 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.44/6.77 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.44/6.77 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.44/6.77 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.44/6.77 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 6.44/6.77 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.44/6.77 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.44/6.77 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.44/6.77 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.44/6.77 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.44/6.77 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.44/6.77 (declare-fun tptp.power_int_real (tptp.real tptp.int) tptp.real)
% 6.44/6.77 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.44/6.77 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 6.44/6.77 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 6.44/6.77 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.44/6.77 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.44/6.77 (declare-fun tptp.inf_in1870772243966228564d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.44/6.77 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.44/6.77 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.44/6.77 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.44/6.77 (declare-fun tptp.at_infinity_real () tptp.filter_real)
% 6.44/6.77 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 6.44/6.77 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.44/6.77 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 6.44/6.77 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 6.44/6.77 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.44/6.77 (declare-fun tptp.linord1735203802627413978nt_int ((-> tptp.int tptp.int) tptp.list_int) tptp.list_int)
% 6.44/6.77 (declare-fun tptp.linord738340561235409698at_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.44/6.77 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.44/6.77 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.44/6.77 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.44/6.77 (declare-fun tptp.nil_int () tptp.list_int)
% 6.44/6.77 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.44/6.77 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.44/6.77 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.44/6.77 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.44/6.77 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.44/6.77 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.set_Pr5648618587558075414at_nat (tptp.list_P6011104703257516679at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.44/6.77 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.44/6.77 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.44/6.77 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.44/6.77 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 6.44/6.77 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 6.44/6.77 (declare-fun tptp.list_update_complex (tptp.list_complex tptp.nat tptp.complex) tptp.list_complex)
% 6.44/6.77 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 6.44/6.77 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 6.44/6.77 (declare-fun tptp.list_u6180841689913720943at_nat (tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 6.44/6.77 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 6.44/6.77 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.44/6.77 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.nth_Code_integer (tptp.list_Code_integer tptp.nat) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 6.44/6.77 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.44/6.77 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 6.44/6.77 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 6.44/6.77 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 6.44/6.77 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 6.44/6.77 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 6.44/6.77 (declare-fun tptp.nth_Pr8522763379788166057eger_o (tptp.list_P8526636022914148096eger_o tptp.nat) tptp.produc6271795597528267376eger_o)
% 6.44/6.77 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 6.44/6.77 (declare-fun tptp.nth_Pr6456567536196504476um_num (tptp.list_P3744719386663036955um_num tptp.nat) tptp.product_prod_num_num)
% 6.44/6.77 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 6.44/6.77 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 6.44/6.77 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.44/6.77 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 6.44/6.77 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.44/6.77 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.44/6.77 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.44/6.77 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.44/6.77 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 6.44/6.77 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.44/6.77 (declare-fun tptp.produc3607205314601156340eger_o (tptp.list_Code_integer tptp.list_o) tptp.list_P8526636022914148096eger_o)
% 6.44/6.77 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.44/6.77 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.44/6.77 (declare-fun tptp.product_num_num (tptp.list_num tptp.list_num) tptp.list_P3744719386663036955um_num)
% 6.44/6.77 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.44/6.77 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 6.44/6.77 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.44/6.77 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.44/6.77 (declare-fun tptp.remdups_nat (tptp.list_nat) tptp.list_nat)
% 6.44/6.77 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 6.44/6.77 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 6.44/6.77 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 6.44/6.77 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 6.44/6.77 (declare-fun tptp.replic4235873036481779905at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 6.44/6.77 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 6.44/6.77 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.44/6.77 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 6.44/6.77 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 6.44/6.77 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.44/6.77 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 6.44/6.77 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.44/6.77 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 6.44/6.77 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.44/6.77 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.44/6.77 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.44/6.77 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 6.44/6.77 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.44/6.77 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.44/6.77 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.44/6.77 (declare-fun tptp.semiri2816024913162550771omplex ((-> tptp.complex tptp.complex) tptp.nat tptp.complex) tptp.complex)
% 6.44/6.77 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.44/6.77 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.semiri7787848453975740701ux_rat ((-> tptp.rat tptp.rat) tptp.nat tptp.rat) tptp.rat)
% 6.44/6.77 (declare-fun tptp.semiri7260567687927622513x_real ((-> tptp.real tptp.real) tptp.nat tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s3445333598471063425nteger (tptp.list_Code_integer) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.44/6.77 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 6.44/6.77 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.44/6.77 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.44/6.77 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.44/6.77 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.44/6.77 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.44/6.77 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.44/6.77 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 6.44/6.77 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.44/6.77 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.44/6.77 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 6.44/6.77 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.44/6.77 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.44/6.77 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 6.44/6.77 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.44/6.77 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.44/6.77 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.44/6.77 (declare-fun tptp.one () tptp.num)
% 6.44/6.77 (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)
% 6.44/6.77 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.44/6.77 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.44/6.77 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.44/6.77 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.44/6.77 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.44/6.77 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.44/6.77 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.44/6.77 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.44/6.77 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.44/6.77 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.44/6.77 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.44/6.77 (declare-fun tptp.none_num () tptp.option_num)
% 6.44/6.77 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.44/6.77 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.44/6.77 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.44/6.77 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.44/6.77 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.44/6.77 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.44/6.77 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.44/6.77 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 6.44/6.77 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.44/6.77 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 6.44/6.77 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.44/6.77 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 6.44/6.77 (declare-fun tptp.bot_bo7653980558646680370d_enat () tptp.set_Extended_enat)
% 6.44/6.77 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.44/6.77 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 6.44/6.77 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.44/6.77 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 6.44/6.77 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 6.44/6.77 (declare-fun tptp.bot_bot_set_set_int () tptp.set_set_int)
% 6.44/6.77 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 6.44/6.77 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le7866589430770878221at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_set_set_int (tptp.set_set_int tptp.set_set_int) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le4573692005234683329plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool)) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le704812498762024988_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_eq_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le4104064031414453916r_real (tptp.filter_real tptp.filter_real) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le6045566169113846134st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.44/6.77 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le4403425263959731960et_int (tptp.set_set_int tptp.set_set_int) Bool)
% 6.44/6.77 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.44/6.77 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.44/6.77 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.44/6.77 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 6.44/6.77 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 6.44/6.77 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.44/6.77 (declare-fun tptp.ord_mi8085742599997312461d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.44/6.77 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.44/6.77 (declare-fun tptp.order_9091379641038594480t_real ((-> tptp.nat tptp.real)) Bool)
% 6.44/6.77 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.44/6.77 (declare-fun tptp.order_mono_nat_real ((-> tptp.nat tptp.real)) Bool)
% 6.44/6.77 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.44/6.77 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 6.44/6.77 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 6.44/6.77 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.44/6.77 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.44/6.77 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.44/6.77 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.44/6.77 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.44/6.77 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.44/6.77 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 6.44/6.77 (declare-fun tptp.produc851828971589881931at_num ((-> tptp.nat tptp.num tptp.num) tptp.produc2963631642982155120at_num) tptp.produc3368934014287244435at_num)
% 6.44/6.77 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 6.44/6.77 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 6.44/6.77 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 6.44/6.77 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 6.44/6.77 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.44/6.77 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.44/6.77 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.44/6.77 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.44/6.77 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.44/6.77 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 6.44/6.77 (declare-fun tptp.produc1195630363706982562at_num (tptp.nat tptp.product_prod_nat_num) tptp.produc2963631642982155120at_num)
% 6.44/6.77 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.44/6.77 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 6.44/6.77 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 6.44/6.77 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.44/6.77 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 6.44/6.77 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.44/6.77 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.44/6.77 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.44/6.77 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.44/6.77 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.44/6.77 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.44/6.77 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.44/6.77 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.44/6.77 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.44/6.77 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.44/6.77 (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)
% 6.44/6.77 (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)
% 6.44/6.77 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.44/6.77 (declare-fun tptp.produc1917071388513777916omplex ((-> tptp.nat tptp.nat tptp.complex) tptp.product_prod_nat_nat) tptp.complex)
% 6.44/6.77 (declare-fun tptp.produc6840382203811409530at_int ((-> tptp.nat tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.int)
% 6.44/6.77 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.44/6.77 (declare-fun tptp.produc6207742614233964070at_rat ((-> tptp.nat tptp.nat tptp.rat) tptp.product_prod_nat_nat) tptp.rat)
% 6.44/6.77 (declare-fun tptp.produc1703576794950452218t_real ((-> tptp.nat tptp.nat tptp.real) tptp.product_prod_nat_nat) tptp.real)
% 6.44/6.77 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.44/6.77 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.44/6.77 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.produc6174133586879617921nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.44/6.77 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.44/6.77 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 6.44/6.77 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 6.44/6.77 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 6.44/6.77 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.44/6.77 (declare-fun tptp.of_int (tptp.int) tptp.rat)
% 6.44/6.77 (declare-fun tptp.positive (tptp.rat) Bool)
% 6.44/6.77 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 6.44/6.77 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.44/6.77 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 6.44/6.77 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.44/6.77 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.44/6.77 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 6.44/6.77 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.44/6.77 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.44/6.77 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.44/6.77 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.44/6.77 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.44/6.77 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.44/6.77 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.44/6.77 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.44/6.77 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.44/6.77 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 6.44/6.77 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.44/6.77 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.44/6.77 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.44/6.77 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.44/6.77 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 6.44/6.77 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 6.44/6.77 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 6.44/6.77 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.44/6.77 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 6.44/6.77 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 6.44/6.77 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.44/6.77 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.44/6.77 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 6.44/6.77 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 6.44/6.77 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.44/6.77 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 6.44/6.77 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.44/6.77 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.44/6.77 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.44/6.77 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 6.44/6.77 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 6.44/6.77 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.44/6.77 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 6.44/6.77 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.44/6.77 (declare-fun tptp.collect_set_int ((-> tptp.set_int Bool)) tptp.set_set_int)
% 6.44/6.77 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 6.44/6.77 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 6.44/6.77 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 6.44/6.77 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 6.44/6.77 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.44/6.77 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.44/6.77 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 6.44/6.77 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.44/6.77 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.insert8211810215607154385at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.44/6.77 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 6.44/6.77 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.44/6.77 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 6.44/6.77 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 6.44/6.77 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 6.44/6.77 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.44/6.77 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.44/6.77 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.44/6.77 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.44/6.77 (declare-fun tptp.set_or370866239135849197et_int (tptp.set_int tptp.set_int) tptp.set_set_int)
% 6.44/6.77 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.44/6.77 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 6.44/6.77 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 6.44/6.77 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.set_ord_atMost_num (tptp.num) tptp.set_num)
% 6.44/6.77 (declare-fun tptp.set_ord_atMost_rat (tptp.rat) tptp.set_rat)
% 6.44/6.77 (declare-fun tptp.set_ord_atMost_real (tptp.real) tptp.set_real)
% 6.44/6.77 (declare-fun tptp.set_or58775011639299419et_int (tptp.set_int) tptp.set_set_int)
% 6.44/6.77 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 6.44/6.77 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 6.44/6.77 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.44/6.77 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.44/6.77 (declare-fun tptp.set_or8419480210114673929d_enat (tptp.extended_enat) tptp.set_Extended_enat)
% 6.44/6.77 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 6.44/6.77 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 6.44/6.77 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 6.44/6.77 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.44/6.77 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 6.44/6.77 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.44/6.77 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.44/6.77 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 6.44/6.77 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.44/6.77 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.44/6.77 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.44/6.77 (declare-fun tptp.topolo4899668324122417113eq_int ((-> tptp.nat tptp.int)) Bool)
% 6.44/6.77 (declare-fun tptp.topolo4902158794631467389eq_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.44/6.77 (declare-fun tptp.topolo1459490580787246023eq_num ((-> tptp.nat tptp.num)) Bool)
% 6.44/6.77 (declare-fun tptp.topolo4267028734544971653eq_rat ((-> tptp.nat tptp.rat)) Bool)
% 6.44/6.77 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.44/6.77 (declare-fun tptp.topolo3100542954746470799et_int ((-> tptp.nat tptp.set_int)) Bool)
% 6.44/6.77 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.44/6.77 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.44/6.77 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.44/6.77 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 6.44/6.77 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.44/6.77 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.diffs_complex ((-> tptp.nat tptp.complex) tptp.nat) tptp.complex)
% 6.44/6.77 (declare-fun tptp.diffs_int ((-> tptp.nat tptp.int) tptp.nat) tptp.int)
% 6.44/6.77 (declare-fun tptp.diffs_rat ((-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 6.44/6.77 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 6.44/6.77 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.44/6.77 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.pi () tptp.real)
% 6.44/6.77 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 6.44/6.77 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.44/6.77 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 6.44/6.77 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.44/6.77 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.44/6.77 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.44/6.77 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.44/6.77 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.44/6.77 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.44/6.77 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.44/6.77 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.44/6.77 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.44/6.77 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.44/6.77 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.44/6.77 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.44/6.77 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.44/6.77 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 6.44/6.77 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.44/6.77 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.44/6.77 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.44/6.77 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.44/6.77 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.44/6.77 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.44/6.77 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.44/6.77 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 6.44/6.77 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.44/6.77 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 6.44/6.77 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.44/6.77 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 6.44/6.77 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.44/6.77 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.44/6.77 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.44/6.77 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 6.44/6.77 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.44/6.77 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 6.44/6.77 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.44/6.77 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.44/6.77 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.44/6.77 (declare-fun tptp.member_set_int (tptp.set_int tptp.set_set_int) Bool)
% 6.44/6.77 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.44/6.77 (declare-fun tptp.deg () tptp.nat)
% 6.44/6.77 (declare-fun tptp.m () tptp.nat)
% 6.44/6.77 (declare-fun tptp.ma () tptp.nat)
% 6.44/6.77 (declare-fun tptp.mi () tptp.nat)
% 6.44/6.77 (declare-fun tptp.na () tptp.nat)
% 6.44/6.77 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 6.44/6.77 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 6.44/6.77 (declare-fun tptp.xa () tptp.nat)
% 6.44/6.77 (assert (not (or (= tptp.xa tptp.mi) (= tptp.xa tptp.ma))))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 6.44/6.77 (assert (=> (= tptp.mi tptp.ma) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1)))))))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na)) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_nat tptp.xa) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_nat tptp.mi) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.44/6.77 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.44/6.77 (assert (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X) tptp.na) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.ord_less_nat Xa) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert X) Xa)) Xa)))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) _let_1)) (@ (@ tptp.power_power_nat N) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.44/6.77 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit0 N)))))
% 6.44/6.77 (assert (forall ((Ma tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N)) (@ _let_1 M))))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num M) N))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num M) N))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num M) N))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num M) N))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.44/6.77 (assert (= tptp.vEBT_VEBT_high (lambda ((X2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.44/6.77 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_12)))))
% 6.44/6.77 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 6.44/6.77 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N)) (= M N))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N)) (= M N))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N)) (= M N))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N)) (= M N))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N)) (= M N))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N)) (= M N))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.44/6.77 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 6.44/6.77 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))))
% 6.44/6.77 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 6.44/6.77 (assert (= tptp.m (@ tptp.suc tptp.na)))
% 6.44/6.77 (assert (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert tptp.summary) X3)) X3))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) N) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))))
% 6.44/6.77 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B)) N) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) B)) N) (@ (@ tptp.divide_divide_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))
% 6.44/6.77 (assert (forall ((X3 tptp.num)) (= (@ (@ tptp.ord_less_eq_num X3) tptp.one) (= X3 tptp.one))))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.44/6.77 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.44/6.77 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 6.44/6.77 (assert (forall ((Tree tptp.vEBT_VEBT) (X3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X3) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 6.44/6.77 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 6.44/6.77 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.44/6.77 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.44/6.77 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A2))) A2)))
% 6.44/6.77 (assert (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A2))) A2)))
% 6.44/6.77 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A2))) A2)))
% 6.44/6.77 (assert (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (@ (@ tptp.member_list_nat X2) A2))) A2)))
% 6.44/6.77 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A2))) A2)))
% 6.44/6.77 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A2))) A2)))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 6.44/6.77 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))))
% 6.44/6.77 (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 ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low X) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X) (@ (@ tptp.ord_less_eq_nat X) tptp.ma)))))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.44/6.77 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X3))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X3))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X3) Y)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X3) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X3)) N) Y)))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat)) (=> (forall ((N3 tptp.nat)) (not (= X3 (@ (@ tptp.plus_plus_nat N3) N3)))) (not (forall ((N3 tptp.nat)) (not (= X3 (@ (@ tptp.plus_plus_nat N3) (@ tptp.suc N3)))))))))
% 6.44/6.77 (assert (forall ((T tptp.vEBT_VEBT) (X3 tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X3)))))
% 6.44/6.77 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X3) (@ (@ tptp.vEBT_vebt_member T) X3)))))
% 6.44/6.77 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X3) (@ (@ tptp.vEBT_vebt_member T) X3)))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ tptp.set_real2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) N))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ tptp.set_complex2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) N))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X5) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) N))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X3) D)) (@ (@ tptp.vEBT_VEBT_low X3) D)) D) X3)))
% 6.44/6.77 (assert (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y2)) (= X22 Y2))))
% 6.44/6.77 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.44/6.77 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member T) X3) (@ (@ tptp.member_nat X3) (@ tptp.vEBT_set_vebt T))))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X3) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X3)) N) X3)))))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N)))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 6.44/6.77 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N))))))
% 6.44/6.77 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.44/6.77 (assert (forall ((B tptp.real) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X3) Y))))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X3) Y))))))
% 6.44/6.77 (assert (forall ((B tptp.nat) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X3) Y))))))
% 6.44/6.77 (assert (forall ((B tptp.int) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X3) Y))))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num) (B tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.44/6.77 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num) (B tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (M tptp.num) (N tptp.num) (B tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.44/6.77 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num) (B tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.44/6.77 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.44/6.77 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.44/6.77 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.44/6.77 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.44/6.77 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.44/6.77 (assert (forall ((B tptp.real) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X3) Y))))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X3) Y))))))
% 6.44/6.77 (assert (forall ((B tptp.nat) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X3) Y))))))
% 6.44/6.77 (assert (forall ((B tptp.int) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X3) Y))))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 6.44/6.77 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.44/6.77 (assert (forall ((P (-> tptp.extended_enat Bool)) (N tptp.extended_enat)) (=> (forall ((N3 tptp.extended_enat)) (=> (forall ((M2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 6.44/6.77 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.44/6.77 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.44/6.77 (assert (= tptp.suc (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat M) N)))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X3) (@ tptp.suc Y)) (= X3 Y))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 6.44/6.77 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ _let_1 N)) A)))))
% 6.44/6.77 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) A)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) A)))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) A)))))
% 6.44/6.77 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) A)))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((X3 tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X3) Y) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.power_power_complex Y) N)) tptp.one_one_complex))))
% 6.44/6.77 (assert (forall ((X3 tptp.real) (Y tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X3) Y) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.power_power_real Y) N)) tptp.one_one_real))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X3) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X3) N)) (@ (@ tptp.power_power_rat Y) N)) tptp.one_one_rat))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X3) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X3) N)) (@ (@ tptp.power_power_nat Y) N)) tptp.one_one_nat))))
% 6.44/6.77 (assert (forall ((X3 tptp.int) (Y tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X3) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X3) N)) (@ (@ tptp.power_power_int Y) N)) tptp.one_one_int))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (=> (not (= K (@ tptp.suc I2))) (not (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (not (= K (@ tptp.suc J))))))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K) (not (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (not (= K (@ tptp.suc J)))))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (or (@ P N) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N) (@ P I3)))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (and (@ P N) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ P I3)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M3 tptp.nat)) (and (= M (@ tptp.suc M3)) (@ (@ tptp.ord_less_nat N) M3))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K)))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (forall ((I4 tptp.nat)) (@ (@ P I4) (@ tptp.suc I4))) (=> (forall ((I4 tptp.nat) (J tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I4))) (=> (@ (@ tptp.ord_less_nat I4) J) (=> (@ (@ tptp.ord_less_nat J) K2) (=> (@ _let_1 J) (=> (@ (@ P J) K2) (@ _let_1 K2))))))) (@ (@ P I2) J2))))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (forall ((I4 tptp.nat)) (=> (= J2 (@ tptp.suc I4)) (@ P I4))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ P (@ tptp.suc I4)) (@ P I4)))) (@ P I2))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M4) (exists ((M5 tptp.nat)) (= M4 (@ tptp.suc M5))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))))
% 6.44/6.77 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X5 tptp.nat)) (@ (@ R X5) X5)) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z2) (@ _let_1 Z2))))) (=> (forall ((N3 tptp.nat)) (@ (@ R N3) (@ tptp.suc N3))) (@ (@ R M) N)))))))
% 6.44/6.77 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 6.44/6.77 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J2) L2))))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J2) K)))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J2))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N) Q2)) (@ (@ tptp.divide_divide_nat (@ _let_1 N)) Q2)))))
% 6.44/6.77 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc N)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc N)))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) (@ tptp.suc N)))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc N)))))))
% 6.44/6.77 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real A) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat A) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat A) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int A) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (Q2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q2)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q2))) (= (@ (@ tptp.divide_divide_nat M) N) Q2))))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N))) (= (@ (@ tptp.times_times_complex _let_1) A) (@ (@ tptp.times_times_complex A) _let_1)))))
% 6.44/6.77 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (= (@ (@ tptp.times_times_real _let_1) A) (@ (@ tptp.times_times_real A) _let_1)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (= (@ (@ tptp.times_times_rat _let_1) A) (@ (@ tptp.times_times_rat A) _let_1)))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (= (@ (@ tptp.times_times_nat _let_1) A) (@ (@ tptp.times_times_nat A) _let_1)))))
% 6.44/6.77 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (= (@ (@ tptp.times_times_int _let_1) A) (@ (@ tptp.times_times_int A) _let_1)))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A) B)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))))
% 6.44/6.77 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A) B)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.times_times_rat A) B)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))
% 6.44/6.77 (assert (forall ((X3 tptp.complex) (Y tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X3) N))) (let ((_let_2 (@ tptp.times_times_complex Y))) (=> (= (@ (@ tptp.times_times_complex X3) Y) (@ _let_2 X3)) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ _let_2 _let_1)))))))
% 6.44/6.77 (assert (forall ((X3 tptp.real) (Y tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X3) N))) (let ((_let_2 (@ tptp.times_times_real Y))) (=> (= (@ (@ tptp.times_times_real X3) Y) (@ _let_2 X3)) (= (@ (@ tptp.times_times_real _let_1) Y) (@ _let_2 _let_1)))))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X3) N))) (let ((_let_2 (@ tptp.times_times_rat Y))) (=> (= (@ (@ tptp.times_times_rat X3) Y) (@ _let_2 X3)) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ _let_2 _let_1)))))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X3) N))) (let ((_let_2 (@ tptp.times_times_nat Y))) (=> (= (@ (@ tptp.times_times_nat X3) Y) (@ _let_2 X3)) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ _let_2 _let_1)))))))
% 6.44/6.77 (assert (forall ((X3 tptp.int) (Y tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X3) N))) (let ((_let_2 (@ tptp.times_times_int Y))) (=> (= (@ (@ tptp.times_times_int X3) Y) (@ _let_2 X3)) (= (@ (@ tptp.times_times_int _let_1) Y) (@ _let_2 _let_1)))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_nat (@ _let_1 M)) N)))))
% 6.44/6.77 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_real (@ _let_1 M)) N)))))
% 6.44/6.77 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_int (@ _let_1 M)) N)))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_complex (@ _let_1 M)) N)))))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.44/6.77 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.44/6.77 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.44/6.77 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.44/6.77 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (U tptp.nat) (J2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I2) J2)) U)) K))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_complex A) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1)))))))
% 6.44/6.77 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_rat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat (@ _let_2 N)) _let_1)))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1)))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1)))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_real (@ F N)) (@ F N4))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N4))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_num (@ F N)) (@ F N4))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N4))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_int (@ F N)) (@ F N4))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_real (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_rat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_num (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_int (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_set_int (@ F N)) (@ F N4))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N4))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N4))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N4))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N4))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_set_int (@ F N4)) (@ F N))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_rat (@ F N4)) (@ F N))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_num (@ F N4)) (@ F N))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ F N))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_int (@ F N4)) (@ F N))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ P I2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J2) (=> (@ P N3) (@ P (@ tptp.suc N3)))))) (@ P J2))))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ P J2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J2) (=> (@ P (@ tptp.suc N3)) (@ P N3))))) (@ P I2))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.44/6.77 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) __flatten_var_0))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K2 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))))
% 6.44/6.77 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M6) K3)))))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) M)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (forall ((Q3 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q3)))))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (I2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I2) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) I2))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N))) M)))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N)) M)))
% 6.44/6.77 (assert (forall ((V tptp.num) (N tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N))))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.44/6.77 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 6.44/6.77 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X3))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 6.44/6.77 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X3))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 6.44/6.77 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X3))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 6.44/6.77 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X3))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 6.44/6.77 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X3))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 6.44/6.77 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.44/6.77 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.44/6.77 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 6.44/6.77 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.44/6.77 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.44/6.77 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_complex A) N))))))
% 6.44/6.77 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.44/6.77 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.44/6.77 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 6.44/6.77 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.44/6.77 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 6.44/6.77 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N3) (not (@ P M2)))))) (@ P N))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (not (= X3 Y)) (=> (not (@ (@ tptp.ord_less_nat X3) Y)) (@ (@ tptp.ord_less_nat Y) X3)))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J2) (=> (@ (@ tptp.ord_less_eq_nat J2) K) (@ _let_1 K))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 6.44/6.77 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X5 tptp.nat)) (and (@ P X5) (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) X5)))))))))
% 6.44/6.77 (assert (forall ((X3 tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X3) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X3 Y)))))
% 6.44/6.77 (assert (forall ((X3 tptp.list_o) (Y tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X3) (@ tptp.size_size_list_o Y))) (not (= X3 Y)))))
% 6.44/6.77 (assert (forall ((X3 tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X3) (@ tptp.size_size_list_nat Y))) (not (= X3 Y)))))
% 6.44/6.77 (assert (forall ((X3 tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X3) (@ tptp.size_size_list_int Y))) (not (= X3 Y)))))
% 6.44/6.77 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X3) (@ tptp.size_size_num Y))) (not (= X3 Y)))))
% 6.44/6.77 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.44/6.77 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.44/6.77 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.44/6.77 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.44/6.77 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.44/6.77 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.44/6.77 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.44/6.77 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.44/6.77 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.44/6.77 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((X3 tptp.complex)) (= (@ (@ tptp.power_power_complex X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X3) X3)) X3)) X3))))
% 6.44/6.77 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X3) X3)) X3)) X3))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat)) (= (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat X3) X3)) X3)) X3))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat)) (= (@ (@ tptp.power_power_nat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X3) X3)) X3)) X3))))
% 6.44/6.77 (assert (forall ((X3 tptp.int)) (= (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X3) X3)) X3)) X3))))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1))))))
% 6.44/6.77 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1))))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1))))))
% 6.44/6.77 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.44/6.77 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 6.44/6.77 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.44/6.77 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 6.44/6.77 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.44/6.77 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 6.44/6.77 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.44/6.77 (assert (forall ((X3 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 X3) Y)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X3) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X3)) Y)))))))
% 6.44/6.77 (assert (forall ((X3 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 X3) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X3)) Y)))))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X3) Y)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X3)) Y)))))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X3) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X3) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X3)) Y))))))
% 6.44/6.77 (assert (forall ((X3 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 X3) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X3) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X3)) Y)))))))
% 6.44/6.77 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (not (= M6 N2))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.44/6.77 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N2) (= M6 N2)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat) (J2 tptp.nat)) (=> (forall ((I4 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J) (@ (@ tptp.ord_less_nat (@ F I4)) (@ F J)))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ F J2))))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J2)) K) (@ (@ tptp.ord_less_nat I2) K))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat K) L2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2))))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J2)) I2))))
% 6.44/6.77 (assert (forall ((J2 tptp.nat) (I2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J2) I2)) I2))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) K)))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) M))))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J2))))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (L2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L2) (=> (= (@ (@ tptp.plus_plus_nat M) L2) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (exists ((N3 tptp.nat)) (= L2 (@ (@ tptp.plus_plus_nat K) N3))))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2))))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) K)))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) M))))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J2))))))
% 6.44/6.77 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ (@ tptp.plus_plus_nat M6) K3))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N) K)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 6.44/6.77 (assert (forall ((B tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))))))))
% 6.44/6.77 (assert (forall ((B tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B) (=> (@ _let_1 K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat)))))))))))
% 6.44/6.77 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N3) (@ (@ tptp.ord_less_nat (@ F M5)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))))
% 6.44/6.77 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X3))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X3) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X3))))
% 6.44/6.77 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X2) N2))) (@ (@ tptp.vEBT_VEBT_low X2) N2)))))
% 6.44/6.77 (assert (forall ((X3 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)) X3)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X3)) Y)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2)))))))
% 6.44/6.77 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X3) _let_3))) (@ (@ tptp.vEBT_VEBT_low X3) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X3)))))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M) (@ tptp.suc (@ _let_1 N)))))))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat B) A)) C))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) B))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C)))))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.44/6.77 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) N) (= Deg N))))
% 6.44/6.77 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N))) TreeList3) S2))))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N))))))
% 6.44/6.77 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)))
% 6.44/6.77 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.power_power_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.power_power_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.power_power_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.44/6.77 (assert (forall ((X3 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 X3) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X3)) _let_2))))))
% 6.44/6.77 (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))))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 6.44/6.77 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (not (= X3 Y)) (=> (not (@ (@ tptp.ord_less_real X3) Y)) (@ (@ tptp.ord_less_real Y) X3)))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (not (= X3 Y)) (=> (not (@ (@ tptp.ord_less_rat X3) Y)) (@ (@ tptp.ord_less_rat Y) X3)))))
% 6.44/6.77 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (not (= X3 Y)) (=> (not (@ (@ tptp.ord_less_int X3) Y)) (@ (@ tptp.ord_less_int Y) X3)))))
% 6.44/6.77 (assert (forall ((X tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X) X_12))))
% 6.44/6.77 (assert (forall ((X tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_12))))
% 6.44/6.77 (assert (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X))))
% 6.44/6.77 (assert (forall ((X tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (= tptp.times_times_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real B2) A3))))
% 6.44/6.77 (assert (= tptp.times_times_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat B2) A3))))
% 6.44/6.77 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.times_times_nat B2) A3))))
% 6.44/6.77 (assert (= tptp.times_times_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.times_times_int B2) A3))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((X3 tptp.complex)) (= (= tptp.one_one_complex X3) (= X3 tptp.one_one_complex))))
% 6.44/6.77 (assert (forall ((X3 tptp.real)) (= (= tptp.one_one_real X3) (= X3 tptp.one_one_real))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat)) (= (= tptp.one_one_rat X3) (= X3 tptp.one_one_rat))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat)) (= (= tptp.one_one_nat X3) (= X3 tptp.one_one_nat))))
% 6.44/6.77 (assert (forall ((X3 tptp.int)) (= (= tptp.one_one_int X3) (= X3 tptp.one_one_int))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B))) (let ((_let_2 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (= tptp.plus_plus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real B2) A3))))
% 6.44/6.77 (assert (= tptp.plus_plus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat B2) A3))))
% 6.44/6.77 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.plus_plus_nat B2) A3))))
% 6.44/6.77 (assert (= tptp.plus_plus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int B2) A3))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((B3 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))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.44/6.77 (assert (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.44/6.77 (assert (forall ((B3 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))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.44/6.77 (assert (forall ((B3 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))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J2) (= K L2)) (= (@ (@ tptp.plus_plus_real I2) K) (@ (@ tptp.plus_plus_real J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I2 J2) (= K L2)) (= (@ (@ tptp.plus_plus_rat I2) K) (@ (@ tptp.plus_plus_rat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J2) (= K L2)) (= (@ (@ tptp.plus_plus_nat I2) K) (@ (@ tptp.plus_plus_nat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J2) (= K L2)) (= (@ (@ tptp.plus_plus_int I2) K) (@ (@ tptp.plus_plus_int J2) L2)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (exists ((C2 tptp.nat)) (= B2 (@ (@ tptp.plus_plus_nat A3) C2))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J2) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J2) (= K L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (= K L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (= K L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (= K L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J2) (= K L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (= K L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (= K L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (= K L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J2) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (E tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E)) C))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat C) B))))))
% 6.44/6.77 (assert (forall ((X3 tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X3) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X3) W)) (@ (@ tptp.times_times_complex Y) Z)))))
% 6.44/6.77 (assert (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X3) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X3) W)) (@ (@ tptp.times_times_real Y) Z)))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X3) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X3) W)) (@ (@ tptp.times_times_rat Y) Z)))))
% 6.44/6.77 (assert (forall ((X3 tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X3) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X3) Z)) (@ (@ tptp.times_times_complex Y) W)))))
% 6.44/6.77 (assert (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X3) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X3) Z)) (@ (@ tptp.times_times_real Y) W)))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X3) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X3) Z)) (@ (@ tptp.times_times_rat Y) W)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J2) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.real) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J2) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))))
% 6.44/6.77 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))))
% 6.44/6.77 (assert (forall ((M tptp.real) (N tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_real M) N)))))))
% 6.44/6.77 (assert (forall ((M tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_rat M) N)))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))))
% 6.44/6.77 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_int M) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.44/6.77 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B) tptp.one_one_rat)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I3)))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool))) (= (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I3)))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I3)))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I3)))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (X3 tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) I4)))) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs)) (@ P X3)))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (X3 tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) I4)))) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs)) (@ P X3)))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (X3 tptp.product_prod_nat_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I4)))) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X3)))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X3 tptp.vEBT_VEBT)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I4)))) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X3)))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (X3 Bool)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I4)))) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs)) (@ P X3)))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (X3 tptp.nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I4)))) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (@ P X3)))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (X3 tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I4)))) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs)) (@ P X3)))))
% 6.44/6.77 (assert (forall ((X3 tptp.real) (Xs tptp.list_real)) (= (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_real Xs) I3) X3))))))
% 6.44/6.77 (assert (forall ((X3 tptp.complex) (Xs tptp.list_complex)) (= (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs)) (= (@ (@ tptp.nth_complex Xs) I3) X3))))))
% 6.44/6.77 (assert (forall ((X3 tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s5460976970255530739at_nat Xs)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I3) X3))))))
% 6.44/6.77 (assert (forall ((X3 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I3) X3))))))
% 6.44/6.77 (assert (forall ((X3 Bool) (Xs tptp.list_o)) (= (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I3) X3))))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I3) X3))))))
% 6.44/6.77 (assert (forall ((X3 tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I3) X3))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_o Xs) N))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (Xs tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs) N)) (@ tptp.set_real2 Xs)))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (Xs tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs) N)) (@ tptp.set_complex2 Xs)))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N)) (@ tptp.set_Pr5648618587558075414at_nat Xs)))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) N)) (@ tptp.set_VEBT_VEBT2 Xs)))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (Xs tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs) N)) (@ tptp.set_o2 Xs)))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N)) (@ tptp.set_nat2 Xs)))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs) N)) (@ tptp.set_int2 Xs)))))
% 6.44/6.77 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) __flatten_var_0))))
% 6.44/6.77 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A3) tptp.one_one_int)) __flatten_var_0))))
% 6.44/6.77 (assert (= tptp.vEBT_VEBT_low (lambda ((X2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.44/6.77 (assert (= (lambda ((Y5 tptp.list_VEBT_VEBT) (Z3 tptp.list_VEBT_VEBT)) (= Y5 Z3)) (lambda ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I3) (@ (@ tptp.nth_VEBT_VEBT Ys) I3))))))))
% 6.44/6.77 (assert (= (lambda ((Y5 tptp.list_o) (Z3 tptp.list_o)) (= Y5 Z3)) (lambda ((Xs2 tptp.list_o) (Ys tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I3) (@ (@ tptp.nth_o Ys) I3))))))))
% 6.44/6.77 (assert (= (lambda ((Y5 tptp.list_nat) (Z3 tptp.list_nat)) (= Y5 Z3)) (lambda ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I3) (@ (@ tptp.nth_nat Ys) I3))))))))
% 6.44/6.77 (assert (= (lambda ((Y5 tptp.list_int) (Z3 tptp.list_int)) (= Y5 Z3)) (lambda ((Xs2 tptp.list_int) (Ys tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I3) (@ (@ tptp.nth_int Ys) I3))))))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X4 tptp.vEBT_VEBT)) (@ (@ P I3) X4)))) (exists ((Xs2 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_VEBT_VEBT Xs2) I3)))))))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X4 Bool)) (@ (@ P I3) X4)))) (exists ((Xs2 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs2) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_o Xs2) I3)))))))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X4 tptp.nat)) (@ (@ P I3) X4)))) (exists ((Xs2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_nat Xs2) I3)))))))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X4 tptp.int)) (@ (@ P I3) X4)))) (exists ((Xs2 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs2) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_int Xs2) I3)))))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I4) (@ (@ tptp.nth_VEBT_VEBT Ys2) I4)))) (= Xs Ys2)))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_o) (Ys2 tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I4) (@ (@ tptp.nth_o Ys2) I4)))) (= Xs Ys2)))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I4) (@ (@ tptp.nth_nat Ys2) I4)))) (= Xs Ys2)))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_int) (Ys2 tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I4) (@ (@ tptp.nth_int Ys2) I4)))) (= Xs Ys2)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) B))) (= (@ (@ tptp.modulo364778990260209775nteger _let_1) B) _let_1))))
% 6.44/6.77 (assert (forall ((R2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 R2)) (@ (@ tptp.divide_divide_real A) R2)))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) K)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N) K)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.44/6.77 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.44/6.77 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.44/6.77 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.44/6.77 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.44/6.77 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.44/6.77 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((K tptp.num) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) _let_1) tptp.one_one_nat)))))
% 6.44/6.77 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.power_power_real X3) N3))))))
% 6.44/6.77 (assert (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y6) (= X2 Y6)))))
% 6.44/6.77 (assert (forall ((S3 tptp.set_real)) (=> (exists ((X tptp.real)) (@ (@ tptp.member_real X) S3)) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S3) (@ (@ tptp.ord_less_eq_real X5) Z4)))) (exists ((Y3 tptp.real)) (and (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) S3) (@ (@ tptp.ord_less_eq_real X) Y3))) (forall ((Z4 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S3) (@ (@ tptp.ord_less_eq_real X5) Z4))) (@ (@ tptp.ord_less_eq_real Y3) Z4)))))))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A4) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B4) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A4) B4)) C))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A4) B4)) C))))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A4) B4)) C))))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) C))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 A)) (@ _let_1 B))))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A4) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B4) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A4) B4)) C))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A4) B4)) C))))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A4) B4)) C))))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B)) N)) B) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N)) B))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B)) N)) B) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N)) B))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) N)) B) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) B))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) N))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)))
% 6.44/6.77 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))))
% 6.44/6.77 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))))
% 6.44/6.77 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat tptp.one))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int tptp.one))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))
% 6.44/6.77 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger tptp.one))) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X3) N) (@ (@ tptp.modulo_modulo_nat Y) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (= (@ (@ tptp.plus_plus_nat X3) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1))))))
% 6.44/6.77 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))))
% 6.44/6.77 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))))
% 6.44/6.77 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_1))))))
% 6.44/6.77 (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)))))))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (not (forall ((D3 tptp.code_integer)) (not (= B (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) D3)))))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P2 tptp.nat) (M tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P2) (=> (@ (@ tptp.ord_less_nat M) P2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) P2) (=> (@ P N3) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N3)) P2))))) (@ P M)))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (N tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X3) N) (@ (@ tptp.modulo_modulo_nat Y) N)) (=> (@ (@ tptp.ord_less_eq_nat Y) X3) (exists ((Q3 tptp.nat)) (= X3 (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N) Q3))))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (forall ((S2 tptp.nat)) (not (= N (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q2) S2))))))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (forall ((S2 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat Q2) S2))))))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))
% 6.44/6.77 (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)))
% 6.44/6.77 (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)))
% 6.44/6.77 (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)))
% 6.44/6.77 (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)))
% 6.44/6.77 (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)))
% 6.44/6.77 (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)))
% 6.44/6.77 (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)))
% 6.44/6.77 (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)))
% 6.44/6.77 (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)))
% 6.44/6.77 (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)))
% 6.44/6.77 (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)))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N))) (= (@ _let_1 (@ _let_2 Q2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N)) Q2))) (@ _let_1 N)))))))
% 6.44/6.77 (assert (forall ((P (-> tptp.nat Bool)) (X3 tptp.nat) (M7 tptp.nat)) (=> (@ P X3) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M7))) (not (forall ((M5 tptp.nat)) (=> (@ P M5) (not (forall ((X tptp.nat)) (=> (@ P X) (@ (@ tptp.ord_less_eq_nat X) M5)))))))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_real) (B3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) B3) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 (@ tptp.set_real2 Xs)) (@ _let_1 B3)))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_complex) (B3 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) B3) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 (@ tptp.set_complex2 Xs)) (@ _let_1 B3)))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) B3) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ _let_1 B3)))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) B3) (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs)) (@ _let_1 B3)))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) B3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 (@ tptp.set_nat2 Xs)) (@ _let_1 B3)))))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) B3) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B3)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_int)) (= (@ tptp.size_size_list_int Xs3) N))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys2))) (not (= Xs Ys2)))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_o) (Ys2 tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys2))) (not (= Xs Ys2)))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys2))) (not (= Xs Ys2)))))
% 6.44/6.77 (assert (forall ((Xs tptp.list_int) (Ys2 tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys2))) (not (= Xs Ys2)))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 6.44/6.77 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (=> (forall ((Xs3 tptp.list_VEBT_VEBT)) (=> (forall ((Ys3 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))))
% 6.44/6.77 (assert (forall ((P (-> tptp.list_o Bool)) (Xs tptp.list_o)) (=> (forall ((Xs3 tptp.list_o)) (=> (forall ((Ys3 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys3)) (@ tptp.size_size_list_o Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))))
% 6.44/6.77 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys3 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys3)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))))
% 6.44/6.77 (assert (forall ((P (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (forall ((Xs3 tptp.list_int)) (=> (forall ((Ys3 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys3)) (@ tptp.size_size_list_int Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))))
% 6.44/6.77 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) N)) N)) (@ (@ tptp.modulo_modulo_nat A2) N)))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.44/6.77 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.44/6.77 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.44/6.77 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.44/6.77 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.44/6.77 (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))))))))))
% 6.44/6.77 (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))))))))))
% 6.44/6.77 (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))))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.pow K) L2)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((U tptp.real) (X3 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 X3) Y)) (=> (@ _let_2 X3) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) Y)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.44/6.77 (assert (forall ((U tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_rat X3) Y)) (=> (@ _let_2 X3) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X3) Y)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X3) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low X3) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X3))))))))
% 6.44/6.77 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.44/6.77 (assert (forall ((X22 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y2)) (= X22 Y2))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.44/6.77 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N) K)) (or (= M N) (= K tptp.zero_zero_nat)))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))))
% 6.44/6.77 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.44/6.77 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg) (=> (= Mi Ma) (and (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1))))) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X3) Y)) (and (= X3 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X3) Y) tptp.zero_zero_nat) (and (= X3 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 6.44/6.77 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 6.44/6.77 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 6.44/6.77 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 6.44/6.77 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 6.44/6.77 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 6.44/6.77 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 6.44/6.77 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) A) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (@ _let_1 M) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N)) (and (= M _let_1) (= N _let_1))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N) _let_1) (and (= M _let_1) (= N _let_1))))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N)))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (or (= X3 Mi) (= X3 Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X3) _let_1))))))
% 6.44/6.77 (assert (forall ((X3 tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X3) X3))) (= X3 tptp.zero_zero_real))))
% 6.44/6.77 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X3) M) _let_1) (or (= M tptp.zero_zero_nat) (= X3 _let_1))))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X3) N)) (or (@ _let_1 X3) (= N tptp.zero_zero_nat))))))
% 6.44/6.77 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (= K tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat M) N)))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.44/6.77 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.44/6.77 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.44/6.77 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.44/6.77 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.44/6.77 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (and (@ (@ tptp.ord_less_eq_nat Mi) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.times_times_rat C) A) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) X3)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X3 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X3) X3)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X3 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 6.44/6.77 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X3) X3)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X3 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.44/6.77 (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)))))))))
% 6.44/6.77 (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)))))))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat A) B)))))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_rat A) B))))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) A) B))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C) A)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.44/6.77 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) B) A))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat C) B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))))))
% 6.44/6.77 (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)))))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.44/6.77 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.44/6.77 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat A) B)) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.44/6.77 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat A) A))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat B) A) tptp.one_one_rat) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat B) A)) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 6.44/6.77 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 6.44/6.77 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 6.44/6.77 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 6.44/6.77 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.44/6.77 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.44/6.77 (assert (forall ((A tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.77 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.77 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.77 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.44/6.77 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N)) N) M))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) M)) N) M))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.44/6.77 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 6.44/6.77 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 6.44/6.77 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 6.44/6.77 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 6.44/6.77 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 6.44/6.77 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X3) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X3) _let_1))) (@ (@ tptp.vEBT_VEBT_low X3) _let_1)) (= X3 Mi) (= X3 Ma)))))))
% 6.44/6.77 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X3 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 X3) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X3) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X3 Mi) (= X3 Ma) (and (@ (@ tptp.ord_less_nat X3) Ma) (@ (@ tptp.ord_less_nat Mi) X3) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X3) _let_2)))))))))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ _let_1 B))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_rat B) A)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat B) A)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))))
% 6.44/6.77 (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))))))))
% 6.44/6.77 (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))))))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.44/6.77 (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))))))))
% 6.44/6.77 (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))))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) B)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat B) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (@ (@ tptp.ord_less_eq_real A) B))))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (@ (@ tptp.ord_less_eq_rat A) B))))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.ord_less_eq_nat A) B))))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.ord_less_eq_int A) B))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.44/6.77 (assert (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.44/6.77 (assert (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.44/6.77 (assert (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))))
% 6.44/6.77 (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)))
% 6.44/6.77 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.44/6.77 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.44/6.77 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.44/6.77 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.44/6.77 (assert (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.44/6.77 (assert (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.44/6.77 (assert (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.44/6.77 (assert (forall ((X3 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 X3) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X3) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X3 Y))))))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_2 X3) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_rat X3) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (= X3 Y))))))))
% 6.44/6.77 (assert (forall ((X3 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 X3) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X3) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X3 Y))))))))
% 6.44/6.77 (assert (forall ((X3 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 X3) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X3) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X3 Y))))))))
% 6.44/6.77 (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))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.44/6.77 (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))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_rat)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) tptp.zero_zero_rat) (and (= X3 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 6.44/6.77 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X3 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.44/6.77 (assert (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X3 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_integer)) (= _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_1 tptp.one_one_Code_integer)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I3 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ P I3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I3 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ P I3))))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.44/6.77 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I3 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ (@ P I3) J3)))))))
% 6.44/6.77 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I3 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ (@ P I3) J3)))))))
% 6.44/6.77 (assert (forall ((X3 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X3) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X3) K)) X3)))))
% 6.44/6.77 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B3) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B3) N))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))))
% 6.44/6.77 (assert (forall ((A2 tptp.int) (N tptp.int)) (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) N)) N)) (@ (@ tptp.modulo_modulo_int A2) N)))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 B)))))))
% 6.44/6.77 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (@ _let_1 A))))))
% 6.44/6.77 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 6.44/6.77 (assert (forall ((K tptp.int) (I2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K) (= (@ _let_1 (@ (@ tptp.divide_divide_int I2) K)) (@ (@ tptp.ord_less_eq_int K) I2))))))
% 6.44/6.77 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.44/6.77 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A)))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 6.44/6.77 (assert (forall ((L2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L2) K) (=> (@ _let_1 L2) (@ _let_1 (@ (@ tptp.divide_divide_int K) L2)))))))
% 6.44/6.77 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) L2)) (or (= K tptp.zero_zero_int) (= L2 tptp.zero_zero_int) (and (@ _let_1 K) (@ _let_1 L2)) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B4 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B4)) (@ _let_1 B))))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (A4 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A4) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A4) B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.44/6.77 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (= (@ (@ tptp.divide_divide_int I2) K) tptp.zero_zero_int) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I2))))))
% 6.44/6.77 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (=> (= (@ (@ tptp.modulo_modulo_int A2) N) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B3) N) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ tptp.divide_divide_int B3) N))))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B4 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B4))))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (A4 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A4) B))))))
% 6.44/6.77 (assert (forall ((X3 tptp.complex)) (= (= tptp.zero_zero_complex X3) (= X3 tptp.zero_zero_complex))))
% 6.44/6.77 (assert (forall ((X3 tptp.real)) (= (= tptp.zero_zero_real X3) (= X3 tptp.zero_zero_real))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat)) (= (= tptp.zero_zero_rat X3) (= X3 tptp.zero_zero_rat))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat)) (= (= tptp.zero_zero_nat X3) (= X3 tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((X3 tptp.int)) (= (= tptp.zero_zero_int X3) (= X3 tptp.zero_zero_int))))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.44/6.77 (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)))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N) tptp.zero_zero_rat))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) N) tptp.zero_zero_real))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) N) tptp.zero_zero_int))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N) tptp.zero_zero_complex))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) N) A)))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (= (@ (@ tptp.power_power_real X5) N) A) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.power_power_real Y4) N) A)) (= Y4 X5)))))))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X3)))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.44/6.77 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.44/6.77 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.44/6.77 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.44/6.77 (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)))))))))
% 6.44/6.77 (assert (forall ((D1 tptp.rat) (D22 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat E2))) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (= A B)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B tptp.zero_zero_rat))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 6.44/6.77 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 6.44/6.77 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 6.44/6.77 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 6.44/6.77 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.44/6.77 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.44/6.77 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat)))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat)))))
% 6.44/6.77 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real)))))
% 6.44/6.77 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int)))))
% 6.44/6.77 (assert (forall ((A tptp.complex) (N tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex)))))
% 6.44/6.77 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))))
% 6.44/6.77 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.44/6.77 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.44/6.77 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P tptp.zero_zero_nat)))))
% 6.44/6.77 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X5 tptp.nat)) (@ (@ P X5) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X5) Y3) (@ (@ P (@ tptp.suc X5)) (@ tptp.suc Y3)))) (@ (@ P M) N))))))
% 6.44/6.77 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc N3)))) (@ P N)))))
% 6.44/6.77 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 6.44/6.77 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 6.44/6.77 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.44/6.77 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 6.44/6.77 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (not (@ P N3)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N3) (not (@ P M2))))))) (@ P N)))))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.44/6.77 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 6.44/6.77 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))))
% 6.44/6.77 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 6.44/6.77 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))))
% 6.44/6.77 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 6.44/6.77 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 6.44/6.77 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (= A B))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (= A B))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (= A B))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (= A B))))))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.44/6.77 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 6.44/6.77 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.44/6.77 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))))
% 6.44/6.77 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))))
% 6.44/6.77 (assert (= tptp.neg_numeral_dbl_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) X2))))
% 6.44/6.77 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat X2) X2))))
% 6.44/6.77 (assert (= tptp.neg_numeral_dbl_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) X2))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A) B))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.44/6.77 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.44/6.77 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.44/6.77 (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)))))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.44/6.77 (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)))))))))
% 6.44/6.77 (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)))))))))
% 6.44/6.77 (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)))))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.44/6.77 (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)))))))))
% 6.44/6.77 (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)))))))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.44/6.77 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.44/6.77 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.44/6.77 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.44/6.77 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.44/6.77 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.44/6.77 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (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)))))
% 6.44/6.77 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X3) Y) tptp.zero_zero_real) (and (= X3 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X3) Y) tptp.zero_zero_rat) (and (= X3 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X3) Y) tptp.zero_zero_nat) (and (= X3 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))))
% 6.44/6.77 (assert (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X3) Y) tptp.zero_zero_int) (and (= X3 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))))
% 6.44/6.77 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X3) Y) tptp.zero_zero_real) (and (= X3 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))))
% 6.44/6.77 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X3) Y) tptp.zero_zero_rat) (and (= X3 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))))
% 6.44/6.77 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X3) Y) tptp.zero_zero_nat) (and (= X3 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))))
% 6.44/6.77 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X3) Y) tptp.zero_zero_int) (and (= X3 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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)))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.77 (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))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat B) A))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.44/6.78 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.44/6.78 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.44/6.78 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.44/6.78 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.44/6.78 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.44/6.78 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.44/6.78 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.44/6.78 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.44/6.78 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.44/6.78 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.44/6.78 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.44/6.78 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X3) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X3) Y)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat)))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X3) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X3) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X3) Y)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X3) Y)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X3) Y)) tptp.zero_zero_real)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X3) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X3) Y)) tptp.zero_zero_rat)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X3) Y)) tptp.zero_zero_real)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X3) Y)) tptp.zero_zero_rat)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) 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 X3) Y))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X3) Y))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat A) C))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) 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 X3) Y))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X3) Y))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X3) Y)) tptp.zero_zero_real)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X3) Y)) tptp.zero_zero_rat)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X3) Y)) tptp.zero_zero_real)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X3) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X3) Y)) tptp.zero_zero_rat)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X3) Y)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X3) Y)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)) (not (= C tptp.zero_zero_rat))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 6.44/6.78 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X3 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X3) Y) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X3) Z) (@ (@ tptp.times_times_complex W) Y)))))))
% 6.44/6.78 (assert (forall ((Y tptp.real) (Z tptp.real) (X3 tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X3) Y) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X3) Z) (@ (@ tptp.times_times_real W) Y)))))))
% 6.44/6.78 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X3) Y) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X3) Z) (@ (@ tptp.times_times_rat W) Y)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B (@ (@ tptp.times_times_rat A) C)) (= (@ (@ tptp.divide_divide_rat B) C) A)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A) C) B) (= A (@ (@ tptp.divide_divide_rat B) C))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (= B (@ (@ tptp.times_times_rat A) C))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (= (@ (@ tptp.times_times_rat A) C) B)))))
% 6.44/6.78 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (= A B)))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_int))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) A))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.44/6.78 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.44/6.78 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.44/6.78 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N)))))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (and (@ P tptp.zero_zero_nat) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ P (@ tptp.suc I3))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M6 tptp.nat)) (= N (@ tptp.suc M6))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (or (@ P tptp.zero_zero_nat) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N) (@ P (@ tptp.suc I3))))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (not (@ P I)))) (@ P K2)))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I2) K2) J2))))))
% 6.44/6.78 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B3) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ tptp.divide_divide_nat B3) N))))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) (@ tptp.suc N)) A))))))
% 6.44/6.78 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.44/6.78 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J2)))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J2) K))))))
% 6.44/6.78 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N) (= N tptp.zero_zero_nat)))))
% 6.44/6.78 (assert (forall ((Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X3) N3)) Y))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))) (let ((_let_3 (= _let_1 N))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (= (@ (@ tptp.pow X3) tptp.one) X3)))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X3) _let_1))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.44/6.78 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.44/6.78 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.44/6.78 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.44/6.78 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.44/6.78 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.plus_plus_rat A) C))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.plus_plus_real Y) E2)))) (@ (@ tptp.ord_less_eq_real X3) Y))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat X3) (@ (@ tptp.plus_plus_rat Y) E2)))) (@ (@ tptp.ord_less_eq_rat X3) Y))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) A)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.one_one_rat))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X3) Y)) X3)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X3) Y)) X3)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X3) Y)) X3)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X3)) X3)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X3)) X3)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X3)) X3)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) X3)) (@ (@ tptp.times_times_real Y) Y)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X3) X3)) (@ (@ tptp.times_times_rat Y) Y)))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X3) X3)) (@ (@ tptp.times_times_int Y) Y)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) X3)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X3 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X3) X3)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X3 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X3) X3)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X3 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X3) Y)) tptp.zero_zero_real)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X3) Y)) tptp.zero_zero_rat)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) 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 X3) Y))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X3) Y))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X3) Y)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X3) Y)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X3) Y)) tptp.zero_zero_real)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X3) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X3) Y)) tptp.zero_zero_rat)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X3) Z)) (@ (@ tptp.divide_divide_real Y) W)))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X3) Z)) (@ (@ tptp.divide_divide_rat Y) W)))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) 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 X3) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X3) (=> (@ (@ tptp.ord_less_rat X3) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X3) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 6.44/6.78 (assert (forall ((Y tptp.real) (X3 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X3) 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 X3) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.44/6.78 (assert (forall ((Y tptp.rat) (X3 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X3) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) X3)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X3) X3)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X3) X3)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) X3)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X3 tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X3) X3)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X3 tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X3) X3)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X3 tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.44/6.78 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.44/6.78 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.44/6.78 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.44/6.78 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 6.44/6.78 (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))))))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.44/6.78 (assert (forall ((Y tptp.real) (X3 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X3) Y)) Z)))))
% 6.44/6.78 (assert (forall ((Y tptp.rat) (X3 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X3) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X3) Y)) Z)))))
% 6.44/6.78 (assert (forall ((Y tptp.real) (Z tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y)) X3) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X3) Y))))))
% 6.44/6.78 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y)) X3) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X3) Y))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)) (and (@ _let_1 tptp.zero_zero_rat) (@ _let_1 B)) (= A tptp.zero_zero_rat))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.one_one_real)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.one_one_rat)))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat)))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int)))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.44/6.78 (assert (forall ((Z tptp.complex) (X3 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X3) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X3) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.44/6.78 (assert (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X3) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.44/6.78 (assert (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X3) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X3) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.44/6.78 (assert (forall ((Z tptp.complex) (X3 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X3) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X3) Z)) Y)) Z)))))
% 6.44/6.78 (assert (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) Z)) Y)) Z)))))
% 6.44/6.78 (assert (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X3) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X3) Z)) Y)) Z)))))
% 6.44/6.78 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X3 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X3) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X3) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 6.44/6.78 (assert (forall ((Y tptp.real) (Z tptp.real) (X3 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X3) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 6.44/6.78 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X3) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X3) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 6.44/6.78 (assert (forall ((Y tptp.complex) (X3 tptp.complex) (Z tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X3) Y)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X3) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 6.44/6.78 (assert (forall ((Y tptp.real) (X3 tptp.real) (Z tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X3) Y)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 6.44/6.78 (assert (forall ((Y tptp.rat) (X3 tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X3) Y)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X3) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 6.44/6.78 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X3 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X3) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X3) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 6.44/6.78 (assert (forall ((Y tptp.real) (Z tptp.real) (X3 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 X3) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 6.44/6.78 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X3) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X3) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) (@ (@ tptp.power_power_rat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_rat A) _let_2) (@ (@ tptp.power_power_rat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.modulo364778990260209775nteger A) B) A)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat))))
% 6.44/6.78 (assert (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.44/6.78 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.44/6.78 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.78 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K2) (not (@ P I)))) (@ P (@ tptp.suc K2))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M) N))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Xs tptp.list_real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs)))))
% 6.44/6.78 (assert (forall ((X3 tptp.complex) (Xs tptp.list_complex)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs)))))
% 6.44/6.78 (assert (forall ((X3 tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s5460976970255530739at_nat Xs)))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 6.44/6.78 (assert (forall ((X3 Bool) (Xs tptp.list_o)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs)))))
% 6.44/6.78 (assert (forall ((X3 tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))))
% 6.44/6.78 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N) K)))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N)) (and (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M)))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I2) (@ _let_1 (@ (@ tptp.power_power_nat I2) N))))))
% 6.44/6.78 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.divide_divide_nat M) N))))))
% 6.44/6.78 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q2)) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N) Q2))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) M)))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N) M) (= N tptp.one_one_nat)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))))
% 6.44/6.78 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X3) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (=> (@ (@ tptp.ord_less_real Z2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z2) X3)) Y)))) (@ (@ tptp.ord_less_eq_real X3) Y))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (forall ((Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (=> (@ (@ tptp.ord_less_rat Z2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z2) X3)) Y)))) (@ (@ tptp.ord_less_eq_rat X3) Y))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.44/6.78 (assert (forall ((Y tptp.real) (Z tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y)) X3) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X3) Y))))))
% 6.44/6.78 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y)) X3) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X3) Y))))))
% 6.44/6.78 (assert (forall ((Y tptp.real) (X3 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X3) Y)) Z)))))
% 6.44/6.78 (assert (forall ((Y tptp.rat) (X3 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X3) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X3) Y)) Z)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.44/6.78 (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))))))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 6.44/6.78 (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)))))))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A) C))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) 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) X3)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X3) A) (=> (@ (@ tptp.ord_less_eq_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X3)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) 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) X3)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)) (= A tptp.zero_zero_rat)))))
% 6.44/6.78 (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)))))))))))))
% 6.44/6.78 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.44/6.78 (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)))))))))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) _let_1))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) _let_1))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) A)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) A)))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) A)))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) A)))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) tptp.one_one_real)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) tptp.one_one_rat)))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) tptp.one_one_nat)))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) tptp.one_one_int)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.44/6.78 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 6.44/6.78 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.44/6.78 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.44/6.78 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.44/6.78 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_real A) N)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N)))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_nat A) N)))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_int A) N)))))))
% 6.44/6.78 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.44/6.78 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.44/6.78 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N) Q2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q2)) N)))))
% 6.44/6.78 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I3)) J3)) (@ P I3))))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N)))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I3)) J3)) (@ P J3))))))))))
% 6.44/6.78 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B3) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B3) N))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) 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) X3)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X3) A) (=> (@ (@ tptp.ord_less_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X3)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) 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) X3)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.44/6.78 (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)))))))))))))
% 6.44/6.78 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.44/6.78 (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))))))))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X3) Y))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat X3) Y))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X3) Y))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X3) Y))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= X3 Y))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_rat X3) _let_2) (@ (@ tptp.power_power_rat Y) _let_2)) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= X3 Y))))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= X3 Y))))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= X3 Y))))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 N) tptp.zero_zero_nat))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (@ _let_1 N) tptp.zero_zero_int))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 M) tptp.zero_zero_nat))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (@ _let_1 M) tptp.zero_zero_int))))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ (@ tptp.plus_plus_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (or (and (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q4)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q4))) (@ P Q4))))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N))) M) tptp.one_one_nat))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X3) Y))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat X3) Y))))))
% 6.44/6.78 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X3) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X3) Y))))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X3) Y))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X3 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat) (and (= X3 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X3 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X3 tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) (or (not (= X3 tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat)))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X3 tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat)))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.44/6.78 (assert (forall ((B4 tptp.real) (A4 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B4) A4)) (@ (@ tptp.ord_less_real A4) B4))))
% 6.44/6.78 (assert (forall ((B4 tptp.rat) (A4 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B4) A4)) (@ (@ tptp.ord_less_rat A4) B4))))
% 6.44/6.78 (assert (forall ((B4 tptp.num) (A4 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B4) A4)) (@ (@ tptp.ord_less_num A4) B4))))
% 6.44/6.78 (assert (forall ((B4 tptp.nat) (A4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B4) A4)) (@ (@ tptp.ord_less_nat A4) B4))))
% 6.44/6.78 (assert (forall ((B4 tptp.int) (A4 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B4) A4)) (@ (@ tptp.ord_less_int A4) B4))))
% 6.44/6.78 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ P N))))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.44/6.78 (assert (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_real))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_rat))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((M tptp.code_integer) (X3 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X3))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X3) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M))))))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X3))) (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) X3) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 6.44/6.78 (assert (forall ((M tptp.int) (X3 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X3))) (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) X3) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 6.44/6.78 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((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 TreeList) I4)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N))) (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) TreeList) Summary)) Deg)))))))))))))))
% 6.44/6.78 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((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 TreeList) I4)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N))) (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) TreeList) Summary)) Deg)))))))))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X3) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X3) N)) (@ _let_1 N)))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X3) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X3) N)) (@ _let_1 M)))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 6.44/6.78 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.44/6.78 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X3 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X3))))
% 6.44/6.78 (assert (forall ((Z tptp.real) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X3) Y))))))
% 6.44/6.78 (assert (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X3) Y))))))
% 6.44/6.78 (assert (forall ((Z tptp.int) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X3) Y))))))
% 6.44/6.78 (assert (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X3) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_eq_real X3) Y)))))
% 6.44/6.78 (assert (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X3) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X3) Y)))))
% 6.44/6.78 (assert (forall ((Z tptp.int) (X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X3) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X3) Y)))))
% 6.44/6.78 (assert (forall ((Q2 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R2)) (= R2 tptp.zero_zero_nat))))
% 6.44/6.78 (assert (forall ((Q2 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R2)) (= R2 tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_num) (Ys2 tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_num Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6456567536196504476um_num (@ (@ tptp.product_num_num Xs) Ys2)) N) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_num Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_Code_integer) (Ys2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s3445333598471063425nteger Xs)) _let_1)) (= (@ (@ tptp.nth_Pr8522763379788166057eger_o (@ (@ tptp.produc3607205314601156340eger_o Xs) Ys2)) N) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.nth_Code_integer Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys2)) N) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys2)) N) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys2)) N) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys2)) N) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys2)) N) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs) Ys2)) N) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs) Ys2)) N) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs) Ys2)) N) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N) K)) (@ _let_1 K)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N) K)) (@ _let_1 K)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N) K)) (@ _let_1 K)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_o Ys2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_nat Ys2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_int Ys2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_o) (Ys2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_o) (Ys2 tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_o Ys2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_o) (Ys2 tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_nat Ys2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_o) (Ys2 tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_int Ys2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_nat) (Ys2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_nat) (Ys2 tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_o Ys2)))))
% 6.44/6.78 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))))
% 6.44/6.78 (assert (forall ((K tptp.int) (I2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K) I2) (=> (@ P K) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I4) (=> (@ P I4) (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))))) (@ P I2))))))
% 6.44/6.78 (assert (forall ((K tptp.int) (I2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I2) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I4) (=> (@ P I4) (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))))) (@ P I2))))))
% 6.44/6.78 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))))
% 6.44/6.78 (assert (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W Z))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I3 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I3 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ P J3))))))))
% 6.44/6.78 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((B4 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q5)) R4)) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (@ _let_1 Q5)))))))
% 6.44/6.78 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I2) J2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J2)))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 6.44/6.78 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (and (= M tptp.one_one_int) (= N tptp.one_one_int))))))
% 6.44/6.78 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))))
% 6.44/6.78 (assert (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B4 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))))
% 6.44/6.78 (assert (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B4 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R2) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))))
% 6.44/6.78 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.44/6.78 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_1 Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int R4) B) (=> (@ (@ tptp.ord_less_int R2) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))
% 6.44/6.78 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_2 Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ _let_1 R2) (=> (@ _let_1 R4) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))
% 6.44/6.78 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L2) tptp.zero_zero_int)))
% 6.44/6.78 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.44/6.78 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 6.44/6.78 (assert (forall ((M tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q3 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q3))))))
% 6.44/6.78 (assert (forall ((M tptp.int) (D tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q4 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q4))))))
% 6.44/6.78 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M) N) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))))
% 6.44/6.78 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L2) L2)))
% 6.44/6.78 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)))
% 6.44/6.78 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((K tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N) K))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) K)))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((M tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M) K)) M))))
% 6.44/6.78 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I2) K) I2) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I2))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (X3 tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X3) (= A X3) (@ (@ tptp.ord_less_eq_int X3) A))))
% 6.44/6.78 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) B))))))
% 6.44/6.78 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ tptp.ord_less_int B))) (=> (@ _let_2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (@ _let_2 _let_1)))))))
% 6.44/6.78 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.44/6.78 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.44/6.78 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 6.44/6.78 (assert (forall ((X3 tptp.produc3368934014287244435at_num)) (not (forall ((F2 (-> tptp.nat tptp.num tptp.num)) (A5 tptp.nat) (B5 tptp.nat) (Acc tptp.num)) (not (= X3 (@ (@ tptp.produc851828971589881931at_num F2) (@ (@ tptp.produc1195630363706982562at_num A5) (@ (@ tptp.product_Pair_nat_num B5) Acc)))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B5 tptp.nat) (Acc tptp.nat)) (not (= X3 (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A5) (@ (@ tptp.product_Pair_nat_nat B5) Acc)))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.nat)) (=> (not (= X3 tptp.zero_zero_nat)) (=> (not (= X3 (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X3 (@ tptp.suc (@ tptp.suc Va))))))))))
% 6.44/6.78 (assert (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X3) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_real X3) Y)))))
% 6.44/6.78 (assert (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X3) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X3) Y)))))
% 6.44/6.78 (assert (forall ((Z tptp.int) (X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X3) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X3) Y)))))
% 6.44/6.78 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X3 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X3))))
% 6.44/6.78 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va2) Vb) Vc)))))
% 6.44/6.78 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X tptp.int)) (=> (@ P X) (@ P (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int K) D))))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (X3 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X3))))
% 6.44/6.78 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N 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 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 6.44/6.78 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))))
% 6.44/6.78 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X3 tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat X3) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X3 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X3) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X3) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X3) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat Mi) X3) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X3 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList) Summary)) X3) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X3) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X3) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))))
% 6.44/6.78 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 6.44/6.78 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B5)))))))
% 6.44/6.78 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B5))))))
% 6.44/6.78 (assert (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A3 Bool) (B2 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B2))))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I2 tptp.nat) (X3 tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2))) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 X3)) I2) Y) (@ _let_1 Y)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I2 tptp.nat) (X3 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3)) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_o) (I2 tptp.nat) (X3 Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs) I2) X3)) (@ tptp.size_size_list_o Xs))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_nat) (I2 tptp.nat) (X3 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs) I2) X3)) (@ tptp.size_size_list_nat Xs))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_int) (I2 tptp.nat) (X3 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs) I2) X3)) (@ tptp.size_size_list_int Xs))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N)))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (Xs tptp.list_nat) (X3 tptp.nat)) (=> (not (= I2 J2)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I2) X3)) J2) (@ (@ tptp.nth_nat Xs) J2)))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (Xs tptp.list_int) (X3 tptp.int)) (=> (not (= I2 J2)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I2) X3)) J2) (@ (@ tptp.nth_int Xs) J2)))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X3 tptp.vEBT_VEBT)) (=> (not (= I2 J2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3)) J2) (@ (@ tptp.nth_VEBT_VEBT Xs) J2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_nat) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs) I2) (@ (@ tptp.nth_nat Xs) I2)) Xs)))
% 6.44/6.78 (assert (forall ((Xs tptp.list_int) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs) I2) (@ (@ tptp.nth_int Xs) I2)) Xs)))
% 6.44/6.78 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) (@ (@ tptp.nth_VEBT_VEBT Xs) I2)) Xs)))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X3))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X3))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X3))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X3))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X3))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X3))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X3))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X3))) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X3))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X3))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))))
% 6.44/6.78 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 6.44/6.78 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 6.44/6.78 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 6.44/6.78 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 6.44/6.78 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 6.44/6.78 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 6.44/6.78 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 6.44/6.78 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 6.44/6.78 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 6.44/6.78 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X3))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X3))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X3))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X3))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X3))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X3))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X3))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X3))) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X3))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))))
% 6.44/6.78 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X3))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I2 tptp.nat) (X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) I2) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3) Xs))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_o) (I2 tptp.nat) (X3 Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) I2) (= (@ (@ (@ tptp.list_update_o Xs) I2) X3) Xs))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_nat) (I2 tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) I2) (= (@ (@ (@ tptp.list_update_nat Xs) I2) X3) Xs))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_int) (I2 tptp.nat) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) I2) (= (@ (@ (@ tptp.list_update_int Xs) I2) X3) Xs))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3)) I2) X3))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_o) (X3 Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs) I2) X3)) I2) X3))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I2) X3)) I2) X3))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I2) X3)) I2) X3))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_VEBT_VEBT2 Xs))))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_o) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (let ((_let_2 (@ tptp.size_size_list_o Xs))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_o2 Xs))))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_nat2 Xs))))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_int) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_int2 Xs))))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= Q2 Q5))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= R2 R4))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (I5 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X3 tptp.vEBT_VEBT) (X6 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.list_u1324408373059187874T_VEBT Xs))) (=> (not (= I2 I5)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I2) X3)) I5) X6) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I5) X6)) I2) X3))))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT)) (=> (not (= X3 (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv Bool)) (not (= X3 (@ (@ tptp.vEBT_Leaf true) Uv)))) (=> (forall ((Uu Bool)) (not (= X3 (@ (@ tptp.vEBT_Leaf Uu) true)))) (=> (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2)))))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X3))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X3))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.44/6.78 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X3))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X3))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X3) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X3) Z)) (@ (@ tptp.plus_plus_real Y) Z)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X3) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X3) Z)) (@ (@ tptp.plus_plus_rat Y) Z)))))
% 6.44/6.78 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X3) Y)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X3) Z)) (@ (@ tptp.plus_plus_nat Y) Z)))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X3) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X3) Z)) (@ (@ tptp.plus_plus_int Y) Z)))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X3) (=> (not (= X3 (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy2)))))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q2)) (@ (@ tptp.plus_plus_nat N) Q2)))))
% 6.44/6.78 (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 ((X21 Bool) (X222 Bool)) (not (= Y (@ (@ tptp.vEBT_Leaf X21) X222))))))))
% 6.44/6.78 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X212 Bool) (X223 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X212) X223)))))
% 6.44/6.78 (assert (forall ((X3 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu Bool) (Uv Bool) (D3 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu) Uv)) D3)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) Deg3))))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N) Q2)))))
% 6.44/6.78 (assert (forall ((A Bool) (B Bool) (X3 tptp.nat)) (let ((_let_1 (= X3 tptp.one_one_nat))) (let ((_let_2 (= X3 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X3) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.44/6.78 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 6.44/6.78 (assert (forall ((Uv2 Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv2)))))
% 6.44/6.78 (assert (forall ((Uu2 Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu2) true)))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ tptp.vEBT_VEBT_minNull X3) Y) (=> (=> (= X3 (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv Bool)) (= X3 (@ (@ tptp.vEBT_Leaf true) Uv))) Y) (=> (=> (exists ((Uu Bool)) (= X3 (@ (@ tptp.vEBT_Leaf Uu) true))) Y) (=> (=> (exists ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) Y))))))))))
% 6.44/6.78 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 6.44/6.78 (assert (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R2)) (= (@ (@ tptp.divide_divide_int K) L2) Q2))))
% 6.44/6.78 (assert (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R2)) (= (@ (@ tptp.modulo_modulo_int K) L2) R2))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_real) (A2 tptp.set_real) (X3 tptp.real) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) A2) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) I2) X3))) A2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_complex) (A2 tptp.set_complex) (X3 tptp.complex) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs) I2) X3))) A2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (X3 tptp.product_prod_nat_nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) A2) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) I2) X3))) A2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_nat) (A2 tptp.set_nat) (X3 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I2) X3))) A2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (X3 tptp.vEBT_VEBT) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (=> (@ (@ tptp.member_VEBT_VEBT X3) A2) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3))) A2)))))
% 6.44/6.78 (assert (forall ((Xs tptp.list_int) (A2 tptp.set_int) (X3 tptp.int) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I2) X3))) A2)))))
% 6.44/6.78 (assert (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X3))))
% 6.44/6.78 (assert (forall ((X3 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2)) X5)))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ 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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2)) X5)))))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw)))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ 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 (= X3 (@ (@ 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) (Vd tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd)) X5)))))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X5)))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ 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 (= X3 (@ (@ 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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2)) X5)))))))))))
% 6.44/6.78 (assert (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy))))
% 6.44/6.78 (assert (forall ((X3 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X5)))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)) Ux)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2)) X5)))))))))
% 6.44/6.78 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.44/6.78 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.44/6.78 (assert (forall ((L2 tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (=> (= K (@ (@ tptp.times_times_int Q2) L2)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) tptp.zero_zero_int))))))
% 6.44/6.78 (assert (forall ((A Bool) (B Bool) (X3 tptp.nat)) (let ((_let_1 (= X3 tptp.one_one_nat))) (let ((_let_2 (= X3 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X3) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.44/6.78 (assert (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2))))
% 6.44/6.78 (assert (forall ((X3 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) X3))) (let ((_let_4 (= X3 tptp.one_one_nat))) (let ((_let_5 (= X3 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))))))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real X3) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) N) X3))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_complex) (X3 tptp.complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs)) (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs) N) X3))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_P6011104703257516679at_nat) (X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) N) X3))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) N) X3))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (X3 Bool)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o X3) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) N) X3))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) N) X3))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int X3) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) N) X3))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3) Xs) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I2) X3)))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_o) (X3 Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (= (= (@ (@ (@ tptp.list_update_o Xs) I2) X3) Xs) (= (@ (@ tptp.nth_o Xs) I2) X3)))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (= (= (@ (@ (@ tptp.list_update_nat Xs) I2) X3) Xs) (= (@ (@ tptp.nth_nat Xs) I2) X3)))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (= (= (@ (@ (@ tptp.list_update_int Xs) I2) X3) Xs) (= (@ (@ tptp.nth_int Xs) I2) X3)))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (J2 tptp.nat) (X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3)) J2))) (let ((_let_2 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (and (=> _let_2 (= _let_1 X3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs) J2)))))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_o) (X3 Bool) (J2 tptp.nat)) (let ((_let_1 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs) I2) X3)) J2) (and (=> _let_1 X3) (=> (not _let_1) (@ (@ tptp.nth_o Xs) J2))))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_nat) (J2 tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I2) X3)) J2))) (let ((_let_2 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (and (=> _let_2 (= _let_1 X3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs) J2)))))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (Xs tptp.list_int) (J2 tptp.nat) (X3 tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I2) X3)) J2))) (let ((_let_2 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (and (=> _let_2 (= _let_1 X3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs) J2)))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.real Bool)) (P3 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.rat Bool)) (P3 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.real Bool)) (P3 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.rat Bool)) (P3 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (not (@ (@ tptp.ord_less_real X) T)))))))
% 6.44/6.78 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (not (@ (@ tptp.ord_less_rat X) T)))))))
% 6.44/6.78 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (not (@ (@ tptp.ord_less_num X) T)))))))
% 6.44/6.78 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (not (@ (@ tptp.ord_less_nat X) T)))))))
% 6.44/6.78 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (not (@ (@ tptp.ord_less_int X) T)))))))
% 6.44/6.78 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (@ (@ tptp.ord_less_real T) X))))))
% 6.44/6.78 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (@ (@ tptp.ord_less_rat T) X))))))
% 6.44/6.78 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (@ (@ tptp.ord_less_num T) X))))))
% 6.44/6.78 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (@ (@ tptp.ord_less_nat T) X))))))
% 6.44/6.78 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (@ (@ tptp.ord_less_int T) X))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.real Bool)) (P3 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z2) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.rat Bool)) (P3 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z2) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z2) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z2) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.real Bool)) (P3 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z2) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.rat Bool)) (P3 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z2) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z2) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z2) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))))
% 6.44/6.78 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z2) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z2) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z2) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z2) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z2) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z2) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z2) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z2) (not (= X T)))))))
% 6.44/6.78 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.44/6.78 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.44/6.78 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.44/6.78 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.44/6.78 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.44/6.78 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z2) (not (@ (@ tptp.ord_less_real T) X)))))))
% 6.44/6.78 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z2) (not (@ (@ tptp.ord_less_rat T) X)))))))
% 6.44/6.78 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z2) (not (@ (@ tptp.ord_less_num T) X)))))))
% 6.44/6.78 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (@ (@ tptp.ord_less_nat T) X)))))))
% 6.44/6.78 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z2) (not (@ (@ tptp.ord_less_int T) X)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X3)) (=> (forall ((Uv Bool)) (not (= X3 (@ (@ tptp.vEBT_Leaf true) Uv)))) (=> (forall ((Uu Bool)) (not (= X3 (@ (@ tptp.vEBT_Leaf Uu) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))))))))))
% 6.44/6.78 (assert (forall ((K tptp.int) (L2 tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K) L2)) (@ (@ tptp.modulo_modulo_int K) L2)))))
% 6.44/6.78 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary)) X3) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X3) X3))) _let_1) TreeList) Summary)))))
% 6.44/6.78 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (not (@ (@ tptp.ord_less_eq_real X) T)))))))
% 6.44/6.78 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (not (@ (@ tptp.ord_less_eq_rat X) T)))))))
% 6.44/6.78 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (not (@ (@ tptp.ord_less_eq_num X) T)))))))
% 6.44/6.78 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (not (@ (@ tptp.ord_less_eq_nat X) T)))))))
% 6.44/6.78 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (not (@ (@ tptp.ord_less_eq_int X) T)))))))
% 6.44/6.78 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (@ (@ tptp.ord_less_eq_real T) X))))))
% 6.44/6.78 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (@ (@ tptp.ord_less_eq_rat T) X))))))
% 6.44/6.78 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (@ (@ tptp.ord_less_eq_num T) X))))))
% 6.44/6.78 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (@ (@ tptp.ord_less_eq_nat T) X))))))
% 6.44/6.78 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (@ (@ tptp.ord_less_eq_int T) X))))))
% 6.44/6.78 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z2) (@ (@ tptp.ord_less_eq_real X) T))))))
% 6.44/6.78 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z2) (@ (@ tptp.ord_less_eq_rat X) T))))))
% 6.44/6.78 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z2) (@ (@ tptp.ord_less_eq_num X) T))))))
% 6.44/6.78 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (@ (@ tptp.ord_less_eq_nat X) T))))))
% 6.44/6.78 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z2) (@ (@ tptp.ord_less_eq_int X) T))))))
% 6.44/6.78 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z2) (not (@ (@ tptp.ord_less_eq_real T) X)))))))
% 6.44/6.78 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z2) (not (@ (@ tptp.ord_less_eq_rat T) X)))))))
% 6.44/6.78 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z2) (not (@ (@ tptp.ord_less_eq_num T) X)))))))
% 6.44/6.78 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (@ (@ tptp.ord_less_eq_nat T) X)))))))
% 6.44/6.78 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z2) (not (@ (@ tptp.ord_less_eq_int T) X)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (X6 tptp.int) (P Bool) (P3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X3 X6) (=> (=> _let_2 (= P P3)) (= (=> (@ _let_1 X3) P) (=> _let_2 P3))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (X6 tptp.int) (P Bool) (P3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X3 X6) (=> (=> _let_2 (= P P3)) (= (and (@ _let_1 X3) P) (and _let_2 P3))))))))
% 6.44/6.78 (assert (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L2))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2))) (= (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R2)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L2) Q2)) R2)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (@ (@ tptp.ord_less_int R2) L2))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R2) (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))))
% 6.44/6.78 (assert (= tptp.vEBT_invar_vebt (lambda ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (or (and (exists ((A3 Bool) (B2 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A3) B2))) (= A22 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= A22 (@ (@ tptp.plus_plus_nat N2) N2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) 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))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N2))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A22 (@ (@ tptp.plus_plus_nat N2) _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 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 N2)) (= A22 (@ (@ tptp.plus_plus_nat N2) N2)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3)))) (=> _let_1 (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.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X2) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.suc N2))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 _let_3)) (= A22 (@ (@ tptp.plus_plus_nat N2) _let_3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3)))) (=> _let_1 (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.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X2) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))))))
% 6.44/6.78 (assert (forall ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A12) A23) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A5) B5))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (=> (= M5 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_1))) (not (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (=> (= M5 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_1))) (not (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M5)) (=> (= M5 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2))))))))))))))))))))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M5)) (=> (= M5 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))))))))))))))))))))
% 6.44/6.78 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N 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 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 6.44/6.78 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (=> (@ (@ tptp.vEBT_vebt_member Tree) X3) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X3) (@ (@ tptp.vEBT_VEBT_membermima Tree) X3))))))
% 6.44/6.78 (assert (forall ((X3 tptp.extended_enat) (Y tptp.extended_enat) (Z tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X3) Y)) Z) (and (@ (@ tptp.ord_le72135733267957522d_enat X3) Z) (@ (@ tptp.ord_le72135733267957522d_enat Y) Z)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X3) Y)) Z) (and (@ (@ tptp.ord_less_real X3) Z) (@ (@ tptp.ord_less_real Y) Z)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X3) Y)) Z) (and (@ (@ tptp.ord_less_rat X3) Z) (@ (@ tptp.ord_less_rat Y) Z)))))
% 6.44/6.78 (assert (forall ((X3 tptp.num) (Y tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X3) Y)) Z) (and (@ (@ tptp.ord_less_num X3) Z) (@ (@ tptp.ord_less_num Y) Z)))))
% 6.44/6.78 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X3) Y)) Z) (and (@ (@ tptp.ord_less_nat X3) Z) (@ (@ tptp.ord_less_nat Y) Z)))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X3) Y)) Z) (and (@ (@ tptp.ord_less_int X3) Z) (@ (@ tptp.ord_less_int Y) Z)))))
% 6.44/6.78 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.44/6.78 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.44/6.78 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.44/6.78 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.44/6.78 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.44/6.78 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.44/6.78 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.44/6.78 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C) A)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.44/6.78 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.44/6.78 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.44/6.78 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.44/6.78 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.44/6.78 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.44/6.78 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X2 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X2) (@ (@ tptp.vEBT_VEBT_membermima T2) X2)))))
% 6.44/6.78 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((M5 tptp.nat)) (@ (@ P M5) tptp.zero_zero_nat)) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P N3) (@ (@ tptp.modulo_modulo_nat M5) N3)) (@ (@ P M5) N3)))) (@ (@ P M) N)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (X3 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X3))))
% 6.44/6.78 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)))
% 6.44/6.78 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)))
% 6.44/6.78 (assert (forall ((Ux2 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) Ux2) Uy)) Uz))))
% 6.44/6.78 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X3 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va2) Vb)) X3) (or (= X3 Mi) (= X3 Ma)))))
% 6.44/6.78 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (= (@ (@ P A5) B5) (@ (@ P B5) A5))) (=> (forall ((A5 tptp.nat)) (@ (@ P A5) tptp.zero_zero_nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.plus_plus_nat A5) B5))))) (@ (@ P A) B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((A3 tptp.extended_enat) (B2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2) B2))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_max_rat A3) B2) B2))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B2 tptp.num)) (= (@ (@ tptp.ord_max_num A3) B2) B2))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B2) B2))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B2) B2))))
% 6.44/6.78 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2) A3))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (= (@ (@ tptp.ord_max_rat A3) B2) A3))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (= (@ (@ tptp.ord_max_num A3) B2) A3))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B2) A3))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B2) A3))))
% 6.44/6.78 (assert (forall ((Z tptp.extended_enat) (X3 tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))))
% 6.44/6.78 (assert (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))))
% 6.44/6.78 (assert (forall ((Z tptp.num) (X3 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))))
% 6.44/6.78 (assert (forall ((Z tptp.nat) (X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))))
% 6.44/6.78 (assert (forall ((Z tptp.int) (X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))))
% 6.44/6.78 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat B) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))))
% 6.44/6.78 (assert (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))))
% 6.44/6.78 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 6.44/6.78 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 6.44/6.78 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))))
% 6.44/6.78 (assert (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 6.44/6.78 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2)))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (= A3 (@ (@ tptp.ord_max_rat A3) B2)))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (= A3 (@ (@ tptp.ord_max_num A3) B2)))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (= A3 (@ (@ tptp.ord_max_nat A3) B2)))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (= A3 (@ (@ tptp.ord_max_int A3) B2)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C) A)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)) (@ (@ tptp.ord_le2932123472753598470d_enat B) A))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.44/6.78 (assert (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.44/6.78 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))))
% 6.44/6.78 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))))
% 6.44/6.78 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 6.44/6.78 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (D tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A) (=> (@ (@ tptp.ord_less_eq_rat D) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C) D)) (@ (@ tptp.ord_max_rat A) B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (and (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2)) (not (= A3 B2))))))
% 6.44/6.78 (assert (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (= A3 (@ (@ tptp.ord_max_real A3) B2)) (not (= A3 B2))))))
% 6.44/6.78 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (= A3 (@ (@ tptp.ord_max_rat A3) B2)) (not (= A3 B2))))))
% 6.44/6.78 (assert (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (= A3 (@ (@ tptp.ord_max_num A3) B2)) (not (= A3 B2))))))
% 6.44/6.78 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (= A3 (@ (@ tptp.ord_max_nat A3) B2)) (not (= A3 B2))))))
% 6.44/6.78 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (= A3 (@ (@ tptp.ord_max_int A3) B2)) (not (= A3 B2))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat C) A)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((Z tptp.extended_enat) (X3 tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))))
% 6.44/6.78 (assert (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))))
% 6.44/6.78 (assert (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))))
% 6.44/6.78 (assert (forall ((Z tptp.num) (X3 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))))
% 6.44/6.78 (assert (forall ((Z tptp.nat) (X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))))
% 6.44/6.78 (assert (forall ((Z tptp.int) (X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N)) K) L2) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N) (@ (@ tptp.divide_divide_int K) _let_1)) L2)))))))
% 6.44/6.78 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.44/6.78 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 6.44/6.78 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.44/6.78 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.44/6.78 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B) (@ _let_2 R2)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A))) (@ _let_1 B)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R2)) tptp.one_one_int)))))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X3) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 _let_2) (not (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B5))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) (=> (= X3 _let_1) (not (= Y _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (=> (= X3 _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)))) (=> (= X3 (@ (@ (@ (@ 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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat 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))) (=> (= X3 _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))))))))))))))))))))
% 6.44/6.78 (assert (forall ((R2 tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R2))) (=> (not (= R2 tptp.zero_zero_complex)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C)) (@ (@ tptp.plus_plus_complex B) (@ _let_1 D)))))))))
% 6.44/6.78 (assert (forall ((R2 tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (=> (not (= R2 tptp.zero_zero_real)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D)))))))))
% 6.44/6.78 (assert (forall ((R2 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D)))))))))
% 6.44/6.78 (assert (forall ((R2 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D)))))))))
% 6.44/6.78 (assert (forall ((R2 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D)))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.44/6.78 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N)) (= M N))))
% 6.44/6.78 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 6.44/6.78 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.44/6.78 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.44/6.78 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.44/6.78 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.44/6.78 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.44/6.78 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.44/6.78 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.44/6.78 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 6.44/6.78 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.44/6.78 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.44/6.78 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 6.44/6.78 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.44/6.78 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat A) B))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_rat A) B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 6.44/6.78 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.44/6.78 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.78 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)))
% 6.44/6.78 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.44/6.78 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 6.44/6.78 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.44/6.78 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.44/6.78 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.44/6.78 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) A)) (@ _let_1 B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)) (@ _let_1 B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 6.44/6.78 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N)))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit1 N)))))
% 6.44/6.78 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.44/6.78 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 6.44/6.78 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L2) L2)))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_rat B) A))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.44/6.78 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.44/6.78 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.44/6.78 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) _let_1) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C) A)) B)) (@ _let_1 B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.times_times_rat C) A))) (@ _let_1 B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.modulo364778990260209775nteger B) A) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M)))) (= (@ _let_1 (@ tptp.bit0 N)) (@ tptp.bit0 (@ _let_1 N))))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M) _let_1))))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))))
% 6.44/6.78 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N) K) L2)) (@ _let_1 L2)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N) K) L2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N))) (@ _let_1 N)))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N)) (not (@ _let_1 N))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.dvd_dvd_nat A) B)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N)) (@ tptp.bit1 N))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.44/6.78 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 6.44/6.78 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) tptp.one)))))
% 6.44/6.78 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W) Z))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N)))))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ (@ tptp.divide_divide_nat N) _let_1))))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N) _let_1)))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_rat))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_2 (= A tptp.zero_zero_rat)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer)) (= N tptp.zero_zero_nat)))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat)) (= N tptp.zero_zero_nat)))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int)) (= N tptp.zero_zero_nat)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_set_complex (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) A)))) (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) B)))) (and (@ (@ tptp.dvd_dvd_complex A) B) (not (@ (@ tptp.dvd_dvd_complex B) A))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) A)))) (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) B)))) (and (@ (@ tptp.dvd_dvd_real A) B) (not (@ (@ tptp.dvd_dvd_real B) A))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) A)))) (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) B)))) (and (@ (@ tptp.dvd_dvd_nat A) B) (not (@ (@ tptp.dvd_dvd_nat B) A))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) A)))) (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) B)))) (and (@ (@ tptp.dvd_dvd_int A) B) (not (@ (@ tptp.dvd_dvd_int B) A))))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) A)))) (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) B)))) (and (@ (@ tptp.dvd_dvd_Code_integer A) B) (not (@ (@ tptp.dvd_dvd_Code_integer B) A))))))
% 6.44/6.78 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.44/6.78 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.44/6.78 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((X3 tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X3))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y) Z)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X3))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_real Y) Z)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X3))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_rat Y) Z)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X3))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_int Y) Z)))))))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 6.44/6.78 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 6.44/6.78 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) A)))
% 6.44/6.78 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (= A B) (= C D)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (= A B) (= C D)))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (= A B) (= C D)))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) C) (@ _let_1 C))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) C) (@ _let_1 C))))))
% 6.44/6.78 (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) (=> (@ (@ tptp.dvd_dvd_Code_integer B) C) (@ _let_1 C))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 C)) B) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C)))))
% 6.44/6.78 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat Z) _let_2)) _let_2))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 6.44/6.78 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 6.44/6.78 (assert (= (lambda ((H tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 6.44/6.78 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.44/6.78 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.44/6.78 (assert (= (lambda ((X2 tptp.complex)) X2) (@ tptp.times_times_complex tptp.one_one_complex)))
% 6.44/6.78 (assert (= (lambda ((X2 tptp.real)) X2) (@ tptp.times_times_real tptp.one_one_real)))
% 6.44/6.78 (assert (= (lambda ((X2 tptp.rat)) X2) (@ tptp.times_times_rat tptp.one_one_rat)))
% 6.44/6.78 (assert (= (lambda ((X2 tptp.nat)) X2) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.44/6.78 (assert (= (lambda ((X2 tptp.int)) X2) (@ tptp.times_times_int tptp.one_one_int)))
% 6.44/6.78 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A3 tptp.extended_enat) (B2 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A3) B2)) B2) A3))))
% 6.44/6.78 (assert (= tptp.ord_max_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A3) B2)) B2) A3))))
% 6.44/6.78 (assert (= tptp.ord_max_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A3) B2)) B2) A3))))
% 6.44/6.78 (assert (= tptp.ord_max_num (lambda ((A3 tptp.num) (B2 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A3) B2)) B2) A3))))
% 6.44/6.78 (assert (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B2)) B2) A3))))
% 6.44/6.78 (assert (= tptp.ord_max_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B2)) B2) A3))))
% 6.44/6.78 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X) T))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T)))))))))
% 6.44/6.78 (assert (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real K4) D4))) T)))))))))
% 6.44/6.78 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat K4) D4))) T)))))))))
% 6.44/6.78 (assert (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K4) D4))) T)))))))))
% 6.44/6.78 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X) T)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T))))))))
% 6.44/6.78 (assert (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real K4) D4))) T))))))))
% 6.44/6.78 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat K4) D4))) T))))))))
% 6.44/6.78 (assert (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K4) D4))) T))))))))
% 6.44/6.78 (assert (= tptp.dvd_dvd_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (=> (= A3 tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))))
% 6.44/6.78 (assert (= tptp.dvd_dvd_real (lambda ((A3 tptp.real) (B2 tptp.real)) (=> (= A3 tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 6.44/6.78 (assert (= tptp.dvd_dvd_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (=> (= A3 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.44/6.78 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.44/6.78 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.44/6.78 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C) D)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (= (lambda ((Y5 tptp.complex) (Z3 tptp.complex)) (= Y5 Z3)) (lambda ((A3 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A3) B2) tptp.zero_zero_complex))))
% 6.44/6.78 (assert (= (lambda ((Y5 tptp.real) (Z3 tptp.real)) (= Y5 Z3)) (lambda ((A3 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real A3) B2) tptp.zero_zero_real))))
% 6.44/6.78 (assert (= (lambda ((Y5 tptp.rat) (Z3 tptp.rat)) (= Y5 Z3)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A3) B2) tptp.zero_zero_rat))))
% 6.44/6.78 (assert (= (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3)) (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B2) tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 6.44/6.78 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat B) C))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A) B) (=> (@ (@ tptp.dvd_dvd_rat C) D) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.44/6.78 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat A) C))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B2 tptp.code_integer) (A3 tptp.code_integer)) (exists ((K3 tptp.code_integer)) (= A3 (@ (@ tptp.times_3573771949741848930nteger B2) K3))))))
% 6.44/6.78 (assert (= tptp.dvd_dvd_real (lambda ((B2 tptp.real) (A3 tptp.real)) (exists ((K3 tptp.real)) (= A3 (@ (@ tptp.times_times_real B2) K3))))))
% 6.44/6.78 (assert (= tptp.dvd_dvd_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (exists ((K3 tptp.rat)) (= A3 (@ (@ tptp.times_times_rat B2) K3))))))
% 6.44/6.78 (assert (= tptp.dvd_dvd_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (exists ((K3 tptp.nat)) (= A3 (@ (@ tptp.times_times_nat B2) K3))))))
% 6.44/6.78 (assert (= tptp.dvd_dvd_int (lambda ((B2 tptp.int) (A3 tptp.int)) (exists ((K3 tptp.int)) (= A3 (@ (@ tptp.times_times_int B2) K3))))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (not (forall ((K2 tptp.rat)) (not (= A (@ (@ tptp.times_times_rat B) K2))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((P2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P2) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (@ (@ tptp.times_times_nat X5) Y3)) (=> (@ (@ tptp.dvd_dvd_nat X5) A) (not (@ (@ tptp.dvd_dvd_nat Y3) B)))))))))
% 6.44/6.78 (assert (forall ((P2 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P2) (@ (@ tptp.times_times_int A) B)) (not (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (= P2 (@ (@ tptp.times_times_int X5) Y3)) (=> (@ (@ tptp.dvd_dvd_int X5) A) (not (@ (@ tptp.dvd_dvd_int Y3) B)))))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B6 tptp.nat) (C4 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B6) C4)) (@ (@ tptp.dvd_dvd_nat B6) B) (@ (@ tptp.dvd_dvd_nat C4) C))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B6 tptp.int) (C4 tptp.int)) (and (= A (@ (@ tptp.times_times_int B6) C4)) (@ (@ tptp.dvd_dvd_int B6) B) (@ (@ tptp.dvd_dvd_int C4) C))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C) D)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 6.44/6.78 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 6.44/6.78 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 6.44/6.78 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 C))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 B))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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 ((X tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real K4) D4)))) (= (or (@ P X) (@ Q X)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X5 tptp.rat) (K2 tptp.rat)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K2) D4))))) (=> (forall ((X5 tptp.rat) (K2 tptp.rat)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K2) D4))))) (forall ((X tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat K4) D4)))) (= (or (@ P X) (@ Q X)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.44/6.78 (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 ((X tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K4) D4)))) (= (or (@ P X) (@ Q X)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.44/6.78 (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 ((X tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real K4) D4)))) (= (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X5 tptp.rat) (K2 tptp.rat)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K2) D4))))) (=> (forall ((X5 tptp.rat) (K2 tptp.rat)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K2) D4))))) (forall ((X tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat K4) D4)))) (= (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.44/6.78 (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 ((X tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K4) D4)))) (= (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) C)) A) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B) A)) (@ (@ tptp.times_times_rat C) A)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((X22 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X32)))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (= A B)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C) B) A) (= C (@ (@ tptp.minus_minus_rat A) B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.minus_minus_rat C) B)) (= (@ (@ tptp.plus_plus_rat A) B) C))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A) B) C) (= A (@ (@ tptp.plus_plus_rat C) B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A2) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat C) D)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 6.44/6.78 (assert (forall ((X3 tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X3) Y) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X3) N)) (@ (@ tptp.power_8256067586552552935nteger Y) N)))))
% 6.44/6.78 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X3) Y) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X3) N)) (@ (@ tptp.power_power_nat Y) N)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X3) Y) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.power_power_real Y) N)))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X3) Y) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X3) N)) (@ (@ tptp.power_power_int Y) N)))))
% 6.44/6.78 (assert (forall ((X3 tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X3) Y) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.power_power_complex Y) N)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)))))
% 6.44/6.78 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo_modulo_nat M) N)))))))
% 6.44/6.78 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo_modulo_int M) N)))))))
% 6.44/6.78 (assert (forall ((K tptp.code_integer) (M tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger M) N)))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ _let_1 A))))))
% 6.44/6.78 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ _let_1 A))))))
% 6.44/6.78 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ _let_1 A))))))
% 6.44/6.78 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.44/6.78 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.44/6.78 (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 (@ (@ tptp.modulo364778990260209775nteger A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C))))
% 6.44/6.78 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A4) B4)) C))))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A4) B4)) C))))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 6.44/6.78 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.44/6.78 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z22)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X3) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X3) Z)) (@ (@ tptp.minus_minus_real Y) Z)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X3) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X3) Z)) (@ (@ tptp.minus_minus_rat Y) Z)))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X3) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X3) Z)) (@ (@ tptp.minus_minus_int Y) Z)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.44/6.78 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int) (M tptp.nat) (L2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L2) R2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 L2)) R2)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_rat _let_2) _let_2))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A3) B2)) tptp.zero_zero_real))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A3) B2)) tptp.zero_zero_rat))))
% 6.44/6.78 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A3) B2)) tptp.zero_zero_int))))
% 6.44/6.78 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 6.44/6.78 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.44/6.78 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.44/6.78 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A3) B2)) tptp.zero_zero_real))))
% 6.44/6.78 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A3) B2)) tptp.zero_zero_rat))))
% 6.44/6.78 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A3) B2)) tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Z2) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X) S))))) (=> (@ (@ tptp.ord_less_real X) Z2) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X) S))))) (=> (@ (@ tptp.ord_less_rat X) Z2) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X) S))))) (=> (@ (@ tptp.ord_less_nat X) Z2) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X) S))))) (=> (@ (@ tptp.ord_less_int X) Z2) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Z2) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X) S)))) (=> (@ (@ tptp.ord_less_real X) Z2) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X) S)))) (=> (@ (@ tptp.ord_less_rat X) Z2) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X) S)))) (=> (@ (@ tptp.ord_less_nat X) Z2) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X) S)))) (=> (@ (@ tptp.ord_less_int X) Z2) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X) S))))) (=> (@ (@ tptp.ord_less_real Z2) X) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X) S))))) (=> (@ (@ tptp.ord_less_rat Z2) X) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X) S))))) (=> (@ (@ tptp.ord_less_nat Z2) X) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X) S))))) (=> (@ (@ tptp.ord_less_int Z2) X) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X) S)))) (=> (@ (@ tptp.ord_less_real Z2) X) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X) S)))) (=> (@ (@ tptp.ord_less_rat Z2) X) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X) S)))) (=> (@ (@ tptp.ord_less_nat Z2) X) (= _let_1 _let_1)))))))
% 6.44/6.78 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X) S)))) (=> (@ (@ tptp.ord_less_int Z2) X) (= _let_1 _let_1)))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((I2 tptp.real) (K tptp.real) (N tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N) (@ (@ tptp.ord_less_eq_real I2) (@ (@ tptp.minus_minus_real N) K)))))
% 6.44/6.78 (assert (forall ((I2 tptp.rat) (K tptp.rat) (N tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) N) (@ (@ tptp.ord_less_eq_rat I2) (@ (@ tptp.minus_minus_rat N) K)))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat N) K)))))
% 6.44/6.78 (assert (forall ((I2 tptp.int) (K tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N) (@ (@ tptp.ord_less_eq_int I2) (@ (@ tptp.minus_minus_int N) K)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((I2 tptp.real) (K tptp.real) (N tptp.real) (J2 tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N) (@ (@ tptp.plus_plus_real J2) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N) K)) J2)))))))))
% 6.44/6.78 (assert (forall ((I2 tptp.rat) (K tptp.rat) (N tptp.rat) (J2 tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N) (@ (@ tptp.plus_plus_rat J2) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N) K)) J2)))))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (K tptp.nat) (N tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat J2) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N) K)) J2)))))))))
% 6.44/6.78 (assert (forall ((I2 tptp.int) (K tptp.int) (N tptp.int) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N) (@ (@ tptp.plus_plus_int J2) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N) K)) J2)))))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat A) B)) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C) D))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X3) X3)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.minus_minus_real X3) Y)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X3) X3)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X3) Y)) (@ (@ tptp.minus_minus_rat X3) Y)))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X3) X3)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X3) Y)) (@ (@ tptp.minus_minus_int X3) Y)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X3))) (= (@ (@ 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 X3) A)) B))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X3))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y)) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y) B))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X3) A)) B))))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X3))) (= (@ (@ 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 X3) A)) B))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.product_prod_num_num)) (=> (not (= X3 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N3 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N3))))) (=> (forall ((N3 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N3))))) (=> (forall ((M5 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit0 N3))))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit1 N3))))) (=> (forall ((M5 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit0 N3))))) (not (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit1 N3))))))))))))))))
% 6.44/6.78 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) N) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 6.44/6.78 (assert (forall ((B tptp.nat) (A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B)) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 6.44/6.78 (assert (forall ((B tptp.int) (A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B)) N) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.44/6.78 (assert (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B2) A3) tptp.zero_zero_nat))))
% 6.44/6.78 (assert (= tptp.dvd_dvd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B2) A3) tptp.zero_zero_int))))
% 6.44/6.78 (assert (= tptp.dvd_dvd_Code_integer (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B2) A3) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) (@ _let_1 N))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) (@ _let_1 N))))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (N tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))))
% 6.44/6.78 (assert (forall ((A tptp.complex) (N tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B))))))
% 6.44/6.78 (assert (forall ((X3 tptp.code_integer) (Y tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X3) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X3) N)) (@ (@ tptp.power_8256067586552552935nteger Y) M))))))
% 6.44/6.78 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X3) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X3) N)) (@ (@ tptp.power_power_nat Y) M))))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X3) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.power_power_real Y) M))))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X3) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X3) N)) (@ (@ tptp.power_power_int Y) M))))))
% 6.44/6.78 (assert (forall ((X3 tptp.complex) (Y tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X3) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.power_power_complex Y) M))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (not (@ (@ tptp.dvd_dvd_nat N) M))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M) N) (@ _let_1 M))))))
% 6.44/6.78 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_int M) N) (=> (@ (@ tptp.dvd_dvd_int N) M) (= M N))))))))
% 6.44/6.78 (assert (forall ((K tptp.int) (M tptp.int) (T tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (not (= K tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M) T) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 T)))))))
% 6.44/6.78 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (=> (not (= K tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M) N))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X5) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D3)) (= (@ _let_2 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D3))))))))))
% 6.44/6.78 (assert (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X3 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 X3) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D)) (= (@ _let_2 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y)) D))) (exists ((X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A) B))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X5) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D)) (= (@ _let_3 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D)))))))))))))))))
% 6.44/6.78 (assert (forall ((I2 tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I2) K) (=> (@ P K) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I4) K) (=> (@ P I4) (@ P (@ (@ tptp.minus_minus_int I4) tptp.one_one_int))))) (@ P I2))))))
% 6.44/6.78 (assert (forall ((I2 tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I2) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_int I4) K) (=> (@ P I4) (@ P (@ (@ tptp.minus_minus_int I4) tptp.one_one_int))))) (@ P I2))))))
% 6.44/6.78 (assert (forall ((K tptp.int) (N tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N) (@ (@ tptp.times_times_int K) M))) (@ _let_1 N)))))
% 6.44/6.78 (assert (forall ((A tptp.int) (D tptp.int) (X3 tptp.int) (T tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X3))) (let ((_let_2 (@ tptp.dvd_dvd_int A))) (=> (@ _let_2 D) (= (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C) D))) T))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.rat Bool)) (L2 tptp.rat)) (= (exists ((X2 tptp.rat)) (@ P (@ (@ tptp.times_times_rat L2) X2))) (exists ((X2 tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L2) (@ (@ tptp.plus_plus_rat X2) tptp.zero_zero_rat)) (@ P X2))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 6.44/6.78 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X3 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X3) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X3) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 6.44/6.78 (assert (forall ((Y tptp.real) (Z tptp.real) (X3 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 X3) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X3) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 6.44/6.78 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X3) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X3) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 6.44/6.78 (assert (forall ((Z tptp.complex) (X3 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X3) Z)) Y)) Z)))))
% 6.44/6.78 (assert (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X3) Z)) Y)) Z)))))
% 6.44/6.78 (assert (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X3) Z)) Y)) Z)))))
% 6.44/6.78 (assert (forall ((Z tptp.complex) (X3 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X3) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.44/6.78 (assert (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X3) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.44/6.78 (assert (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X3) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.44/6.78 (assert (forall ((X3 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X3) X3)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X3) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X3) tptp.one_one_complex)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X3) X3)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X3) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X3) tptp.one_one_real)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X3) X3)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X3) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X3) tptp.one_one_rat)))))
% 6.44/6.78 (assert (forall ((X3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X3) X3)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X3) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X3) tptp.one_one_int)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N tptp.zero_zero_nat)))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N tptp.zero_zero_nat)))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N tptp.zero_zero_nat)))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 6.44/6.78 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1))))))
% 6.44/6.78 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1))))))
% 6.44/6.78 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_1))))))
% 6.44/6.78 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))))
% 6.44/6.78 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))))
% 6.44/6.78 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_1))))))
% 6.44/6.78 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))))
% 6.44/6.78 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))))
% 6.44/6.78 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat K) N)))))
% 6.44/6.78 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 6.44/6.78 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D3))))))))
% 6.44/6.78 (assert (forall ((Z tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int Z) N)))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N)) (not (@ (@ tptp.dvd_dvd_nat N) M)))))
% 6.44/6.78 (assert (forall ((D tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P1 X5) (@ P1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P1 X5))))) (=> (exists ((X_1 tptp.int)) (@ P1 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))))
% 6.44/6.78 (assert (forall ((D tptp.int) (P3 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P3 X5) (@ P3 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((X_1 tptp.int)) (@ P3 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))))
% 6.44/6.78 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I2 tptp.int)) (=> (@ P K) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I4) (=> (@ P I4) (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I4) K) (=> (@ P I4) (@ P (@ (@ tptp.minus_minus_int I4) tptp.one_one_int))))) (@ P I2))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 6.44/6.78 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.44/6.78 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.44/6.78 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B5 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B5 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B5) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B5) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B5)))))))))))))))
% 6.44/6.78 (assert (forall ((A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B5 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B5 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B5) tptp.one_one_nat) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_times_nat A) B5) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B5)))))))))))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B5 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B5 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B5) tptp.one_one_int) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_times_int A) B5) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B5)))))))))))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B5))))))))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B5))))))))
% 6.44/6.78 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B5))))))))
% 6.44/6.78 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 6.44/6.78 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 6.44/6.78 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((Y tptp.real) (Z tptp.real) (X3 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 X3) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X3) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 6.44/6.78 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X3) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X3) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 6.44/6.78 (assert (= (lambda ((Y5 tptp.code_integer) (Z3 tptp.code_integer)) (= Y5 Z3)) (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide6298287555418463151nteger A3) _let_1) (@ (@ tptp.divide6298287555418463151nteger B2) _let_1))))))))
% 6.44/6.78 (assert (= (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide_divide_nat A3) _let_1) (@ (@ tptp.divide_divide_nat B2) _let_1))))))))
% 6.44/6.78 (assert (= (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3)) (lambda ((A3 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide_divide_int A3) _let_1) (@ (@ tptp.divide_divide_int B2) _let_1))))))))
% 6.44/6.78 (assert (forall ((Y tptp.real) (Z tptp.real) (X3 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 X3) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X3) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 6.44/6.78 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X3) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X3) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 6.44/6.78 (assert (forall ((X3 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X3))) (=> (not (= X3 tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X3) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X3))) (=> (not (= X3 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X3) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X3))) (=> (not (= X3 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X3) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))))
% 6.44/6.78 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))))
% 6.44/6.78 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat))))
% 6.44/6.78 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (X3 tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X3 tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X3) (@ (@ tptp.power_8256067586552552935nteger X3) N)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (X3 tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X3 tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X3) (@ (@ tptp.power_power_rat X3) N)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (X3 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X3 tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X3) (@ (@ tptp.power_power_nat X3) N)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X3 tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X3) (@ (@ tptp.power_power_real X3) N)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (X3 tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X3 tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X3) (@ (@ tptp.power_power_int X3) N)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (X3 tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X3 tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X3) (@ (@ tptp.power_power_complex X3) N)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat A) A)) A))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X3) Y)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y) X3)) _let_1)))))
% 6.44/6.78 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X3) Y)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y) X3)) _let_1)))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X3) Y)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y) X3)) _let_1)))))
% 6.44/6.78 (assert (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X3) Y)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y) X3)) _let_1)))))
% 6.44/6.78 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M)) M) (= N tptp.one_one_nat)))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N)) M) (= N tptp.one_one_nat)))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I2) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.44/6.78 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X tptp.int)) (=> (@ P X) (@ P (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K) D))))))))))
% 6.44/6.78 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L2)) (or (@ (@ tptp.dvd_dvd_int L2) K) (and (= L2 tptp.zero_zero_int) (@ _let_1 K)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2))))))
% 6.44/6.78 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (=> (@ (@ tptp.ord_less_eq_int L2) K) (= (@ (@ tptp.modulo_modulo_int K) L2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) L2)) L2))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((U tptp.real) (V tptp.real) (R2 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_eq_real R2) S) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.minus_minus_real V) U))) S))) V))))))
% 6.44/6.78 (assert (forall ((U tptp.rat) (V tptp.rat) (R2 tptp.rat) (S tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (=> (@ (@ tptp.ord_less_eq_rat R2) S) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R2) (@ (@ tptp.minus_minus_rat V) U))) S))) V))))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 6.44/6.78 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 6.44/6.78 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))))
% 6.44/6.78 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (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)))))))
% 6.44/6.78 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 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 X3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S)) X3) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X3) _let_2))) _let_4))))))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_Code_integer))))))))
% 6.44/6.78 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_nat))))))))
% 6.44/6.78 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_int))))))))
% 6.44/6.78 (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))))))))))
% 6.44/6.78 (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))))))))))
% 6.44/6.78 (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))))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) N)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N)))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (@ _let_1 A))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (@ _let_1 A))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (@ _let_1 A))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.44/6.78 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X3 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 X3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd2)) X3) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X3) _let_2))) _let_4))))))))
% 6.44/6.78 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (=> (@ (@ tptp.ord_less_eq_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K) L2)) L2)) tptp.one_one_int))))))
% 6.44/6.78 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X3 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 X3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Vc)) X3) (or (= X3 Mi) (= X3 Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X3) _let_2))) _let_4)))))))))
% 6.44/6.78 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X3)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X3) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X3) (=> (not (= X3 Mi)) (=> (not (= X3 Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X3) _let_2))) _let_4))))))))))))))))
% 6.44/6.78 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 6.44/6.78 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 6.44/6.78 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 6.44/6.78 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_rat (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (assert (forall ((W tptp.real) (Y tptp.real) (X3 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X3))) (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 X3) (= Y Z)))))))
% 6.44/6.78 (assert (forall ((W tptp.rat) (Y tptp.rat) (X3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X3))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X3) (= Y Z)))))))
% 6.44/6.78 (assert (forall ((W tptp.nat) (Y tptp.nat) (X3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X3))) (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 X3) (= Y Z)))))))
% 6.44/6.78 (assert (forall ((W tptp.int) (Y tptp.int) (X3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X3))) (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 X3) (= Y Z)))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X3) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X3)) Y)))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X3)) Y)))))))
% 6.44/6.78 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X3) Y)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X3)) Y)))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X3) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X3)) Y)))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (@ _let_1 A))))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)))) (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)) (= X3 (@ (@ (@ (@ 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))))))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X3) Xa2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (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)) (= X3 (@ (@ (@ (@ 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))))))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X3) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) 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)) (= X3 (@ (@ (@ (@ 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))))))))))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X3) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ 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)) (= X3 (@ (@ (@ (@ 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 ((Vd tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) _let_2) (= (@ (@ tptp.minus_8373710615458151222nteger _let_2) B) (@ _let_1 B)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (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)))))))))
% 6.44/6.78 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_1 (= A tptp.zero_zero_rat))))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X3) Xa2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high 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)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) 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))))))))))))))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X3) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (not (= X3 (@ (@ tptp.vEBT_Leaf Uu) Uv)))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ 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)) (= X3 (@ (@ (@ (@ 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 ((Vd tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X3) Xa2) Y) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X3 (@ (@ tptp.vEBT_Leaf Uu) Uv))) Y) (=> (=> (exists ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2))) Y) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ 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)) (= X3 (@ (@ (@ (@ 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 ((Vd tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (= 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))))))))))))))))
% 6.44/6.78 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X3) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X3))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X3) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X3 Mi) (= X3 Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X3) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X3) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ 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)) (= X3 (@ (@ (@ (@ 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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high 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)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) 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))))))))))))))))))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ 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 (= X3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high 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)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) 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))))))))))))))))))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((L2 tptp.num) (R2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L2) (@ (@ tptp.product_Pair_nat_nat Q2) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R2))))))))))
% 6.44/6.78 (assert (forall ((L2 tptp.num) (R2 tptp.int) (Q2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L2) (@ (@ tptp.product_Pair_int_int Q2) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_int L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R2))))))))))
% 6.44/6.78 (assert (forall ((L2 tptp.num) (R2 tptp.code_integer) (Q2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L2) (@ (@ tptp.produc1086072967326762835nteger Q2) R2)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R2))))))))))
% 6.44/6.78 (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))))))))
% 6.44/6.78 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X3) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 _let_2) (=> (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B5))) (=> (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) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) (=> (= X3 _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) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (=> (= X3 _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))) (=> (= X3 _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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat 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))) (=> (= X3 _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))))))))))))))))))))))
% 6.44/6.78 (assert (forall ((X3 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 X3) _let_1) (@ (@ tptp.divide_divide_nat Y) _let_1)) (=> (= (@ _let_2 X3) (@ _let_2 Y)) (= X3 Y)))))))
% 6.44/6.78 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.44/6.78 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.44/6.78 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 6.44/6.78 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.44/6.78 (assert (forall ((X3 tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X3) Y) (=> (=> (= X3 tptp.zero_zero_nat) _let_1) (=> (=> (= X3 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X3 _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)))))))))))))))))))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool)) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (=> (@ P X3) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X3)) I2))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (N tptp.nat) (P (-> tptp.int Bool)) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N) (=> (@ P X3) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X3)) I2))))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (N tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N) (=> (@ P X3) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X3)) I2))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 6.44/6.78 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 6.44/6.78 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 6.44/6.78 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 6.44/6.78 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 6.44/6.78 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 6.44/6.78 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 6.44/6.78 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K))))
% 6.44/6.78 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.44/6.78 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ _let_1 (@ _let_1 I2)) I2)))))
% 6.44/6.78 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) K))))))
% 6.44/6.78 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)))
% 6.44/6.78 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 6.44/6.78 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 6.44/6.78 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.44/6.78 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.44/6.78 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.44/6.78 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 6.44/6.78 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 6.44/6.78 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 6.44/6.78 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 6.44/6.78 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.44/6.78 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.44/6.78 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.44/6.78 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.44/6.78 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.44/6.78 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) B))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= M N))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= M N))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M N))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M N))))
% 6.44/6.78 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= M N))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (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)))))
% 6.44/6.78 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat A) B)))))
% 6.44/6.78 (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))))
% 6.44/6.78 (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))))
% 6.44/6.78 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) B))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (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))))))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B))))))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 6.44/6.78 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 6.44/6.78 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 6.44/6.78 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 6.44/6.78 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 6.44/6.78 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 6.44/6.79 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X3)) Y) (@ (@ tptp.dvd_dvd_int X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X3)) Y) (@ (@ tptp.dvd_dvd_real X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X3)) Y) (@ (@ tptp.dvd_dvd_complex X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.uminus1351360451143612070nteger X3)) Y) (@ (@ tptp.dvd_dvd_Code_integer X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X3)) Y) (@ (@ tptp.dvd_dvd_rat X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X3))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X3))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y)) (@ _let_1 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X3))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y)) (@ _let_1 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X3))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger Y)) (@ _let_1 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X3))) (= (@ _let_1 (@ tptp.uminus_uminus_rat Y)) (@ _let_1 Y)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat I2) (@ (@ tptp.minus_minus_nat J2) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) J2)))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J2) K)) I2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J2) I2)) K)))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J2) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 6.44/6.79 (assert (forall ((M tptp.nat) (X3 tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X3) (@ (@ tptp.replicate_VEBT_VEBT N) Y)) (and (= M N) (=> (not (= M tptp.zero_zero_nat)) (= X3 Y))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (X3 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X3)) N)))
% 6.44/6.79 (assert (forall ((N tptp.nat) (X3 Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N) X3)) N)))
% 6.44/6.79 (assert (forall ((N tptp.nat) (X3 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N) X3)) N)))
% 6.44/6.79 (assert (forall ((N tptp.nat) (X3 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N) X3)) N)))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.44/6.79 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.44/6.79 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))))
% 6.44/6.79 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.44/6.79 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.44/6.79 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 6.44/6.79 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.44/6.79 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.44/6.79 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.44/6.79 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 6.44/6.79 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 6.44/6.79 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int _let_2) _let_1)))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (let ((_let_2 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real _let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (let ((_let_2 (@ tptp.numeral_numeral_rat M))) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat _let_2)) (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat _let_2) _let_1)))))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 6.44/6.79 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 6.44/6.79 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.44/6.79 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.44/6.79 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 6.44/6.79 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 6.44/6.79 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.44/6.79 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.44/6.79 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 6.44/6.79 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 6.44/6.79 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.divide_divide_real X3) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X3) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (= (@ (@ tptp.divide_divide_rat X3) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X3))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J2) K))) I2) (@ (@ tptp.minus_minus_nat (@ tptp.suc J2)) (@ (@ tptp.plus_plus_nat K) I2))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat I2) (@ tptp.suc (@ (@ tptp.minus_minus_nat J2) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ tptp.suc J2))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N) _let_1) _let_1))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N) _let_1) _let_1))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (N tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X3) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) Y))) (and (= X3 Y) (not (= N tptp.zero_zero_nat))))))
% 6.44/6.79 (assert (forall ((X3 tptp.complex) (N tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N) Y))) (and (= X3 Y) (not (= N tptp.zero_zero_nat))))))
% 6.44/6.79 (assert (forall ((X3 tptp.product_prod_nat_nat) (N tptp.nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.replic4235873036481779905at_nat N) Y))) (and (= X3 Y) (not (= N tptp.zero_zero_nat))))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (N tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X3) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) Y))) (and (= X3 Y) (not (= N tptp.zero_zero_nat))))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (N tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) Y))) (and (= X3 Y) (not (= N tptp.zero_zero_nat))))))
% 6.44/6.79 (assert (forall ((X3 tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) Y))) (and (= X3 Y) (not (= N tptp.zero_zero_nat))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.44/6.79 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N) (@ tptp.pred_numeral K)))))
% 6.44/6.79 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N))))
% 6.44/6.79 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 6.44/6.79 (assert (forall ((I2 tptp.nat) (N tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X3)) I2) X3))))
% 6.44/6.79 (assert (forall ((I2 tptp.nat) (N tptp.nat) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X3)) I2) X3))))
% 6.44/6.79 (assert (forall ((I2 tptp.nat) (N tptp.nat) (X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X3)) I2) X3))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_numeral_dbl_rat _let_1))))))
% 6.44/6.79 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.44/6.79 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.44/6.79 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.44/6.79 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.44/6.79 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.44/6.79 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.44/6.79 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.44/6.79 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.44/6.79 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 6.44/6.79 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.44/6.79 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.44/6.79 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.44/6.79 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.44/6.79 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.44/6.79 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.44/6.79 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.44/6.79 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.44/6.79 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.44/6.79 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.44/6.79 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.44/6.79 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.44/6.79 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.44/6.79 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.79 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= N tptp.one))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= N tptp.one))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= N tptp.one))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N tptp.one))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N tptp.one))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (= N tptp.one))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.44/6.79 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.79 (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)))))))))
% 6.44/6.79 (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)))))))))
% 6.44/6.79 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.44/6.79 (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)))))))))
% 6.44/6.79 (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)))))))))
% 6.44/6.79 (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)))))))))
% 6.44/6.79 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.44/6.79 (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)))))))))
% 6.44/6.79 (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)))))))))
% 6.44/6.79 (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)))))))))
% 6.44/6.79 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.44/6.79 (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)))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Y))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N) (@ tptp.pred_numeral K)))))
% 6.44/6.79 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.pred_numeral K)))))
% 6.44/6.79 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_num N) M))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_num N) M))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_num N) M))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_num N) M))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) (@ tptp.pred_numeral K))))))
% 6.44/6.79 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)))) (not (= M tptp.one)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (not (= M tptp.one)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.44/6.79 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.44/6.79 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.44/6.79 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.44/6.79 (assert (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))
% 6.44/6.79 (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)))
% 6.44/6.79 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 6.44/6.79 (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))
% 6.44/6.79 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.44/6.79 (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))
% 6.44/6.79 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.44/6.79 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.44/6.79 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int A) N))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real A) N))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.complex)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex A) N))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger A) N))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat A) N))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.power_power_int A) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.power_power_real A) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.power_power_complex A) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.power_power_rat A) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (or (@ (@ tptp.ord_less_nat M) N) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.44/6.79 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.44/6.79 (assert (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int)))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_real)))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_complex)))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_Code_integer)))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_rat)))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int _let_1) N) _let_1)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real _let_1) N) _let_1)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_complex _let_1) N) _let_1)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) N) _let_1)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat _let_1) N) _let_1)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N) tptp.one_one_int))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N) tptp.one_one_real))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N) tptp.one_one_complex))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N) tptp.one_one_Code_integer))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N) tptp.one_one_rat))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (= (= X3 (@ (@ tptp.minus_minus_real Y) Z)) (= Y (@ (@ tptp.plus_plus_real X3) Z)))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.44/6.79 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_eq_rat B) (@ tptp.uminus_uminus_rat A)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) A))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_rat B) (@ tptp.uminus_uminus_rat A)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) A))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) A) (@ (@ tptp.times_times_rat B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_rat B))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.times_times_rat A) (@ tptp.uminus_uminus_rat B)))))
% 6.44/6.79 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.44/6.79 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.44/6.79 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.44/6.79 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.44/6.79 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A2 (@ (@ tptp.plus_plus_rat K) A)) (= (@ tptp.uminus_uminus_rat A2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ tptp.uminus_uminus_rat A))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.44/6.79 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B)) A) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) B))))
% 6.44/6.79 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real B)) A) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) B))))
% 6.44/6.79 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.44/6.79 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat B)) A) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) B))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B))))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B))))
% 6.44/6.79 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I2 tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P (@ (@ tptp.minus_minus_nat K) I2))))))
% 6.44/6.79 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L2) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))))
% 6.44/6.79 (assert (forall ((J2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J2) N)) K))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) (or (@ (@ tptp.ord_less_nat N) M) (@ _let_1 N))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L2)) (@ (@ tptp.minus_minus_nat N) L2)))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N)))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 M)))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int) (A4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) (@ (@ tptp.modulo_modulo_int A4) B)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A4)) B)))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (A4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) (@ (@ tptp.modulo364778990260209775nteger A4) B)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A4)) B)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M) N)))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M) N))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X5)) (@ _let_2 Y3)) D3) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X5)) (@ _let_1 Y3)) D3)))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.44/6.79 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.44/6.79 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.44/6.79 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.44/6.79 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.44/6.79 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.44/6.79 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.44/6.79 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.44/6.79 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.44/6.79 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.44/6.79 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.44/6.79 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.44/6.79 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.44/6.79 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.44/6.79 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.44/6.79 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.44/6.79 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.44/6.79 (assert (forall ((W tptp.num) (X3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X3)) (@ (@ tptp.times_times_int X3) (@ tptp.uminus_uminus_int _let_1))))))
% 6.44/6.79 (assert (forall ((W tptp.num) (X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X3)) (@ (@ tptp.times_times_real X3) (@ tptp.uminus_uminus_real _let_1))))))
% 6.44/6.79 (assert (forall ((W tptp.num) (X3 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X3)) (@ (@ tptp.times_times_complex X3) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 6.44/6.79 (assert (forall ((W tptp.num) (X3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X3)) (@ (@ tptp.times_3573771949741848930nteger X3) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 6.44/6.79 (assert (forall ((W tptp.num) (X3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X3)) (@ (@ tptp.times_times_rat X3) (@ tptp.uminus_uminus_rat _let_1))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B)))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int)) (= (= (@ (@ tptp.times_times_int X3) X3) tptp.one_one_int) (or (= X3 tptp.one_one_int) (= X3 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real)) (= (= (@ (@ tptp.times_times_real X3) X3) tptp.one_one_real) (or (= X3 tptp.one_one_real) (= X3 (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.44/6.79 (assert (forall ((X3 tptp.complex)) (= (= (@ (@ tptp.times_times_complex X3) X3) tptp.one_one_complex) (or (= X3 tptp.one_one_complex) (= X3 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.44/6.79 (assert (forall ((X3 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X3) X3) tptp.one_one_Code_integer) (or (= X3 tptp.one_one_Code_integer) (= X3 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (= (= (@ (@ tptp.times_times_rat X3) X3) tptp.one_one_rat) (or (= X3 tptp.one_one_rat) (= X3 (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.44/6.79 (assert (forall ((B3 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B3 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))))
% 6.44/6.79 (assert (forall ((B3 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B3 (@ (@ tptp.plus_plus_real K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B)))))))
% 6.44/6.79 (assert (forall ((B3 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B3 (@ (@ tptp.plus_plus_complex K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B)))))))
% 6.44/6.79 (assert (forall ((B3 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B3 (@ (@ tptp.plus_p5714425477246183910nteger K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B)))))))
% 6.44/6.79 (assert (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B3 (@ (@ tptp.plus_plus_rat K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B)))))))
% 6.44/6.79 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))
% 6.44/6.79 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))))
% 6.44/6.79 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.44/6.79 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.44/6.79 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))
% 6.44/6.79 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))
% 6.44/6.79 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))))
% 6.44/6.79 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.44/6.79 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.44/6.79 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))
% 6.44/6.79 (assert (forall ((Xs tptp.list_real) (N tptp.nat) (X3 tptp.real)) (=> (= (@ tptp.size_size_list_real Xs) N) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs)) (= Y3 X3))) (= Xs (@ (@ tptp.replicate_real N) X3))))))
% 6.44/6.79 (assert (forall ((Xs tptp.list_complex) (N tptp.nat) (X3 tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs) N) (=> (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) (@ tptp.set_complex2 Xs)) (= Y3 X3))) (= Xs (@ (@ tptp.replicate_complex N) X3))))))
% 6.44/6.79 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (N tptp.nat) (X3 tptp.product_prod_nat_nat)) (=> (= (@ tptp.size_s5460976970255530739at_nat Xs) N) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y3) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (= Y3 X3))) (= Xs (@ (@ tptp.replic4235873036481779905at_nat N) X3))))))
% 6.44/6.79 (assert (forall ((Xs tptp.list_VEBT_VEBT) (N tptp.nat) (X3 tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N) (=> (forall ((Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y3) (@ tptp.set_VEBT_VEBT2 Xs)) (= Y3 X3))) (= Xs (@ (@ tptp.replicate_VEBT_VEBT N) X3))))))
% 6.44/6.79 (assert (forall ((Xs tptp.list_o) (N tptp.nat) (X3 Bool)) (=> (= (@ tptp.size_size_list_o Xs) N) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ tptp.set_o2 Xs)) (= Y3 X3))) (= Xs (@ (@ tptp.replicate_o N) X3))))))
% 6.44/6.79 (assert (forall ((Xs tptp.list_nat) (N tptp.nat) (X3 tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs) N) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs)) (= Y3 X3))) (= Xs (@ (@ tptp.replicate_nat N) X3))))))
% 6.44/6.79 (assert (forall ((Xs tptp.list_int) (N tptp.nat) (X3 tptp.int)) (=> (= (@ tptp.size_size_list_int Xs) N) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs)) (= Y3 X3))) (= Xs (@ (@ tptp.replicate_int N) X3))))))
% 6.44/6.79 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X3 tptp.vEBT_VEBT)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (= X5 X3))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs)) X3) Xs))))
% 6.44/6.79 (assert (forall ((Xs tptp.list_o) (X3 Bool)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (= X5 X3))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs)) X3) Xs))))
% 6.44/6.79 (assert (forall ((Xs tptp.list_nat) (X3 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (= X5 X3))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs)) X3) Xs))))
% 6.44/6.79 (assert (forall ((Xs tptp.list_int) (X3 tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (= X5 X3))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs)) X3) Xs))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B)))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) M))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M) N)))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))))
% 6.44/6.79 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat J2) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) J2))))
% 6.44/6.79 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (= (@ (@ tptp.minus_minus_nat J2) I2) K) (= J2 (@ (@ tptp.plus_plus_nat K) I2))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J2) I2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J2) K)) I2)))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J2) K)))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat J2) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) J2)))))
% 6.44/6.79 (assert (forall ((J2 tptp.nat) (K tptp.nat) (I2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J2) K)) I2) (@ (@ tptp.ord_less_eq_nat J2) (@ (@ tptp.plus_plus_nat I2) K)))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))))
% 6.44/6.79 (assert (forall ((M tptp.int) (N tptp.int)) (=> (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.44/6.79 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (and (= M tptp.one_one_int) (= N tptp.one_one_int)) (and (= M _let_1) (= N _let_1)))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 6.44/6.79 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M6) N2)) M6) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M6) N2)) N2)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (@ (@ tptp.dvd_dvd_nat Q2) (@ (@ tptp.minus_minus_nat M) N))))))
% 6.44/6.79 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 6.44/6.79 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L2) tptp.zero_zero_int)) (not (= (@ (@ tptp.modulo_modulo_int K) L2) tptp.zero_zero_int)))))
% 6.44/6.79 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int K))) (=> (not (= (@ _let_1 (@ tptp.uminus_uminus_int L2)) tptp.zero_zero_int)) (not (= (@ _let_1 L2) tptp.zero_zero_int))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N) M)) M) (@ (@ tptp.ord_max_nat N) M))))
% 6.44/6.79 (assert (forall ((Z tptp.extended_enat) (Y tptp.extended_enat) (X3 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X3))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y)) Z))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.44/6.79 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.79 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.44/6.79 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.44/6.79 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.44/6.79 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.79 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.44/6.79 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.44/6.79 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.44/6.79 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.44/6.79 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.44/6.79 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.44/6.79 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.44/6.79 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.44/6.79 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.44/6.79 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))) (= (@ (@ tptp.times_times_rat C) B) (@ tptp.uminus_uminus_rat A))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) C) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.times_times_rat C) B))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B) (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) (@ tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B tptp.zero_zero_rat)) (= A (@ tptp.uminus_uminus_rat B))))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 6.44/6.79 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.44/6.79 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat B) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) (@ tptp.uminus_uminus_rat B))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.44/6.79 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.44/6.79 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) B) (@ tptp.uminus_uminus_rat B))))
% 6.44/6.79 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.44/6.79 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.44/6.79 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.44/6.79 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.44/6.79 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.44/6.79 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ (@ tptp.power_power_int A) N)))))
% 6.44/6.79 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.power_power_real A) N)))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ (@ tptp.power_power_complex A) N)))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ (@ tptp.power_power_rat A) N)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X3)) _let_1) (@ (@ tptp.power_power_int X3) _let_1)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X3)) _let_1) (@ (@ tptp.power_power_real X3) _let_1)))))
% 6.44/6.79 (assert (forall ((X3 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X3)) _let_1) (@ (@ tptp.power_power_complex X3) _let_1)))))
% 6.44/6.79 (assert (forall ((X3 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X3)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X3) _let_1)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X3)) _let_1) (@ (@ tptp.power_power_rat X3) _let_1)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X3)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X3) _let_1))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X3)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X3) _let_1))))))
% 6.44/6.79 (assert (forall ((X3 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X3)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X3) _let_1))))))
% 6.44/6.79 (assert (forall ((X3 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X3)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X3) _let_1))))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X3)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X3) _let_1))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I2))) N))))
% 6.44/6.79 (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)))))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J2) K)) I2) (@ (@ tptp.ord_less_nat J2) (@ (@ tptp.plus_plus_nat I2) K))))))
% 6.44/6.79 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))))
% 6.44/6.79 (assert (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M)) N)))))
% 6.44/6.79 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))))
% 6.44/6.79 (assert (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) 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 J2) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M)) N)))))
% 6.44/6.79 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))))
% 6.44/6.79 (assert (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M) N)))))
% 6.44/6.79 (assert (forall ((Q2 tptp.nat) (N tptp.nat) (R2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R2) M))) (let ((_let_2 (@ tptp.dvd_dvd_nat M))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q2))) (=> (@ _let_3 N) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N) Q2)) (@ _let_2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat _let_1) Q2)))))))))))
% 6.44/6.79 (assert (forall ((R2 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R2) N) (=> (@ (@ tptp.ord_less_eq_nat R2) M) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M) R2)) (= (@ (@ tptp.modulo_modulo_nat M) N) R2))))))
% 6.44/6.79 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N2)) N2)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= _let_1 tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int B) _let_1)))))))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= _let_2 tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) B))))))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.44/6.79 (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)))))))))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B))) (let ((_let_4 (@ (@ tptp.times_times_rat A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 6.44/6.79 (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)))))))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.44/6.79 (assert (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X3) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X3)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.44/6.79 (assert (forall ((Z tptp.complex) (X3 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X3) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X3)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.44/6.79 (assert (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X3) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X3)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.44/6.79 (assert (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X3) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X3)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.44/6.79 (assert (forall ((Z tptp.complex) (X3 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X3) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X3)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.44/6.79 (assert (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X3) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X3)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (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))))))))
% 6.44/6.79 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X3) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (or (= X3 Y) (= X3 (@ tptp.uminus_uminus_int Y)))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X3) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (or (= X3 Y) (= X3 (@ tptp.uminus_uminus_real Y)))))))
% 6.44/6.79 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X3) _let_1) (@ (@ tptp.power_power_complex Y) _let_1)) (or (= X3 Y) (= X3 (@ tptp.uminus1482373934393186551omplex Y)))))))
% 6.44/6.79 (assert (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X3) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (or (= X3 Y) (= X3 (@ tptp.uminus1351360451143612070nteger Y)))))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X3) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (or (= X3 Y) (= X3 (@ tptp.uminus_uminus_rat Y)))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (let ((_let_2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1482373934393186551omplex _let_1)))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M)) (@ _let_1 N))))))))
% 6.44/6.79 (assert (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_real (@ _let_1 M)) (@ _let_1 N))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_rat (@ _let_1 M)) (@ _let_1 N))))))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N))))))))
% 6.44/6.79 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N))))))))
% 6.44/6.79 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 6.44/6.79 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 6.44/6.79 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 6.44/6.79 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))))
% 6.44/6.79 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M6) N2) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M6) N2)) N2))))))
% 6.44/6.79 (assert (= tptp.plus_plus_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N2))))))
% 6.44/6.79 (assert (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M)) N)))))
% 6.44/6.79 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))))
% 6.44/6.79 (assert (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N2))))))
% 6.44/6.79 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B3) N)) (@ (@ tptp.divide_divide_int A2) N))))))
% 6.44/6.79 (assert (forall ((B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.divide_divide_int _let_1) B) _let_1)))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.44/6.79 (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))))))))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))))
% 6.44/6.79 (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)))))))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 6.44/6.79 (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)))))))))))))
% 6.44/6.79 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.44/6.79 (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)))))))))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.44/6.79 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N2 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A3) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N2 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger _let_2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))))))))))
% 6.44/6.79 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A3) _let_1))) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int _let_2)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) _let_1))))))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (or (= A tptp.one_one_rat) (= A (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (@ (@ tptp.power_power_complex _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_2 (@ (@ tptp.power_power_rat _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_zero_nat)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_zero_nat))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_zero_int)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_zero_int))))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))))
% 6.44/6.79 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (assert (= tptp.power_power_rat (lambda ((P4 tptp.rat) (M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P4) (@ (@ tptp.power_power_rat P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.44/6.79 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))))
% 6.44/6.79 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L2) (@ (@ tptp.minus_minus_int (@ (@ tptp.minus_minus_int L2) tptp.one_one_int)) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) L2))))))
% 6.44/6.79 (assert (forall ((B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) B) (@ (@ tptp.minus_minus_int B) tptp.one_one_int)))))
% 6.44/6.79 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B)))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))))
% 6.44/6.79 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ _let_1 B)))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R2 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q2))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (not (= B tptp.zero_zero_int)) (@ (@ (@ tptp.eucl_rel_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.product_Pair_int_int (@ (@ _let_1 _let_2) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int))) (@ (@ _let_1 tptp.zero_zero_int) (@ (@ tptp.minus_minus_int B) R2))))))))))
% 6.44/6.79 (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))))))))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 6.44/6.79 (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)))))))))))))
% 6.44/6.79 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 6.44/6.79 (assert (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X3) (=> (@ (@ tptp.ord_le3102999989581377725nteger X3) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X3) (=> (@ (@ tptp.ord_less_eq_rat X3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X3) (=> (@ (@ tptp.ord_less_eq_int X3) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.44/6.79 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.44/6.79 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) (@ (@ tptp.power_power_complex A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) _let_1))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) K))))
% 6.44/6.79 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat)) (=> (not (= X3 tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X3 (@ tptp.suc N3))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) _let_3)) _let_2))))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))))
% 6.44/6.79 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K) (@ tptp.uminus_uminus_int (@ _let_1 N))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))))
% 6.44/6.79 (assert (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 6.44/6.79 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X3) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X3 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) (=> (= X3 _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))) (=> (= X3 _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))) (=> (= X3 _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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high 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))) (=> (= X3 _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))))))))))))))))))))))))))
% 6.44/6.79 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X3) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 _let_1) (=> (= Y (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B5) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) (=> (= X3 _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))) (=> (= X3 _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))) (=> (= X3 _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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high 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)))) (=> (= X3 _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))))))))))))))))))))))
% 6.44/6.79 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X3) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X3 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) (=> (= X3 _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))) (=> (= X3 _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))))))))))))))))
% 6.44/6.79 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X3) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X3 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (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))) (=> (= X3 _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))))))))))))))))
% 6.44/6.79 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X3) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 _let_1) (=> (= Y (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B5) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) (=> (= X3 _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)))) (=> (= X3 _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))))))))))))))))))
% 6.44/6.79 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X3) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X3 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high 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))) (=> (= X3 _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))))))))))))))))))))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X3) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X3 A))))
% 6.44/6.79 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J2)))))
% 6.44/6.79 (assert (= tptp.minus_minus_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real Y6)))))
% 6.44/6.79 (assert (forall ((U tptp.real) (X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X3) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X3)) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X3) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) (@ tptp.uminus_uminus_real X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X3)) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X3) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.uminus_uminus_real X3)))))
% 6.44/6.79 (assert (forall ((C tptp.real)) (= (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C)) (@ tptp.times_times_real C))))
% 6.44/6.79 (assert (forall ((C tptp.rat)) (= (lambda ((X2 tptp.rat)) (@ (@ tptp.times_times_rat X2) C)) (@ tptp.times_times_rat C))))
% 6.44/6.79 (assert (forall ((C tptp.nat)) (= (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat X2) C)) (@ tptp.times_times_nat C))))
% 6.44/6.79 (assert (forall ((C tptp.int)) (= (lambda ((X2 tptp.int)) (@ (@ tptp.times_times_int X2) C)) (@ tptp.times_times_int C))))
% 6.44/6.79 (assert (forall ((U tptp.real) (X3 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 X3) _let_1)))))
% 6.44/6.79 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X3) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X3 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2))) (=> (= X3 _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))) (=> (= X3 _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)))) (=> (= X3 _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) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (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)))) (=> (= X3 _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))))))))))))))))))))
% 6.44/6.79 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X3) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X3 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2))) (=> (= X3 _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))) (=> (= X3 _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))) (=> (= X3 _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) (Vd 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) Vd))) (=> (= X3 _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))))))))))))))))))
% 6.44/6.79 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X3) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) 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))) (=> (= X3 _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))) (=> (= X3 _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) (Vd 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) Vd))) (=> (= X3 _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)))))))))))))))))
% 6.44/6.79 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (not (= A2 B3)) (@ (@ tptp.ord_less_set_int A2) B3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X3)) (@ tptp.uminus1532241313380277803et_int Y)) (@ (@ tptp.ord_less_eq_set_int Y) X3))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X5))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_nat A2) B3))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.member_real X5))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_real A2) B3))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (forall ((X5 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X5))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_le211207098394363844omplex A2) B3))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X5 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X5))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.member_int X5))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= A2 B3)))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int A2)) (@ tptp.uminus1532241313380277803et_int B3)) (@ (@ tptp.ord_less_eq_set_int B3) A2))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int B3)) (@ tptp.uminus1532241313380277803et_int A2)))))
% 6.44/6.79 (assert (forall ((L2 tptp.set_int) (H2 tptp.set_int) (L3 tptp.set_int) (H3 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int L2) H2) (@ (@ tptp.set_or370866239135849197et_int L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_int L2) H2)) (not (@ (@ tptp.ord_less_eq_set_int L3) H3)))))))
% 6.44/6.79 (assert (forall ((L2 tptp.rat) (H2 tptp.rat) (L3 tptp.rat) (H3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L2) H2) (@ (@ tptp.set_or633870826150836451st_rat L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_rat L2) H2)) (not (@ (@ tptp.ord_less_eq_rat L3) H3)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (assert (forall ((I2 tptp.set_int) (L2 tptp.set_int) (U tptp.set_int)) (= (@ (@ tptp.member_set_int I2) (@ (@ tptp.set_or370866239135849197et_int L2) U)) (and (@ (@ tptp.ord_less_eq_set_int L2) I2) (@ (@ tptp.ord_less_eq_set_int I2) U)))))
% 6.44/6.79 (assert (forall ((I2 tptp.rat) (L2 tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ (@ tptp.set_or633870826150836451st_rat L2) U)) (and (@ (@ tptp.ord_less_eq_rat L2) I2) (@ (@ tptp.ord_less_eq_rat I2) U)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ (@ tptp.ord_less_eq_set_int C) A) (@ (@ tptp.ord_less_eq_set_int B) D))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat B) D))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ P M6))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (@ P M6))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.44/6.79 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (= (@ (@ tptp.ord_less_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_int B) D) (or (@ (@ tptp.ord_less_set_int C) A) (@ (@ tptp.ord_less_set_int B) D)))) (@ _let_1 D))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) D) (or (@ (@ tptp.ord_less_rat C) A) (@ (@ tptp.ord_less_rat B) D)))) (@ _let_1 D))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_nat) (C5 tptp.set_nat) (D4 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C5) (=> (@ (@ tptp.ord_less_eq_set_nat D4) B3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_set_nat C5) D4))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (C5 tptp.set_int) (D4 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int D4) B3) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_set_int C5) D4))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B3)) A2)))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B3)) A2)))
% 6.44/6.79 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C5) (= (@ (@ tptp.minus_minus_set_nat B3) (@ (@ tptp.minus_minus_set_nat C5) A2)) A2)))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C5) (= (@ (@ tptp.minus_minus_set_int B3) (@ (@ tptp.minus_minus_set_int C5) A2)) A2)))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (X3 tptp.real)) (let ((_let_1 (@ tptp.member_real X3))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (X3 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X3))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (X3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X3))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (not (@ (@ tptp.ord_less_eq_set_int B3) A2)))))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.44/6.79 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.44/6.79 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B7 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (@ (@ tptp.ord_less_eq_set_int B3) A2))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (forall ((T2 tptp.real)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.44/6.79 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (forall ((T2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.44/6.79 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B7 tptp.set_Pr1261947904930325089at_nat)) (forall ((T2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C5 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C5) (@ _let_1 C5))))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.set_int) (Z3 tptp.set_int)) (= Y5 Z3)) (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B7) (@ (@ tptp.ord_less_eq_set_int B7) A6)))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)) (forall ((X2 tptp.int)) (=> (@ P X2) (@ Q X2))))))
% 6.44/6.79 (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)))
% 6.44/6.79 (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)))
% 6.44/6.79 (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)))
% 6.44/6.79 (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)))
% 6.44/6.79 (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)))
% 6.44/6.79 (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)))
% 6.44/6.79 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A6))) (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) B7))))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A6))) (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) B7))))))
% 6.44/6.79 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (@ (@ tptp.ord_le4573692005234683329plex_o (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A6))) (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) B7))))))
% 6.44/6.79 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B7 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le704812498762024988_nat_o (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A6))) (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) B7))))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A6))) (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) B7))))))
% 6.44/6.79 (assert (forall ((Y tptp.set_int) (X3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) X3) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X3)) Y))))
% 6.44/6.79 (assert (forall ((Y tptp.set_int) (X3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) (@ tptp.uminus1532241313380277803et_int X3)) (@ (@ tptp.ord_less_eq_set_int X3) (@ tptp.uminus1532241313380277803et_int Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X3) Y) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) (@ tptp.uminus1532241313380277803et_int X3)))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ (@ tptp.ord_less_eq_set_int B3) A2))))))
% 6.44/6.79 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B7) (not (= A6 B7))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C5 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C5) (@ _let_1 C5))))))
% 6.44/6.79 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B7) (not (@ (@ tptp.ord_less_eq_set_int B7) A6))))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_set_int B3) C5) (@ (@ tptp.ord_less_set_int A2) C5)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A6) B7) (= A6 B7)))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A5 tptp.real) (B5 tptp.real) (C3 tptp.real)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B5) (=> (@ (@ P B5) C3) (=> (@ (@ tptp.ord_less_eq_real A5) B5) (=> (@ (@ tptp.ord_less_eq_real B5) C3) (@ _let_1 C3))))))) (=> (forall ((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 ((A5 tptp.real) (B5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A5) X5) (@ (@ tptp.ord_less_eq_real X5) B5) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B5) A5)) D5)) (@ (@ P A5) B5)))))))) (@ (@ P A) B))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.44/6.79 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.44/6.79 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.44/6.79 (assert (= tptp.nat_triangle (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.44/6.79 (assert (forall ((X3 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 X3) Y) (=> (@ _let_2 X3) (=> (=> (= X3 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X3 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X3 _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)))))))))))))))))))))))
% 6.44/6.79 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.44/6.79 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.44/6.79 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.44/6.79 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N)) _let_1)))))
% 6.44/6.79 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.44/6.79 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.44/6.79 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.44/6.79 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.44/6.79 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu3179335615603231917ec_rat _let_1))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu5219082963157363817nc_rat _let_1))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N) M)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N) M)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.unique5706413561485394159nteger (@ (@ tptp.unique3479559517661332726nteger N) M)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D4))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.minus_minus_int X5) D4))))) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D4))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.minus_minus_int X5) D4))))) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (or (@ P X) (@ Q X)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D4))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.plus_plus_int X5) D4))))) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D4))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.plus_plus_int X5) D4))))) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (or (@ P X) (@ Q X)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.44/6.79 (assert (forall ((D tptp.int) (D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X) D4)) T)))))))))
% 6.44/6.79 (assert (forall ((D tptp.int) (D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X) D4)) T))))))))))
% 6.44/6.79 (assert (forall ((D tptp.int) (D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T))))))))))
% 6.44/6.79 (assert (forall ((D tptp.int) (D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T)))))))))))
% 6.44/6.79 (assert (forall ((D tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (= (exists ((X4 tptp.int)) (@ P X4)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X2))))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B3) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (= X T) (= (@ (@ tptp.minus_minus_int X) D4) T))))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B3) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (= X T)) (not (= (@ (@ tptp.minus_minus_int X) D4) T)))))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X) D4)) T)))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B3) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.minus_minus_int X) D4))))))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (= X T) (= (@ (@ tptp.plus_plus_int X) D4) T))))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (= X T)) (not (= (@ (@ tptp.plus_plus_int X) D4) T)))))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) D4)) T))))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.plus_plus_int X) D4)))))))))
% 6.44/6.79 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.44/6.79 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.44/6.79 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.44/6.79 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.44/6.79 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X) D4)) T)))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B3) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.minus_minus_int X) D4))))))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X) D4)) T))))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.plus_plus_int X) D4)))))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P3 X5) (@ P3 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X4 tptp.int)) (@ P X4)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P3 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) A2) (@ P (@ (@ tptp.minus_minus_int Y6) X2))))))))))))))
% 6.44/6.79 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P3 X5) (@ P3 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X4 tptp.int)) (@ P X4)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P3 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) B3) (@ P (@ (@ tptp.plus_plus_int Y6) X2))))))))))))))
% 6.44/6.79 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 6.44/6.79 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 6.44/6.79 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 6.44/6.79 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 6.44/6.79 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M6) N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.unique5026877609467782581ep_nat N2) (@ (@ tptp.unique5055182867167087721od_nat M6) (@ tptp.bit0 N2)))))))
% 6.44/6.79 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M6) N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.unique5024387138958732305ep_int N2) (@ (@ tptp.unique5052692396658037445od_int M6) (@ tptp.bit0 N2)))))))
% 6.44/6.79 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M6) N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.unique4921790084139445826nteger N2) (@ (@ tptp.unique3479559517661332726nteger M6) (@ tptp.bit0 N2)))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 6.44/6.79 (assert (forall ((X3 (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X3) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X3 X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.44/6.79 (assert (forall ((X3 (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X3) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X3 X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.44/6.79 (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)))))))))
% 6.44/6.79 (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))))))))))
% 6.44/6.79 (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))))))))))
% 6.44/6.79 (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))))))))))
% 6.44/6.79 (assert (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_int)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_rat (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_rat _let_3) tptp.one_one_rat))))))))))
% 6.44/6.79 (assert (forall ((X3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X3) X3)))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X3) X3)))
% 6.44/6.79 (assert (forall ((X3 tptp.num)) (@ (@ tptp.ord_less_eq_num X3) X3)))
% 6.44/6.79 (assert (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X3) X3)))
% 6.44/6.79 (assert (forall ((X3 tptp.int)) (@ (@ tptp.ord_less_eq_int X3) X3)))
% 6.44/6.79 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.44/6.79 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.44/6.79 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.44/6.79 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.44/6.79 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.44/6.79 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z) (@ tptp.numeral_numeral_real N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.44/6.79 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_rat Z) (@ tptp.numeral_numeral_rat N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.44/6.79 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (= (@ tptp.ring_1_of_int_int Z) _let_1) (= Z _let_1)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 6.44/6.79 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 6.44/6.79 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 6.44/6.79 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.44/6.79 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat Z)) N))))
% 6.44/6.79 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z)) N))))
% 6.44/6.79 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z)) N))))
% 6.44/6.79 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z)) N))))
% 6.44/6.79 (assert (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W) (@ tptp.ring_1_of_int_rat X3)) (= (@ (@ tptp.power_power_int B) W) X3))))
% 6.44/6.79 (assert (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X3)) (= (@ (@ tptp.power_power_int B) W) X3))))
% 6.44/6.79 (assert (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X3)) (= (@ (@ tptp.power_power_int B) W) X3))))
% 6.44/6.79 (assert (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X3)) (= (@ (@ tptp.power_power_int B) W) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X3) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (= X3 (@ (@ tptp.power_power_int B) W)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X3) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X3 (@ (@ tptp.power_power_int B) W)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X3) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X3 (@ (@ tptp.power_power_int B) W)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X3) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X3 (@ (@ tptp.power_power_int B) W)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.44/6.79 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.44/6.79 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_eq_int Z) _let_1)))))
% 6.44/6.79 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.44/6.79 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.44/6.79 (assert (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.44/6.79 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.44/6.79 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.44/6.79 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_int Z) _let_1)))))
% 6.44/6.79 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.44/6.79 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.44/6.79 (assert (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((B tptp.int) (W tptp.nat) (X3 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 X3)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X3))))
% 6.44/6.79 (assert (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X3)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X3))))
% 6.44/6.79 (assert (forall ((B tptp.int) (W tptp.nat) (X3 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 X3)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X3)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X3) (@ (@ tptp.power_power_int B) W)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X3)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_eq_int X3) (@ (@ tptp.power_power_int B) W)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X3)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X3) (@ (@ tptp.power_power_int B) W)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X3)) N) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 6.44/6.79 (assert (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X3)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))))
% 6.44/6.79 (assert (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))))
% 6.44/6.79 (assert (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))))
% 6.44/6.79 (assert (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 6.44/6.79 (assert (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X3)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X3))))
% 6.44/6.79 (assert (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X3)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X3))))
% 6.44/6.79 (assert (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X3)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X3)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X3) (@ (@ tptp.power_power_int B) W)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X3)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_int X3) (@ (@ tptp.power_power_int B) W)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X3)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X3) (@ (@ tptp.power_power_int B) W)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)) A))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)) A))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)) A))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)) A))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X3))) N) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X3))) N) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X3))) N) (@ tptp.ring_18347121197199848620nteger Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X3))) N) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N) Y))))
% 6.44/6.79 (assert (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 6.44/6.79 (assert (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X3))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))))
% 6.44/6.79 (assert (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X3))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))))
% 6.44/6.79 (assert (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X3))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))))
% 6.44/6.79 (assert (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X3))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X3))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)) A))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X3))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)) A))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X3))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)) A))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X3))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X3))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X3))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X3))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)) A))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X3))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)) A))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X3))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)) A))))
% 6.44/6.79 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X3))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X3))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X3))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X3))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X3))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X3))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.44/6.79 (assert (forall ((N tptp.int) (X3 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X3))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X3)))))
% 6.44/6.79 (assert (forall ((D tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) N) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) D)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real D))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat B) A) (not (= B A))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X3))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X3))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X3))) (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)))))))))))))))))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X3))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X3))) (let ((_let_5 (@ tptp.ord_less_eq_num Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X3))) (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)))))))))))))))))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X3))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X3))) (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)))))))))))))))))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X3))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X3))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X3))) (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)))))))))))))))))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.set_int) (Z3 tptp.set_int)) (= Y5 Z3)) (lambda ((X2 tptp.set_int) (Y6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X2) Y6) (@ (@ tptp.ord_less_eq_set_int Y6) X2)))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.rat) (Z3 tptp.rat)) (= Y5 Z3)) (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y6) (@ (@ tptp.ord_less_eq_rat Y6) X2)))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.num) (Z3 tptp.num)) (= Y5 Z3)) (lambda ((X2 tptp.num) (Y6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y6) (@ (@ tptp.ord_less_eq_num Y6) X2)))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3)) (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y6) (@ (@ tptp.ord_less_eq_nat Y6) X2)))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3)) (lambda ((X2 tptp.int) (Y6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y6) (@ (@ tptp.ord_less_eq_int Y6) X2)))))
% 6.44/6.79 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ (@ tptp.ord_less_eq_set_int A) C)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_eq_rat A) C)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X3) Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) X3) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (=> (@ (@ tptp.ord_less_eq_rat Y) X3) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X3) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X3) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X3) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))))
% 6.44/6.79 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))))
% 6.44/6.79 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))))
% 6.44/6.79 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.set_int) (Z3 tptp.set_int)) (= Y5 Z3)) (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B2) A3) (@ (@ tptp.ord_less_eq_set_int A3) B2)))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.rat) (Z3 tptp.rat)) (= Y5 Z3)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (@ (@ tptp.ord_less_eq_rat A3) B2)))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.num) (Z3 tptp.num)) (= Y5 Z3)) (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (@ (@ tptp.ord_less_eq_num A3) B2)))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (@ (@ tptp.ord_less_eq_nat A3) B2)))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3)) (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (@ (@ tptp.ord_less_eq_int A3) B2)))))
% 6.44/6.79 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (= A B)))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))))
% 6.44/6.79 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 6.44/6.79 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 6.44/6.79 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 6.44/6.79 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= A B)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))))
% 6.44/6.79 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.set_int) (Z3 tptp.set_int)) (= Y5 Z3)) (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B2) (@ (@ tptp.ord_less_eq_set_int B2) A3)))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.rat) (Z3 tptp.rat)) (= Y5 Z3)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (@ (@ tptp.ord_less_eq_rat B2) A3)))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.num) (Z3 tptp.num)) (= Y5 Z3)) (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (@ (@ tptp.ord_less_eq_num B2) A3)))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (@ (@ tptp.ord_less_eq_nat B2) A3)))))
% 6.44/6.79 (assert (= (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3)) (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (@ (@ tptp.ord_less_eq_int B2) A3)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (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) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (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) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (= X3 Y) (@ (@ tptp.ord_less_eq_set_int X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (= X3 Y) (@ (@ tptp.ord_less_eq_rat X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (= X3 Y) (@ (@ tptp.ord_less_eq_num X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (= X3 Y) (@ (@ tptp.ord_less_eq_nat X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (= X3 Y) (@ (@ tptp.ord_less_eq_int X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X3) Y) (@ (@ tptp.ord_less_eq_rat Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X3) Y) (@ (@ tptp.ord_less_eq_num Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X3) Y) (@ (@ tptp.ord_less_eq_nat Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X3) Y) (@ (@ tptp.ord_less_eq_int Y) X3))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.44/6.79 (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) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X3) Y)) (@ (@ tptp.ord_less_eq_rat Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X3) Y)) (@ (@ tptp.ord_less_eq_num Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X3) Y)) (@ (@ tptp.ord_less_eq_nat Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X3) Y)) (@ (@ tptp.ord_less_eq_int Y) X3))))
% 6.44/6.79 (assert (forall ((Y tptp.set_int) (X3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X3) (= (@ (@ tptp.ord_less_eq_set_int X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((Y tptp.rat) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X3) (= (@ (@ tptp.ord_less_eq_rat X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((Y tptp.num) (X3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X3) (= (@ (@ tptp.ord_less_eq_num X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((Y tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X3) (= (@ (@ tptp.ord_less_eq_nat X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((Y tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X3) (= (@ (@ tptp.ord_less_eq_int X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X3) X_12))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X3) X_12))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat)) (exists ((X_12 tptp.nat)) (@ (@ tptp.ord_less_nat X3) X_12))))
% 6.44/6.79 (assert (forall ((X3 tptp.int)) (exists ((X_12 tptp.int)) (@ (@ tptp.ord_less_int X3) X_12))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real X3) Z2) (@ (@ tptp.ord_less_real Z2) Y))))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (exists ((Z2 tptp.rat)) (and (@ (@ tptp.ord_less_rat X3) Z2) (@ (@ tptp.ord_less_rat Z2) Y))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (not (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (not (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y) (not (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (not (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y) (not (= X3 Y)))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.44/6.79 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y4) X5) (@ P Y4))) (@ P X5))) (@ P A))))
% 6.44/6.79 (assert (forall ((Y tptp.real) (X3 tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X3)) (= (not (@ (@ tptp.ord_less_real X3) Y)) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((Y tptp.rat) (X3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y) X3)) (= (not (@ (@ tptp.ord_less_rat X3) Y)) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((Y tptp.num) (X3 tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X3)) (= (not (@ (@ tptp.ord_less_num X3) Y)) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((Y tptp.nat) (X3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X3)) (= (not (@ (@ tptp.ord_less_nat X3) Y)) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((Y tptp.int) (X3 tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X3)) (= (not (@ (@ tptp.ord_less_int X3) Y)) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X3) Y)) (=> (not (= X3 Y)) (@ (@ tptp.ord_less_real Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X3) Y)) (=> (not (= X3 Y)) (@ (@ tptp.ord_less_rat Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X3) Y)) (=> (not (= X3 Y)) (@ (@ tptp.ord_less_num Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X3) Y)) (=> (not (= X3 Y)) (@ (@ tptp.ord_less_nat Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X3) Y)) (=> (not (= X3 Y)) (@ (@ tptp.ord_less_int Y) X3)))))
% 6.44/6.79 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 6.44/6.79 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 6.44/6.79 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 6.44/6.79 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 6.44/6.79 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.44/6.79 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.44/6.79 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.44/6.79 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.44/6.79 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.44/6.79 (assert (= (lambda ((P5 (-> tptp.nat Bool))) (exists ((X7 tptp.nat)) (@ P5 X7))) (lambda ((P6 (-> tptp.nat Bool))) (exists ((N2 tptp.nat)) (and (@ P6 N2) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N2) (not (@ P6 M6)))))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A5 tptp.real) (B5 tptp.real)) (=> (@ (@ tptp.ord_less_real A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.real)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.real) (B5 tptp.real)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.rat)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ tptp.ord_less_num A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.num)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.nat)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_int A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.int)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_rat B) C) (@ _let_1 C))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X3) Y)) (or (@ (@ tptp.ord_less_real Y) X3) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X3) Y)) (or (@ (@ tptp.ord_less_rat Y) X3) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X3) Y)) (or (@ (@ tptp.ord_less_num Y) X3) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X3) Y)) (or (@ (@ tptp.ord_less_nat Y) X3) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X3) Y)) (or (@ (@ tptp.ord_less_int Y) X3) (= X3 Y)))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 6.44/6.79 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 6.44/6.79 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 6.44/6.79 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 6.44/6.79 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 6.44/6.79 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (not (= X3 Y)) (=> (not (@ (@ tptp.ord_less_real X3) Y)) (@ (@ tptp.ord_less_real Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (not (= X3 Y)) (=> (not (@ (@ tptp.ord_less_rat X3) Y)) (@ (@ tptp.ord_less_rat Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (not (= X3 Y)) (=> (not (@ (@ tptp.ord_less_num X3) Y)) (@ (@ tptp.ord_less_num Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (not (= X3 Y)) (=> (not (@ (@ tptp.ord_less_nat X3) Y)) (@ (@ tptp.ord_less_nat Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (not (= X3 Y)) (=> (not (@ (@ tptp.ord_less_int X3) Y)) (@ (@ tptp.ord_less_int Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (not (@ (@ tptp.ord_less_real Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (not (@ (@ tptp.ord_less_rat Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y) (not (@ (@ tptp.ord_less_num Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (not (@ (@ tptp.ord_less_nat Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y) (not (@ (@ tptp.ord_less_int Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (not (= X3 Y)) (or (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_real Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (= (not (= X3 Y)) (or (@ (@ tptp.ord_less_rat X3) Y) (@ (@ tptp.ord_less_rat Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (not (= X3 Y)) (or (@ (@ tptp.ord_less_num X3) Y) (@ (@ tptp.ord_less_num Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (not (= X3 Y)) (or (@ (@ tptp.ord_less_nat X3) Y) (@ (@ tptp.ord_less_nat Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (not (= X3 Y)) (or (@ (@ tptp.ord_less_int X3) Y) (@ (@ tptp.ord_less_int Y) X3)))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.44/6.79 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real)) (not (@ (@ tptp.ord_less_real X3) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (not (@ (@ tptp.ord_less_rat X3) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.num)) (not (@ (@ tptp.ord_less_num X3) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat)) (not (@ (@ tptp.ord_less_nat X3) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.int)) (not (@ (@ tptp.ord_less_int X3) X3))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (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) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (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) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (not (@ (@ tptp.ord_less_real Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (not (@ (@ tptp.ord_less_rat Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y) (not (@ (@ tptp.ord_less_num Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (not (@ (@ tptp.ord_less_nat Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y) (not (@ (@ tptp.ord_less_int Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X3) Y) (=> (@ (@ tptp.ord_less_real Y) X3) P))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X3) Y) (=> (@ (@ tptp.ord_less_rat Y) X3) P))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X3) Y) (=> (@ (@ tptp.ord_less_num Y) X3) P))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X3) Y) (=> (@ (@ tptp.ord_less_nat Y) X3) P))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X3) Y) (=> (@ (@ tptp.ord_less_int Y) X3) P))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X3) Y) (= X3 Y) (@ (@ tptp.ord_less_real Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X3) Y) (= X3 Y) (@ (@ tptp.ord_less_rat Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X3) Y) (= X3 Y) (@ (@ tptp.ord_less_num Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y) (= X3 Y) (@ (@ tptp.ord_less_nat Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X3) Y) (= X3 Y) (@ (@ tptp.ord_less_int Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (not (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (not (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y) (not (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (not (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y) (not (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (not (= Y X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (not (= Y X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y) (not (= Y X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (not (= Y X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y) (not (= Y X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (not (@ (@ tptp.ord_less_real Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (not (@ (@ tptp.ord_less_rat Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y) (not (@ (@ tptp.ord_less_num Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (not (@ (@ tptp.ord_less_nat Y) X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y) (not (@ (@ tptp.ord_less_int Y) X3)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_int (lambda ((N2 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M6)) tptp.one_one_real)))))
% 6.44/6.79 (assert (= tptp.ord_less_int (lambda ((N2 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N2)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M6)))))
% 6.44/6.79 (assert (forall ((X3 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 X3)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X3) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X3) D))) _let_1))))))
% 6.44/6.79 (assert (forall ((N tptp.int) (X3 tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X3))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X3))))))
% 6.44/6.79 (assert (forall ((N tptp.int) (X3 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X3))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X3)))) tptp.one_one_real)))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X3) (not (@ (@ tptp.ord_less_real X3) Y)))))
% 6.44/6.79 (assert (forall ((Y tptp.set_int) (X3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X3) (not (@ (@ tptp.ord_less_set_int X3) Y)))))
% 6.44/6.79 (assert (forall ((Y tptp.rat) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X3) (not (@ (@ tptp.ord_less_rat X3) Y)))))
% 6.44/6.79 (assert (forall ((Y tptp.num) (X3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X3) (not (@ (@ tptp.ord_less_num X3) Y)))))
% 6.44/6.79 (assert (forall ((Y tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X3) (not (@ (@ tptp.ord_less_nat X3) Y)))))
% 6.44/6.79 (assert (forall ((Y tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X3) (not (@ (@ tptp.ord_less_int X3) Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X3) Y)) (@ (@ tptp.ord_less_eq_real Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X3) Y)) (@ (@ tptp.ord_less_eq_rat Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X3) Y)) (@ (@ tptp.ord_less_eq_num Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X3) Y)) (@ (@ tptp.ord_less_eq_nat Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X3) Y)) (@ (@ tptp.ord_less_eq_int Y) X3))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (not (@ (@ tptp.ord_less_set_int A) B)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (= A B)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_rat A) B)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (= A B)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X3) Y)) (= (@ (@ tptp.ord_less_eq_real X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (not (@ (@ tptp.ord_less_set_int X3) Y)) (= (@ (@ tptp.ord_less_eq_set_int X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X3) Y)) (= (@ (@ tptp.ord_less_eq_rat X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X3) Y)) (= (@ (@ tptp.ord_less_eq_num X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X3) Y)) (= (@ (@ tptp.ord_less_eq_nat X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X3) Y)) (= (@ (@ tptp.ord_less_eq_int X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (= (not (@ (@ tptp.ord_less_real X3) Y)) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X3) Y) (= (not (@ (@ tptp.ord_less_set_int X3) Y)) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (= (not (@ (@ tptp.ord_less_rat X3) Y)) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y) (= (not (@ (@ tptp.ord_less_num X3) Y)) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y) (= (not (@ (@ tptp.ord_less_nat X3) Y)) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y) (= (not (@ (@ tptp.ord_less_int X3) Y)) (= X3 Y)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((Z tptp.rat) (Y tptp.rat)) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (@ (@ tptp.ord_less_eq_rat Y) X5))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((Y tptp.rat) (Z tptp.rat)) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y) (@ (@ tptp.ord_less_eq_rat X5) Z))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 6.44/6.79 (assert (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y6) (not (@ (@ tptp.ord_less_eq_real Y6) X2))))))
% 6.44/6.79 (assert (= tptp.ord_less_set_int (lambda ((X2 tptp.set_int) (Y6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X2) Y6) (not (@ (@ tptp.ord_less_eq_set_int Y6) X2))))))
% 6.44/6.79 (assert (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y6) (not (@ (@ tptp.ord_less_eq_rat Y6) X2))))))
% 6.44/6.79 (assert (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y6) (not (@ (@ tptp.ord_less_eq_num Y6) X2))))))
% 6.44/6.79 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y6) (not (@ (@ tptp.ord_less_eq_nat Y6) X2))))))
% 6.44/6.79 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y6) (not (@ (@ tptp.ord_less_eq_int Y6) X2))))))
% 6.44/6.79 (assert (forall ((Y tptp.real) (X3 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X3)) (@ (@ tptp.ord_less_real X3) Y))))
% 6.44/6.79 (assert (forall ((Y tptp.rat) (X3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X3)) (@ (@ tptp.ord_less_rat X3) Y))))
% 6.44/6.79 (assert (forall ((Y tptp.num) (X3 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X3)) (@ (@ tptp.ord_less_num X3) Y))))
% 6.44/6.79 (assert (forall ((Y tptp.nat) (X3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X3)) (@ (@ tptp.ord_less_nat X3) Y))))
% 6.44/6.79 (assert (forall ((Y tptp.int) (X3 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X3)) (@ (@ tptp.ord_less_int X3) Y))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B2 tptp.real)) (or (@ (@ tptp.ord_less_real A3) B2) (= A3 B2)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A3) B2) (= A3 B2)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (or (@ (@ tptp.ord_less_rat A3) B2) (= A3 B2)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B2 tptp.num)) (or (@ (@ tptp.ord_less_num A3) B2) (= A3 B2)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B2) (= A3 B2)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (or (@ (@ tptp.ord_less_int A3) B2) (= A3 B2)))))
% 6.44/6.79 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B2) (not (= A3 B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B2) (not (= A3 B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (not (= A3 B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_num (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (not (= A3 B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (not (= A3 B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (not (= A3 B2))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_set_int B) C) (@ (@ tptp.ord_less_set_int A) C)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B2) (not (@ (@ tptp.ord_less_eq_real B2) A3))))))
% 6.44/6.79 (assert (= tptp.ord_less_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B2) (not (@ (@ tptp.ord_less_eq_set_int B2) A3))))))
% 6.44/6.79 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (not (@ (@ tptp.ord_less_eq_rat B2) A3))))))
% 6.44/6.79 (assert (= tptp.ord_less_num (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (not (@ (@ tptp.ord_less_eq_num B2) A3))))))
% 6.44/6.79 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (not (@ (@ tptp.ord_less_eq_nat B2) A3))))))
% 6.44/6.79 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (not (@ (@ tptp.ord_less_eq_int B2) A3))))))
% 6.44/6.79 (assert (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X3) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W2) (=> (@ (@ tptp.ord_less_real W2) X3) (@ (@ tptp.ord_less_eq_real Y) W2)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 6.44/6.79 (assert (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X3) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W2) (=> (@ (@ tptp.ord_less_rat W2) X3) (@ (@ tptp.ord_less_eq_rat Y) W2)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) W2) (=> (@ (@ tptp.ord_less_real W2) Y) (@ (@ tptp.ord_less_eq_real W2) Z)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) W2) (=> (@ (@ tptp.ord_less_rat W2) Y) (@ (@ tptp.ord_less_eq_rat W2) Z)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_real (lambda ((B2 tptp.real) (A3 tptp.real)) (or (@ (@ tptp.ord_less_real B2) A3) (= A3 B2)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_set_int (lambda ((B2 tptp.set_int) (A3 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int B2) A3) (= A3 B2)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (or (@ (@ tptp.ord_less_rat B2) A3) (= A3 B2)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (or (@ (@ tptp.ord_less_num B2) A3) (= A3 B2)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B2) A3) (= A3 B2)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (or (@ (@ tptp.ord_less_int B2) A3) (= A3 B2)))))
% 6.44/6.79 (assert (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B2) A3) (not (= A3 B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_set_int (lambda ((B2 tptp.set_int) (A3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B2) A3) (not (= A3 B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (not (= A3 B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (not (= A3 B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (not (= A3 B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (not (= A3 B2))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int C) B) (@ (@ tptp.ord_less_set_int C) A)))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_rat C) A)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B2) A3) (not (@ (@ tptp.ord_less_eq_real A3) B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_set_int (lambda ((B2 tptp.set_int) (A3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B2) A3) (not (@ (@ tptp.ord_less_eq_set_int A3) B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (not (@ (@ tptp.ord_less_eq_rat A3) B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (not (@ (@ tptp.ord_less_eq_num A3) B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (not (@ (@ tptp.ord_less_eq_nat A3) B2))))))
% 6.44/6.79 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (not (@ (@ tptp.ord_less_eq_int A3) B2))))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.44/6.79 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B) (@ (@ tptp.ord_less_eq_set_int A) B))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.44/6.79 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.44/6.79 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.44/6.79 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (@ (@ tptp.ord_less_eq_set_int B) A))))
% 6.44/6.79 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.44/6.79 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.44/6.79 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.44/6.79 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y6) (= X2 Y6)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_set_int (lambda ((X2 tptp.set_int) (Y6 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X2) Y6) (= X2 Y6)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_rat (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y6) (= X2 Y6)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_num (lambda ((X2 tptp.num) (Y6 tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y6) (= X2 Y6)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y6) (= X2 Y6)))))
% 6.44/6.79 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y6 tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y6) (= X2 Y6)))))
% 6.44/6.79 (assert (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y6) (not (= X2 Y6))))))
% 6.44/6.79 (assert (= tptp.ord_less_set_int (lambda ((X2 tptp.set_int) (Y6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X2) Y6) (not (= X2 Y6))))))
% 6.44/6.79 (assert (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y6) (not (= X2 Y6))))))
% 6.44/6.79 (assert (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y6) (not (= X2 Y6))))))
% 6.44/6.79 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y6) (not (= X2 Y6))))))
% 6.44/6.79 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y6) (not (= X2 Y6))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X3) Y)) (@ (@ tptp.ord_less_real Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X3) Y)) (@ (@ tptp.ord_less_rat Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X3) Y)) (@ (@ tptp.ord_less_num Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X3) Y)) (@ (@ tptp.ord_less_nat Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X3) Y)) (@ (@ tptp.ord_less_int Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X3) Y)) (@ (@ tptp.ord_less_eq_real Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X3) Y)) (@ (@ tptp.ord_less_eq_rat Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X3) Y)) (@ (@ tptp.ord_less_eq_num Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X3) Y)) (@ (@ tptp.ord_less_eq_nat Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X3) Y)) (@ (@ tptp.ord_less_eq_int Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_eq_real X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int X3) Y) (@ (@ tptp.ord_less_eq_set_int X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (@ (@ tptp.ord_less_eq_rat X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y) (@ (@ tptp.ord_less_eq_num X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (@ (@ tptp.ord_less_eq_nat X3) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y) (@ (@ tptp.ord_less_eq_int X3) Y))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.44/6.79 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_int A) B)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.44/6.79 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.44/6.79 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (@ (@ tptp.ord_less_set_int A) B)))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.44/6.79 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ (@ tptp.ord_less_real X3) Z)))))
% 6.44/6.79 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X3) Y) (=> (@ (@ tptp.ord_less_set_int Y) Z) (@ (@ tptp.ord_less_set_int X3) Z)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ (@ tptp.ord_less_rat X3) Z)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ (@ tptp.ord_less_num X3) Z)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X3) Z)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X3) Z)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.44/6.79 (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) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.44/6.79 (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) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.44/6.79 (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.44/6.79 (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) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_real Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X3) Y) (@ (@ tptp.ord_less_rat Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X3) Y) (@ (@ tptp.ord_less_num Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X3) Y) (@ (@ tptp.ord_less_nat Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X3) Y) (@ (@ tptp.ord_less_int Y) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (or (@ (@ tptp.ord_less_real X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X3) Y) (or (@ (@ tptp.ord_less_set_int X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (or (@ (@ tptp.ord_less_rat X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y) (or (@ (@ tptp.ord_less_num X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y) (or (@ (@ tptp.ord_less_nat X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y) (or (@ (@ tptp.ord_less_int X3) Y) (= X3 Y)))))
% 6.44/6.79 (assert (forall ((X3 tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X3) Y) (= (@ (@ tptp.ord_ma741700101516333627d_enat X3) Y) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X3) Y) (= (@ (@ tptp.ord_max_set_int X3) Y) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (= (@ (@ tptp.ord_max_rat X3) Y) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y) (= (@ (@ tptp.ord_max_num X3) Y) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y) (= (@ (@ tptp.ord_max_nat X3) Y) Y))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y) (= (@ (@ tptp.ord_max_int X3) Y) Y))))
% 6.44/6.79 (assert (forall ((Y tptp.extended_enat) (X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) X3) (= (@ (@ tptp.ord_ma741700101516333627d_enat X3) Y) X3))))
% 6.44/6.79 (assert (forall ((Y tptp.set_int) (X3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X3) (= (@ (@ tptp.ord_max_set_int X3) Y) X3))))
% 6.44/6.79 (assert (forall ((Y tptp.rat) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X3) (= (@ (@ tptp.ord_max_rat X3) Y) X3))))
% 6.44/6.79 (assert (forall ((Y tptp.num) (X3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X3) (= (@ (@ tptp.ord_max_num X3) Y) X3))))
% 6.44/6.79 (assert (forall ((Y tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X3) (= (@ (@ tptp.ord_max_nat X3) Y) X3))))
% 6.44/6.79 (assert (forall ((Y tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X3) (= (@ (@ tptp.ord_max_int X3) Y) X3))))
% 6.44/6.79 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A3 tptp.extended_enat) (B2 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A3) B2)) B2) A3))))
% 6.44/6.79 (assert (= tptp.ord_max_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A3) B2)) B2) A3))))
% 6.44/6.79 (assert (= tptp.ord_max_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A3) B2)) B2) A3))))
% 6.44/6.79 (assert (= tptp.ord_max_num (lambda ((A3 tptp.num) (B2 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A3) B2)) B2) A3))))
% 6.44/6.79 (assert (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B2)) B2) A3))))
% 6.44/6.79 (assert (= tptp.ord_max_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B2)) B2) A3))))
% 6.44/6.79 (assert (forall ((X3 (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X3) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.44/6.79 (assert (forall ((X3 (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X3) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 6.44/6.79 (assert (forall ((X3 tptp.real)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X3) (@ (@ tptp.ord_less_real X3) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X3) (@ (@ tptp.ord_less_rat X3) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X5)) X3) (@ (@ tptp.ord_less_real X3) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X5) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y4)) X3) (@ (@ tptp.ord_less_real X3) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X5)))))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X5)) X3) (@ (@ tptp.ord_less_rat X3) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X5) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y4)) X3) (@ (@ tptp.ord_less_rat X3) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X5)))))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_int)))) (@ (@ tptp.unique5052692396658037445od_int M) N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_nat)))) (@ (@ tptp.unique5055182867167087721od_nat M) N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q4) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_Code_integer)))) (@ (@ tptp.unique3479559517661332726nteger M) N)))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (assert (forall ((X3 tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X3)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X3)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N)) (@ tptp.nat_set_decode X3)) (@ (@ tptp.member_nat N) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.44/6.79 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 6.44/6.79 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.44/6.79 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.44/6.79 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 6.44/6.79 (assert (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex))
% 6.44/6.79 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 6.44/6.79 (assert (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))
% 6.44/6.79 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 6.44/6.79 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 6.44/6.79 (assert (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger))
% 6.44/6.79 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not P))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not P))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not P))))
% 6.44/6.79 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 6.44/6.79 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 6.44/6.79 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.44/6.79 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.44/6.79 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 6.44/6.79 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 6.44/6.79 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 6.44/6.79 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 6.44/6.79 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 6.44/6.79 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 6.44/6.79 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 6.44/6.79 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 6.44/6.79 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 6.44/6.79 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 6.44/6.79 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 6.44/6.79 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 6.44/6.79 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N) (@ tptp.zero_n2687167440665602831ol_nat (not (= N _let_1)))))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bitM K)))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))))
% 6.44/6.79 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 6.44/6.79 (assert (forall ((Q2 tptp.int) (R2 tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q2) R2)) (@ (@ tptp.plus_plus_int Q2) (@ tptp.zero_n2684676970156552555ol_int (not (= R2 tptp.zero_zero_int)))))))
% 6.44/6.79 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P2))) P2)))
% 6.44/6.79 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P2))) P2)))
% 6.44/6.79 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P2))) P2)))
% 6.44/6.79 (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)))
% 6.44/6.79 (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)))
% 6.44/6.79 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5052692396658037445od_int M) N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5055182867167087721od_nat M) N)))))
% 6.44/6.79 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q4) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique3479559517661332726nteger M) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.44/6.79 (assert (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P2) (@ tptp.zero_n2687167440665602831ol_nat Q2)) (= P2 Q2))))
% 6.44/6.79 (assert (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P2) (@ tptp.zero_n2684676970156552555ol_int Q2)) (= P2 Q2))))
% 6.44/6.79 (assert (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P2) (@ tptp.zero_n356916108424825756nteger Q2)) (= P2 Q2))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (and P Q)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.44/6.79 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 6.44/6.79 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.44/6.79 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.44/6.79 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.44/6.79 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.44/6.79 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 6.44/6.79 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 6.44/6.79 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 6.44/6.79 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.44/6.79 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.44/6.79 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 6.44/6.79 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P4 Bool)) (@ (@ (@ tptp.if_complex P4) tptp.one_one_complex) tptp.zero_zero_complex))))
% 6.44/6.79 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P4 Bool)) (@ (@ (@ tptp.if_real P4) tptp.one_one_real) tptp.zero_zero_real))))
% 6.44/6.79 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P4 Bool)) (@ (@ (@ tptp.if_rat P4) tptp.one_one_rat) tptp.zero_zero_rat))))
% 6.44/6.79 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P4 Bool)) (@ (@ (@ tptp.if_nat P4) tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.44/6.79 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P4 Bool)) (@ (@ (@ tptp.if_int P4) tptp.one_one_int) tptp.zero_zero_int))))
% 6.44/6.79 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P4 Bool)) (@ (@ (@ tptp.if_Code_integer P4) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.79 (assert (forall ((P (-> tptp.complex Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P2)) (and (=> P2 (@ P tptp.one_one_complex)) (=> (not P2) (@ P tptp.zero_zero_complex))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.real Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P2)) (and (=> P2 (@ P tptp.one_one_real)) (=> (not P2) (@ P tptp.zero_zero_real))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.rat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P2)) (and (=> P2 (@ P tptp.one_one_rat)) (=> (not P2) (@ P tptp.zero_zero_rat))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.nat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P2)) (and (=> P2 (@ P tptp.one_one_nat)) (=> (not P2) (@ P tptp.zero_zero_nat))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.int Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P2)) (and (=> P2 (@ P tptp.one_one_int)) (=> (not P2) (@ P tptp.zero_zero_int))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.code_integer Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P2)) (and (=> P2 (@ P tptp.one_one_Code_integer)) (=> (not P2) (@ P tptp.zero_z3403309356797280102nteger))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.complex Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P2)) (not (or (and P2 (not (@ P tptp.one_one_complex))) (and (not P2) (not (@ P tptp.zero_zero_complex))))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.real Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P2)) (not (or (and P2 (not (@ P tptp.one_one_real))) (and (not P2) (not (@ P tptp.zero_zero_real))))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.rat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P2)) (not (or (and P2 (not (@ P tptp.one_one_rat))) (and (not P2) (not (@ P tptp.zero_zero_rat))))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.nat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P2)) (not (or (and P2 (not (@ P tptp.one_one_nat))) (and (not P2) (not (@ P tptp.zero_zero_nat))))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.int Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P2)) (not (or (and P2 (not (@ P tptp.one_one_int))) (and (not P2) (not (@ P tptp.zero_zero_int))))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.code_integer Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P2)) (not (or (and P2 (not (@ P tptp.one_one_Code_integer))) (and (not P2) (not (@ P tptp.zero_z3403309356797280102nteger))))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N)) (@ tptp.bit1 (@ tptp.bitM N)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 N)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N))) tptp.one_one_complex))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.bitM N)) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 N))) tptp.one_one_real))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.bitM N)) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 N))) tptp.one_one_rat))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.bitM N)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) tptp.one_one_int))))
% 6.44/6.79 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bitM W))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A5 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.nat) (B5 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B5)) (@ (@ tptp.times_times_nat _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.44/6.79 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A5 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A5) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.int) (B5 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B5)) (@ (@ tptp.times_times_int _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.44/6.79 (assert (forall ((P (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A5 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A5) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B5)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.44/6.79 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (exists ((N3 tptp.nat)) (and (not (@ P N3)) (@ P (@ tptp.suc N3))))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.ring_1_of_int_real Z2)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_rat X3) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) X3))))
% 6.44/6.79 (assert (forall ((X3 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real X3) (@ tptp.ring_1_of_int_real Z2)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat X3) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.44/6.79 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide6298287555418463151nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.44/6.79 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 6.44/6.79 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 6.44/6.79 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 6.44/6.79 (assert (= tptp.unique4921790084139445826nteger (lambda ((L tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 6.44/6.79 (assert (= tptp.nat_set_decode (lambda ((X2 tptp.nat)) (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat _let_1) N2))))))))))
% 6.44/6.79 (assert (forall ((X3 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 X3) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X3) _let_1)) (= (@ tptp.archim8280529875227126926d_real X3) Y)))))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_rat Y))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X3) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X3) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X3) Y)))))))
% 6.44/6.79 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M6) N2))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M6)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q4)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M6) N2)) N2))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X3) (@ (@ 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 X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X3) (@ (@ 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 X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X3)))))
% 6.44/6.79 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X3))) (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X3))) (@ (@ tptp.plus_plus_rat X3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 6.44/6.79 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int M) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N) (@ (@ tptp.plus_plus_int N) tptp.one_one_int))) (@ (@ tptp.times_times_int M) (@ (@ tptp.minus_minus_int M) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_int N))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_int N))))
% 6.44/6.79 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 6.44/6.79 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))))
% 6.44/6.79 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) A))))
% 6.44/6.79 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) A))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X3)) (@ tptp.archim7778729529865785530nd_rat Y)))))
% 6.44/6.79 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N2)) (@ (@ tptp.modulo_modulo_nat M6) N2)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A2)))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) A2)))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A2)))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) A2)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) tptp.zero_zero_rat))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) A2)) tptp.zero_zero_rat))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) tptp.zero_zero_rat))))
% 6.44/6.79 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) tptp.zero_zero_rat))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (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))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.pred_numeral N)))))))
% 6.44/6.79 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ tptp.pred_numeral N)))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N2 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_integer (= N2 tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A3) _let_1)))))))
% 6.44/6.79 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A3) _let_1)))))))
% 6.44/6.79 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A3) _let_1)))))))
% 6.44/6.79 (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)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N)) (@ _let_1 N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.44/6.79 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)))
% 6.44/6.79 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.44/6.79 (assert (forall ((L2 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) tptp.one_one_int) tptp.one_one_int)))
% 6.44/6.79 (assert (forall ((L2 tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.44/6.79 (assert (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.44/6.79 (assert (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.44/6.79 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.44/6.79 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1745604003318907178nteger N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.44/6.79 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se1745604003318907178nteger M) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N))) _let_1)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2000444600071755411sk_int N))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q2)) (@ (@ tptp.bit_se2925701944663578781it_nat N) Q2)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int) (R2 tptp.int) (S tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ tptp.bit_concat_bit N))) (= (= (@ (@ _let_2 K) L2) (@ (@ _let_2 R2) S)) (and (= (@ _let_1 K) (@ _let_1 R2)) (= L2 S)))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) B)) (@ _let_1 B)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc N)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X5)))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)))) (let ((_let_2 (@ tptp.bit_ri631733984087533419it_int N))) (= (= (@ _let_2 A) (@ _let_2 B)) (= (@ _let_1 A) (@ _let_1 B)))))))
% 6.44/6.79 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ _let_1 tptp.zero_zero_int)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N) M)) _let_2) _let_1) A))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4203085406695923979it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4205575877204974255it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7879613467334960850it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7882103937844011126it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2159334234014336723it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2161824704523386999it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.44/6.79 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.44/6.79 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int))))
% 6.44/6.79 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.44/6.79 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ tptp.suc N)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) A)) (@ _let_1 A))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))
% 6.44/6.79 (assert (forall ((X3 tptp.complex) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X3))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X3) (@ (@ tptp.plus_plus_nat M) I3)))) I6) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I6))))))
% 6.44/6.79 (assert (forall ((X3 tptp.rat) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_rat X3) (@ (@ tptp.plus_plus_nat M) I3)))) I6) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I6))))))
% 6.44/6.79 (assert (forall ((X3 tptp.int) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X3))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X3) (@ (@ tptp.plus_plus_nat M) I3)))) I6) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I6))))))
% 6.44/6.79 (assert (forall ((X3 tptp.real) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X3))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X3) (@ (@ tptp.plus_plus_nat M) I3)))) I6) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I6))))))
% 6.44/6.79 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I3)))) _let_1)))))
% 6.44/6.79 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I3)))) _let_1)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat N) (@ tptp.bit_se2002935070580805687sk_nat N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) (@ tptp.bit_se2000444600071755411sk_int N)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (assert (forall ((F (-> tptp.nat tptp.rat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_rat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (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)))))))
% 6.44/6.79 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.44/6.79 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.44/6.79 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.44/6.79 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G M)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.44/6.79 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N2 tptp.nat) (A3 tptp.code_integer)) (@ (@ tptp.modulo364778990260209775nteger A3) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)))))
% 6.44/6.79 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (@ (@ tptp.modulo_modulo_int A3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.44/6.79 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M))))
% 6.44/6.79 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.44/6.79 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.modulo_modulo_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.44/6.79 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (= (= (@ (@ tptp.bit_se1745604003318907178nteger N) A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) A))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) A) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) A))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) A) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) A))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) M))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 6.44/6.79 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_rat (@ F N)) (@ F M))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F M))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F M))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger N)) (= N tptp.zero_zero_nat))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N)) (= N tptp.zero_zero_nat))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N)) (= N tptp.zero_zero_nat))))
% 6.44/6.79 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))
% 6.44/6.79 (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))))))
% 6.44/6.79 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_2)))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) tptp.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 6.44/6.79 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X3))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X3)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X3)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X3))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X3)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.44/6.79 (assert (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X3))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X3)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.44/6.79 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.44/6.79 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.44/6.79 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.44/6.79 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 6.44/6.79 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.44/6.79 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.44/6.79 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))))
% 6.44/6.80 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))
% 6.44/6.80 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))))
% 6.44/6.80 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 6.44/6.80 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer))))))))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int))))))))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2925701944663578781it_nat N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat))))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.44/6.80 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) K5)) (@ (@ tptp.groups2906978787729119204at_rat G) K5)))))
% 6.44/6.80 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) K5)) (@ (@ tptp.groups1300246762558778688al_rat G) K5)))))
% 6.44/6.80 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) K5)) (@ (@ tptp.groups3906332499630173760nt_rat G) K5)))))
% 6.44/6.80 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) K5)) (@ (@ tptp.groups5058264527183730370ex_rat G) K5)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((R2 tptp.int) (F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.times_times_int R2) (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N2 tptp.int)) (@ (@ tptp.times_times_int R2) (@ F N2)))) A2))))
% 6.44/6.80 (assert (forall ((R2 tptp.nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R2) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_nat R2) (@ F N2)))) A2))))
% 6.44/6.80 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_real R2) (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real R2) (@ F N2)))) A2))))
% 6.44/6.80 (assert (forall ((R2 tptp.complex) (F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.times_times_complex R2) (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.times_times_complex R2) (@ F N2)))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (R2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) R2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N2 tptp.int)) (@ (@ tptp.times_times_int (@ F N2)) R2))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (R2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) R2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_nat (@ F N2)) R2))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) R2))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.times_times_complex (@ F N2)) R2))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (G (-> tptp.int tptp.int)) (B3 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) B3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I3)) (@ G J3)))) B3))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B3 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) B3)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I3)) (@ G J3)))) B3))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (B3 tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) B3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I3)) (@ G J3)))) B3))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (B3 tptp.set_complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) B3)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I3 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F I3)) (@ G J3)))) B3))) A2))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) R2))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) R2))) A2))))
% 6.44/6.80 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I3) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N) D)))) _let_1)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat) (X3 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X3))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X3 tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X3)))))))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat) (X3 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X3 tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X3)))))))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X3))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X3 tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X3)))))))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.44/6.80 (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))))))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N)) (= M N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N)) (= M N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) (@ tptp.semiri681578069525770553at_rat N)) (= M N))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) A) A)))
% 6.44/6.80 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) A) A)))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)))
% 6.44/6.80 (assert (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A2)))
% 6.44/6.80 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real) (= A2 tptp.bot_bot_set_real))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 6.44/6.80 (assert (forall ((X3 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X3) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.44/6.80 (assert (forall ((X3 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X3) tptp.zero_zero_int)))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.44/6.80 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.44/6.80 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) (@ tptp.semiri1314217659103216013at_int M))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 6.44/6.80 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 6.44/6.80 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.44/6.80 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.44/6.80 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.44/6.80 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))))
% 6.44/6.80 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int A) B) tptp.bot_bot_set_set_int) (not (@ (@ tptp.ord_less_eq_set_int A) B)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (not (@ (@ tptp.ord_less_eq_set_int A) B)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real A2) B3) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A2) B3))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A2) B3) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A2) B3))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A2) B3) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 6.44/6.80 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.44/6.80 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.44/6.80 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.44/6.80 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.44/6.80 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 6.44/6.80 (assert (forall ((X3 tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X3) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X3)))
% 6.44/6.80 (assert (forall ((X3 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X3) (@ tptp.uminus_uminus_int tptp.one_one_int)) X3)))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int M)) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real M)) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat M)) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat M)) N))))
% 6.44/6.80 (assert (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X3)) (= (@ (@ tptp.power_power_nat B) W) X3))))
% 6.44/6.80 (assert (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X3)) (= (@ (@ tptp.power_power_nat B) W) X3))))
% 6.44/6.80 (assert (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X3)) (= (@ (@ tptp.power_power_nat B) W) X3))))
% 6.44/6.80 (assert (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X3)) (= (@ (@ tptp.power_power_nat B) W) X3))))
% 6.44/6.80 (assert (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W) (@ tptp.semiri681578069525770553at_rat X3)) (= (@ (@ tptp.power_power_nat B) W) X3))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X3) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X3 (@ (@ tptp.power_power_nat B) W)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X3) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X3 (@ (@ tptp.power_power_nat B) W)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X3) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X3 (@ (@ tptp.power_power_nat B) W)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X3) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X3 (@ (@ tptp.power_power_nat B) W)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat X3) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (= X3 (@ (@ tptp.power_power_nat B) W)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) (@ tptp.semiri1314217659103216013at_int M))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 6.44/6.80 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.44/6.80 (assert (forall ((P Bool)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.44/6.80 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.44/6.80 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 6.44/6.80 (assert (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X3))) tptp.one_one_int) tptp.one_one_int)))
% 6.44/6.80 (assert (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3))) tptp.one_one_nat) tptp.one_one_nat)))
% 6.44/6.80 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) tptp.one_one_int)))
% 6.44/6.80 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 6.44/6.80 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat W)))))
% 6.44/6.80 (assert (forall ((N tptp.num) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.semiri5074537144036343181t_real M)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) M))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.44/6.80 (assert (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X3))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.44/6.80 (assert (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X3))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.44/6.80 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)))
% 6.44/6.80 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_int Y))))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_nat Y))))))
% 6.44/6.80 (assert (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X3))))
% 6.44/6.80 (assert (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X3))))
% 6.44/6.80 (assert (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X3))))
% 6.44/6.80 (assert (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X3))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat B) W)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat B) W)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X3)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat B) W)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat B) W)))))
% 6.44/6.80 (assert (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X3))))
% 6.44/6.80 (assert (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X3))))
% 6.44/6.80 (assert (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X3))))
% 6.44/6.80 (assert (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X3))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ tptp.power_power_nat B) W)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ tptp.power_power_nat B) W)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X3)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ tptp.power_power_nat B) W)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ tptp.power_power_nat B) W)))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X3)) N) (@ tptp.semiri8010041392384452111omplex Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N) (@ tptp.semiri1314217659103216013at_int Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N) (@ tptp.semiri5074537144036343181t_real Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N) (@ tptp.semiri681578069525770553at_rat Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N) Y))))
% 6.44/6.80 (assert (forall ((Y tptp.nat) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X3)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)))))
% 6.44/6.80 (assert (forall ((Y tptp.nat) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)))))
% 6.44/6.80 (assert (forall ((Y tptp.nat) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)))))
% 6.44/6.80 (assert (forall ((Y tptp.nat) (X3 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N))) (= (= (@ tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))))
% 6.44/6.80 (assert (forall ((Y tptp.nat) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc M))))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))))
% 6.44/6.80 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))))
% 6.44/6.80 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.inc M)))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int) tptp.one_one_int)))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int)))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X3)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X3) (= N tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X3)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X3) (= N tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X3)) N)) (or (@ _let_1 X3) (= N tptp.zero_zero_nat))))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X3)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X3) (= N tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_int Y))))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_nat Y))))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_int Y))))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_nat Y))))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.zero_zero_int)))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))))
% 6.44/6.80 (assert (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X3))))
% 6.44/6.80 (assert (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X3))))
% 6.44/6.80 (assert (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X3)) (@ _let_1 X3)))))
% 6.44/6.80 (assert (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X3))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X3)) _let_1) (@ (@ tptp.ord_less_nat X3) _let_1)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.44/6.80 (assert (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X3))))
% 6.44/6.80 (assert (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X3))))
% 6.44/6.80 (assert (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X3)) (@ _let_1 X3)))))
% 6.44/6.80 (assert (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X3))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X3)) _let_1) (@ (@ tptp.ord_less_eq_nat X3) _let_1)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_int Y)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.44/6.80 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int B2) A3))))
% 6.44/6.80 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat B2) A3))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.44/6.80 (assert (forall ((A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))))
% 6.44/6.80 (assert (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.44/6.80 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.44/6.80 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.44/6.80 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.44/6.80 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))))
% 6.44/6.80 (assert (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.44/6.80 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.44/6.80 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.44/6.80 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 6.44/6.80 (assert (forall ((A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.bot_bo4199563552545308370d_enat) A)))
% 6.44/6.80 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)))
% 6.44/6.80 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 6.44/6.80 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 6.44/6.80 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 6.44/6.80 (assert (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.bot_bo4199563552545308370d_enat))))
% 6.44/6.80 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 6.44/6.80 (assert (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))))
% 6.44/6.80 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 6.44/6.80 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 6.44/6.80 (assert (forall ((A tptp.extended_enat)) (= (not (= A tptp.bot_bo4199563552545308370d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.bot_bo4199563552545308370d_enat) A))))
% 6.44/6.80 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 6.44/6.80 (assert (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))))
% 6.44/6.80 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X3) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X3) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X3) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X3))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X3))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X3))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X3))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se2925701944663578781it_nat N) M)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X3)) (@ _let_1 X3)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ring_1_of_int_real X3)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X3))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.ring_1_of_int_rat X3)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X3))))
% 6.44/6.80 (assert (forall ((P (-> tptp.num Bool)) (X3 tptp.num)) (=> (@ P tptp.one) (=> (forall ((X5 tptp.num)) (=> (@ P X5) (@ P (@ tptp.inc X5)))) (@ P X3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X3))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 6.44/6.80 (assert (forall ((X3 tptp.set_real) (Y tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X3) Y) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X3) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X3) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X3) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X3) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X3) Y))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 6.44/6.80 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_3 (@ tptp.divide_divide_int A))) (= (@ _let_3 (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) _let_1)))))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_3 (@ tptp.divide_divide_nat A))) (= (@ _let_3 (@ (@ tptp.times_times_nat _let_2) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_3 _let_2)) _let_1)))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.80 (assert (forall ((Y tptp.int) (Z tptp.int) (X3 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 X3) Y)) Z)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((Y tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X3) Y)) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X3) Y)) X3))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X3) Y))))))
% 6.44/6.80 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I2)) (@ tptp.semiri5074537144036343181t_real J2)))))
% 6.44/6.80 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I2)) (@ tptp.semiri681578069525770553at_rat J2)))))
% 6.44/6.80 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I2)) (@ tptp.semiri1316708129612266289at_nat J2)))))
% 6.44/6.80 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J2)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.44/6.80 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ tptp.bit_se2000444600071755411sk_int N2)))))
% 6.44/6.80 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A3) (@ tptp.bit_se2002935070580805687sk_nat N2)))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.44/6.80 (assert (forall ((Z tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))))
% 6.44/6.80 (assert (forall ((P (-> tptp.int Bool)) (Z tptp.int)) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N3))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))) (@ P Z)))))
% 6.44/6.80 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.44/6.80 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.44/6.80 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.44/6.80 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N3))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N))) Z))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.44/6.80 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z5 tptp.int)) (exists ((N2 tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N2)))))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.ord_max_nat X3) Y)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.semiri4216267220026989637d_enat X3)) (@ tptp.semiri4216267220026989637d_enat Y)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X3) Y)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X3)) (@ tptp.semiri1314217659103216013at_int Y)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X3) Y)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X3)) (@ tptp.semiri5074537144036343181t_real Y)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X3) Y)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X3)) (@ tptp.semiri1316708129612266289at_nat Y)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.ord_max_nat X3) Y)) (@ (@ tptp.ord_max_rat (@ tptp.semiri681578069525770553at_rat X3)) (@ tptp.semiri681578069525770553at_rat Y)))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat A2)) (= A2 tptp.bot_bot_set_nat))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real A2)) (= A2 tptp.bot_bot_set_real))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int A2)) (= A2 tptp.bot_bot_set_int))))
% 6.44/6.80 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.44/6.80 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.44/6.80 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.44/6.80 (assert (forall ((X3 tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X3)) (@ tptp.bit0 (@ tptp.inc X3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X3)) (@ tptp.bit1 X3))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X3))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X3) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat Y) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N3)) X3))))))
% 6.44/6.80 (assert (forall ((X3 tptp.num)) (= (@ (@ tptp.plus_plus_num X3) tptp.one) (@ tptp.inc X3))))
% 6.44/6.80 (assert (forall ((Y tptp.int) (Z tptp.int) (X3 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 X3) Y)) Z)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N))))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (forall ((Y4 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X3)))))))
% 6.44/6.80 (assert (forall ((M tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X3))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X3)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))) (and (= N tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 6.44/6.80 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z5 tptp.int)) (exists ((N2 tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))
% 6.44/6.80 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3)))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_int)))
% 6.44/6.80 (assert (forall ((D tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) D)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real D))))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X3))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X3)))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((X3 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X3)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X3)) tptp.one_one_complex))))
% 6.44/6.80 (assert (forall ((X3 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X3)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X3)) tptp.one_one_real))))
% 6.44/6.80 (assert (forall ((X3 tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X3)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X3)) tptp.one_one_rat))))
% 6.44/6.80 (assert (forall ((X3 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X3)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X3)) tptp.one_one_nat))))
% 6.44/6.80 (assert (forall ((X3 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X3)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X3)) tptp.one_one_int))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_3 (@ tptp.semiri4939895301339042750nteger N))) (let ((_let_4 (@ tptp.times_3573771949741848930nteger _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_4 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.44/6.80 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_4 (@ tptp.times_times_int _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_4 (@ tptp.times_times_nat _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri8010041392384452111omplex N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.44/6.80 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= K (@ tptp.semiri1314217659103216013at_int N3)))))))
% 6.44/6.80 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 6.44/6.80 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))))))))
% 6.44/6.80 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M6)))))
% 6.44/6.80 (assert (= tptp.ord_less_eq_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M6)) tptp.one_one_real)))))
% 6.44/6.80 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J2)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) tptp.zero_zero_int) (exists ((N3 tptp.nat)) (= X3 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X3)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X3) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X3) D))) _let_1))))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) tptp.one_one_Code_integer) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) E)))))))
% 6.44/6.80 (assert (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) E)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) N))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _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)) X3)) C))) (= X3 tptp.zero_zero_real)))))))
% 6.44/6.80 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 6.44/6.80 (assert (forall ((P (-> tptp.int Bool)) (X3 tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X3) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X3) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X3)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X3) Y) (@ P tptp.zero_zero_int))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X3))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X3))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X3))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X3)))) tptp.one_one_real)))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X3)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X3) tptp.one_one_real)) N)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X3))) (@ (@ tptp.power_power_real (@ _let_1 X3)) N))))))
% 6.44/6.80 (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)))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.44/6.80 (assert (forall ((A tptp.complex) (D tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (@ (@ tptp.plus_plus_complex (@ _let_2 A)) (@ (@ tptp.times_times_complex _let_1) D))))))))
% 6.44/6.80 (assert (forall ((A tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A)) (@ (@ tptp.times_times_int _let_1) D))))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (D tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (let ((_let_2 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat (@ _let_2 A)) (@ (@ tptp.times_times_rat _let_1) D))))))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A)) (@ (@ tptp.times_times_nat _let_1) D))))))))
% 6.44/6.80 (assert (forall ((A tptp.real) (D tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real (@ _let_2 A)) (@ (@ tptp.times_times_real _let_1) D))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.44/6.80 (assert (forall ((A tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A)) (@ (@ tptp.times_times_int _let_2) D)))) _let_1))))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat _let_2) D)))) _let_1))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X3))) (@ (@ tptp.power_power_real (@ _let_1 X3)) N))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X3))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X3 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X3)))))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X3))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X3 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X3)))))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X3))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X3 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X3)))))))))))
% 6.44/6.80 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_complex (= N2 tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M6)))) (@ (@ (@ tptp.if_complex (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.44/6.80 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M6)))) (@ (@ (@ tptp.if_int (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.44/6.80 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M6)))) (@ (@ (@ tptp.if_real (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.44/6.80 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M6)))) (@ (@ (@ tptp.if_nat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.44/6.80 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_rat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_rat) (@ (@ tptp.produc6207742614233964070at_rat (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ tptp.semiri681578069525770553at_rat M6)))) (@ (@ (@ tptp.if_rat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.44/6.80 (assert (forall ((H2 tptp.real) (Z tptp.real) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)))) (let ((_let_4 (@ tptp.power_power_real Z))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z) H2))) (=> (not (= H2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N)) (@ _let_4 N))) H2)) (@ _let_3 (@ _let_4 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H2)))))))))))))
% 6.44/6.80 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.power_power_complex Z))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z) H2))) (=> (not (= H2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N)) (@ _let_3 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H2))))))))))))
% 6.44/6.80 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.times_times_complex _let_2) Z)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z) N))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N)))))))))
% 6.44/6.80 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.times_times_real _let_2) Z)) _let_4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s7457072308508201937r_real Z) N))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N)))))))))
% 6.44/6.80 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.times_times_rat _let_2) Z)) _let_4) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s4028243227959126397er_rat Z) N))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N)))))))))
% 6.44/6.80 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I3 tptp.complex)) (@ (@ tptp.plus_plus_complex I3) tptp.one_one_complex))) N2) tptp.zero_zero_complex))))
% 6.44/6.80 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I3 tptp.int)) (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))) N2) tptp.zero_zero_int))))
% 6.44/6.80 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I3 tptp.real)) (@ (@ tptp.plus_plus_real I3) tptp.one_one_real))) N2) tptp.zero_zero_real))))
% 6.44/6.80 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat))) N2) tptp.zero_zero_nat))))
% 6.44/6.80 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I3 tptp.rat)) (@ (@ tptp.plus_plus_rat I3) tptp.one_one_rat))) N2) tptp.zero_zero_rat))))
% 6.44/6.80 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_complex Z))) (=> (not (= H2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((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 N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.44/6.80 (assert (forall ((H2 tptp.rat) (Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_rat Z))) (=> (not (= H2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_rat H2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) Q4)) (@ (@ tptp.power_power_rat Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.44/6.80 (assert (forall ((H2 tptp.real) (Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_real Z))) (=> (not (= H2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((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 N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.44/6.80 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K3)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N2))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat X3) (@ tptp.set_ord_lessThan_nat Y)) (= X3 Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (= (@ tptp.set_ord_lessThan_int X3) (@ tptp.set_ord_lessThan_int Y)) (= X3 Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (= (@ tptp.set_or5984915006950818249n_real X3) (@ tptp.set_or5984915006950818249n_real Y)) (= X3 Y))))
% 6.44/6.80 (assert (forall ((I2 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat I2) K))))
% 6.44/6.80 (assert (forall ((I2 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I2) K))))
% 6.44/6.80 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I2) K))))
% 6.44/6.80 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I2) K))))
% 6.44/6.80 (assert (forall ((I2 tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I2) K))))
% 6.44/6.80 (assert (= (@ tptp.bit_se1146084159140164899it_int tptp.zero_zero_int) tptp.bot_bot_nat_o))
% 6.44/6.80 (assert (= (@ tptp.bit_se1148574629649215175it_nat tptp.zero_zero_nat) tptp.bot_bot_nat_o))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_lessThan_rat X3)) (@ tptp.set_ord_lessThan_rat Y)) (@ (@ tptp.ord_less_eq_rat X3) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X3)) (@ tptp.set_ord_lessThan_num Y)) (@ (@ tptp.ord_less_eq_num X3) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X3)) (@ tptp.set_ord_lessThan_nat Y)) (@ (@ tptp.ord_less_eq_nat X3) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X3)) (@ tptp.set_ord_lessThan_int Y)) (@ (@ tptp.ord_less_eq_int X3) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X3)) (@ tptp.set_or5984915006950818249n_real Y)) (@ (@ tptp.ord_less_eq_real X3) Y))))
% 6.44/6.80 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.44/6.80 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.44/6.80 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.44/6.80 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.44/6.80 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N))))
% 6.44/6.80 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))))
% 6.44/6.80 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N))))
% 6.44/6.80 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N))))
% 6.44/6.80 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N)))))
% 6.44/6.80 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N)))))
% 6.44/6.80 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N))))
% 6.44/6.80 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N)))))
% 6.44/6.80 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N)))))
% 6.44/6.80 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N)))))
% 6.44/6.80 (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)))
% 6.44/6.80 (assert (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X3))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))
% 6.44/6.80 (assert (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 6.44/6.80 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N)))))
% 6.44/6.80 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N))))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.modulo_modulo_int A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.semiri1314217659103216013at_int M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.semiri1316708129612266289at_nat M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))))
% 6.44/6.80 (assert (forall ((M tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))) (= _let_1 _let_1))))
% 6.44/6.80 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N3)) (not (@ (@ tptp.bit_se1146084159140164899it_int B) N3)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) B)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N) (@ (@ tptp.bit_se1146084159140164899it_int B) N))))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N3)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B) N3)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) B)) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (@ (@ tptp.bit_se1148574629649215175it_nat B) N))))))
% 6.44/6.80 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.44/6.80 (assert (forall ((X3 tptp.int)) (not (= (@ tptp.set_ord_lessThan_int X3) tptp.bot_bot_set_int))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (not (= (@ tptp.set_or5984915006950818249n_real X3) tptp.bot_bot_set_real))))
% 6.44/6.80 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int A) B)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N) (@ (@ tptp.bit_se1146084159140164899it_int B) N)))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) N) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (@ (@ tptp.bit_se1148574629649215175it_nat B) N)))))
% 6.44/6.80 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se4203085406695923979it_int M) A)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N) (not (= M N))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) N) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (not (= M N))))))
% 6.44/6.80 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 6.44/6.80 (assert (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat X2) U2))))))
% 6.44/6.80 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_num X2) U2))))))
% 6.44/6.80 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) U2))))))
% 6.44/6.80 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_int X2) U2))))))
% 6.44/6.80 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_real X2) U2))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.suc N)))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) N) (= N tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N) (= N tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.numeral_numeral_nat N)))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se2923211474154528505it_int M) A)) N) (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1146084159140164899it_int A) N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) A)) N) (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))))
% 6.44/6.80 (assert (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.zero_n356916108424825756nteger B)) N) (and B (= N tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.zero_n2684676970156552555ol_int B)) N) (and B (= N tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.zero_n2687167440665602831ol_nat B)) N) (and B (= N tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((N tptp.extended_enat)) (= (= (@ tptp.set_or8419480210114673929d_enat N) tptp.bot_bo7653980558646680370d_enat) (= N tptp.bot_bo4199563552545308370d_enat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.bot_bot_nat))))
% 6.44/6.80 (assert (forall ((M tptp.rat) (N tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M)) (@ tptp.set_ord_lessThan_rat N)) (@ (@ tptp.ord_less_rat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N)) (@ (@ tptp.ord_less_num M) N))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.44/6.80 (assert (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N)) (@ (@ tptp.ord_less_int M) N))))
% 6.44/6.80 (assert (forall ((M tptp.real) (N tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M)) (@ tptp.set_or5984915006950818249n_real N)) (@ (@ tptp.ord_less_real M) N))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) A) (@ (@ tptp.bit_se2923211474154528505it_int N) A)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X3) N))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X3) N))))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X3) N))))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X3) N))))))
% 6.44/6.80 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_complex)))))))
% 6.44/6.80 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_real)))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_rat)))))))
% 6.44/6.80 (assert (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_complex))))))
% 6.44/6.80 (assert (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_real))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_rat))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (R2 tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int F) _let_1)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) R2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I3)) R2))) _let_1)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (R2 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat F) _let_1)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) R2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I3)) R2))) _let_1)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (R2 tptp.real)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) _let_1)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) R2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I3)) R2))) _let_1)))))
% 6.44/6.80 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X3) N)))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X3) N)))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X3) N)))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X3) N)))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))))
% 6.44/6.80 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (@ (@ (@ (@ (@ tptp.if_nat_int_int (@ (@ tptp.bit_se1146084159140164899it_int A3) N2)) tptp.bit_se4203085406695923979it_int) tptp.bit_se7879613467334960850it_int) N2) A3))))
% 6.44/6.80 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (@ (@ (@ (@ (@ tptp.if_nat_nat_nat (@ (@ tptp.bit_se1148574629649215175it_nat A3) N2)) tptp.bit_se4205575877204974255it_nat) tptp.bit_se7882103937844011126it_nat) N2) A3))))
% 6.44/6.80 (assert (forall ((Q (-> tptp.int tptp.nat)) (P (-> tptp.int tptp.nat)) (N tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_int N))) (=> (forall ((X5 tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat P) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat Q) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))))
% 6.44/6.80 (assert (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N))) (=> (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))))))
% 6.44/6.80 (assert (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (=> (forall ((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))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L2)) N) (or (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N)) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) (@ (@ tptp.minus_minus_nat N) M)))))))
% 6.44/6.80 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N)))))
% 6.44/6.80 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) N)))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N)))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N)))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N)))))))
% 6.44/6.80 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N)))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N)))))))
% 6.44/6.80 (assert (forall ((Z tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N))) (@ _let_1 N))))))
% 6.44/6.80 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N))) (@ _let_1 N))))))
% 6.44/6.80 (assert (forall ((Z tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N))) (@ _let_1 N))))))
% 6.44/6.80 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N))) (@ _let_1 N))))))
% 6.44/6.80 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K3))))))))
% 6.44/6.80 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K3))))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K3))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N) K))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N) K))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N) K))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N) K))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N) K))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex)))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger)))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int)))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real)))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat)))))
% 6.44/6.80 (assert (forall ((Z tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N))) M))))))
% 6.44/6.80 (assert (forall ((Z tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N))) M))))))
% 6.44/6.80 (assert (forall ((Z tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N))) M))))))
% 6.44/6.80 (assert (forall ((Z tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N))) M))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.44/6.80 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N2) K3) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N2)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((Z tptp.rat) (H2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_rat Z))) (@ (@ tptp.times_times_rat (@ _let_2 P4)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) N))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (=> (forall ((N3 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N3) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (=> (forall ((N3 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N3) (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))))
% 6.44/6.80 (assert (forall ((A tptp.nat)) (=> (forall ((N3 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N3) (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))))
% 6.44/6.80 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N3) M2) (= (@ _let_1 M2) (@ _let_1 N3))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (not (@ _let_1 N3)))))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.rat)) (K5 tptp.rat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_rat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) K5) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) K5))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_int (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K5) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) K5))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_nat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) K5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) K5))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_real (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) K5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) K5))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X3))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_complex (@ _let_2 X3)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_rat (@ _let_2 X3)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X3))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_int (@ _let_2 X3)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X3))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_real (@ _let_2 X3)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X3))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X3) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X3) tptp.one_one_rat)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X3))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X3) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X3))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X3) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X3))) (=> (not (= X3 tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X3) tptp.one_one_complex)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (=> (not (= X3 tptp.one_one_rat)) (= (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X3) tptp.one_one_rat)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X3))) (=> (not (= X3 tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X3) tptp.one_one_real)))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.44/6.80 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A3 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger A3) (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))))))))
% 6.44/6.80 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int A3) (@ (@ tptp.power_power_int _let_1) N2))))))))
% 6.44/6.80 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat A3) (@ (@ tptp.power_power_nat _let_1) N2))))))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.bit_se727722235901077358nd_nat A) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))))
% 6.44/6.80 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K3 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int _let_1) N2))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X3))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X3 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N))) (@ _let_1 X3)))))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X3))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X3 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 N))) (@ _let_1 X3)))))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X3))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X3 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N))) (@ _let_1 X3)))))))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ F I3)) (@ G I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) tptp.one_one_nat)))) _let_1))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (N tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.power_power_complex Y) N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X3) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3)))) (@ (@ tptp.power_power_complex X3) I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (N tptp.nat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X3) N)) (@ (@ tptp.power_power_rat Y) N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X3) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3)))) (@ (@ tptp.power_power_rat X3) I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (N tptp.nat) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X3) N)) (@ (@ tptp.power_power_int Y) N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X3) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3)))) (@ (@ tptp.power_power_int X3) I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.power_power_real Y) N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X3) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3)))) (@ (@ tptp.power_power_real X3) I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (N tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X3) _let_1)) (@ (@ tptp.power_power_complex Y) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X3) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X3) P4)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (N tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X3) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X3) P4)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X3) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X3) P4)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X3) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X3) P4)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.44/6.80 (assert (forall ((R2 tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R2) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R2) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))))
% 6.44/6.80 (assert (forall ((R2 tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R2) (@ tptp.semiri4939895301339042750nteger K))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K)) (@ (@ tptp.times_3573771949741848930nteger R2) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K))))))
% 6.44/6.80 (assert (forall ((R2 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R2))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R2) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R2) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))))
% 6.44/6.80 (assert (forall ((R2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R2))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R2) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))))
% 6.44/6.80 (assert (forall ((R2 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R2))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R2) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K)) (@ (@ tptp.times_times_rat R2) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) N) (or (@ (@ tptp.bit_se9216721137139052372nteger A) N) (= N tptp.zero_zero_nat))))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N) (= N tptp.zero_zero_nat))))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (= N tptp.zero_zero_nat))))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N) (or (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.minus_8373710615458151222nteger A) tptp.one_one_Code_integer)) N) (= N tptp.zero_zero_nat))))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N) (or (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int A) tptp.one_one_int)) N) (= N tptp.zero_zero_nat))))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.minus_minus_nat A) tptp.one_one_nat)) N) (= N tptp.zero_zero_nat))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.times_times_complex (@ _let_1 X3)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.power_power_rat X3) N)) (@ (@ tptp.times_times_rat (@ _let_1 X3)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_rat X3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X3) N)) (@ (@ tptp.times_times_int (@ _let_1 X3)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.times_times_real (@ _let_1 X3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J tptp.nat)) (not (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc J)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N))))))))))
% 6.44/6.80 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N))))))))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1148574629649215175it_nat _let_2) N))))))))))
% 6.44/6.80 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A3 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A3) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))))
% 6.44/6.80 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_int _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A3) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))))
% 6.44/6.80 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_nat _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A3) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))))
% 6.44/6.80 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M6 tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.44/6.80 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M6)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.44/6.80 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N2)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 6.44/6.80 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N2))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) K) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K) N)))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X3)) tptp.zero_zero_real) (= X3 tptp.zero_zero_real))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X3)) tptp.zero_zero_real) (= X3 tptp.zero_zero_complex))))
% 6.44/6.80 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 6.44/6.80 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 6.44/6.80 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 6.44/6.80 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat _let_1) N2))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X3))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X3) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X3) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.44/6.80 (assert (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F) S3))) (@ (@ tptp.groups8097168146408367636l_real G) S3)))))
% 6.44/6.80 (assert (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S3))) (@ (@ tptp.groups8778361861064173332t_real G) S3)))))
% 6.44/6.80 (assert (forall ((S3 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) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups6381953495645901045omplex F) S3))) (@ (@ tptp.groups4567486121110086003t_real G) S3)))))
% 6.44/6.80 (assert (forall ((S3 tptp.set_nat) (F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S3))) (@ (@ tptp.groups6591440286371151544t_real G) S3)))))
% 6.44/6.80 (assert (forall ((S3 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S3) (@ (@ 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) S3))) (@ (@ tptp.groups6591440286371151544t_real G) S3)))))
% 6.44/6.80 (assert (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S3))) (@ (@ tptp.groups5808333547571424918x_real G) S3)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X3)) N))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X3)) N))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F I3)))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F I3)))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) A2))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I3 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ F I3)))) A2))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X3)) Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X3) Y)))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X3)) Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X3) Y)))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((W tptp.real) (N tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N) (@ (@ tptp.power_power_real Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z))))))
% 6.44/6.80 (assert (forall ((W tptp.complex) (N tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N) (@ (@ tptp.power_power_complex Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (R2 tptp.real) (Y tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X3)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X3) Y))) (@ (@ tptp.times_times_real R2) S))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (R2 tptp.real) (Y tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X3)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X3) Y))) (@ (@ tptp.times_times_real R2) S))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X3) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X3) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X3) Y))) E))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X3) Y))) E))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (R2 tptp.real) (Y tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X3)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X3) Y))) (@ (@ tptp.plus_plus_real R2) S))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (R2 tptp.real) (Y tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X3)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X3) Y))) (@ (@ tptp.plus_plus_real R2) S))))))
% 6.44/6.80 (assert (forall ((A tptp.real) (R2 tptp.real) (B tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real R2) S))))))
% 6.44/6.80 (assert (forall ((A tptp.complex) (R2 tptp.real) (B tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) (@ (@ tptp.plus_plus_real R2) S))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X3) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X3) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X3) Y))) E))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X3) Y))) E))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X3) N))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X3)) N))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X3) N))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X3)) N))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X3))) (=> (@ (@ 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)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X3))) (=> (@ (@ 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)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X3) Y))) E))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X3) Y))) E))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X3))) (=> (@ (@ 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)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X3))) (=> (@ (@ 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)))))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X3)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X3) Y))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X3)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X3) Y))))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((W tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((W tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (= (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X3) tptp.one_one_real))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X3) tptp.one_one_real))))
% 6.44/6.80 (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))))))))
% 6.44/6.80 (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))))))))
% 6.44/6.80 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M6)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)))
% 6.44/6.80 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.comm_s2602460028002588243omplex Z) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K3)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.44/6.80 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_real (@ (@ tptp.comm_s7457072308508201937r_real Z) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.44/6.80 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.comm_s4028243227959126397er_rat Z) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat _let_1)))) _let_2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K3)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.44/6.80 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A3 tptp.complex) (N2 tptp.nat)) (@ (@ (@ tptp.if_complex (= N2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A3) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_complex)))))
% 6.44/6.80 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A3 tptp.int) (N2 tptp.nat)) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A3) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_int)))))
% 6.44/6.80 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A3 tptp.real) (N2 tptp.nat)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A3) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_real)))))
% 6.44/6.80 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A3 tptp.rat) (N2 tptp.nat)) (@ (@ (@ tptp.if_rat (= N2 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A3) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_rat)))))
% 6.44/6.80 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A3) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_nat)))))
% 6.44/6.80 (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))))))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X3) A2)) B3) (and (@ (@ tptp.member_nat X3) B3) (@ (@ tptp.ord_less_eq_set_nat A2) B3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X3) A2)) B3) (and (@ (@ tptp.member_real X3) B3) (@ (@ tptp.ord_less_eq_set_real A2) B3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ (@ tptp.insert_complex X3) A2)) B3) (and (@ (@ tptp.member_complex X3) B3) (@ (@ tptp.ord_le211207098394363844omplex A2) B3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.insert8211810215607154385at_nat X3) A2)) B3) (and (@ (@ tptp.member8440522571783428010at_nat X3) B3) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X3) A2)) B3) (and (@ (@ tptp.member_int X3) B3) (@ (@ tptp.ord_less_eq_set_int A2) B3)))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu3 tptp.nat)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.44/6.80 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu3 tptp.int)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu3 tptp.nat)) tptp.one_one_nat)) A2) tptp.one_one_nat)))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups6464643781859351333omplex G) tptp.bot_bot_set_nat) tptp.one_one_complex)))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups129246275422532515t_real G) tptp.bot_bot_set_nat) tptp.one_one_real)))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups73079841787564623at_rat G) tptp.bot_bot_set_nat) tptp.one_one_rat)))
% 6.44/6.80 (assert (forall ((G (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups7440179247065528705omplex G) tptp.bot_bot_set_int) tptp.one_one_complex)))
% 6.44/6.80 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups2316167850115554303t_real G) tptp.bot_bot_set_int) tptp.one_one_real)))
% 6.44/6.80 (assert (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) tptp.bot_bot_set_int) tptp.one_one_rat)))
% 6.44/6.80 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) tptp.bot_bot_set_int) tptp.one_one_nat)))
% 6.44/6.80 (assert (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups713298508707869441omplex G) tptp.bot_bot_set_real) tptp.one_one_complex)))
% 6.44/6.80 (assert (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups1681761925125756287l_real G) tptp.bot_bot_set_real) tptp.one_one_real)))
% 6.44/6.80 (assert (forall ((G (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups4061424788464935467al_rat G) tptp.bot_bot_set_real) tptp.one_one_rat)))
% 6.44/6.80 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) (@ (@ tptp.insert_nat C) tptp.bot_bot_set_nat)) (and (= A B) (= B C)))))
% 6.44/6.80 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) (@ (@ tptp.insert_int C) tptp.bot_bot_set_int)) (and (= A B) (= B C)))))
% 6.44/6.80 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) (@ (@ tptp.insert_real C) tptp.bot_bot_set_real)) (and (= A B) (= B C)))))
% 6.44/6.80 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat A) A) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int A) A) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (= (@ (@ tptp.set_or1222579329274155063t_real A) A) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))
% 6.44/6.80 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 6.44/6.80 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat))) (= (@ (@ tptp.minus_minus_set_nat _let_1) (@ tptp.set_ord_lessThan_nat K)) _let_1))))
% 6.44/6.80 (assert (forall ((K tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int K) tptp.bot_bot_set_int))) (= (@ (@ tptp.minus_minus_set_int _let_1) (@ tptp.set_ord_lessThan_int K)) _let_1))))
% 6.44/6.80 (assert (forall ((K tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real K) tptp.bot_bot_set_real))) (= (@ (@ tptp.minus_minus_set_real _let_1) (@ tptp.set_or5984915006950818249n_real K)) _let_1))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.vEBT_VEBT)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X3)) (@ (@ tptp.insert_VEBT_VEBT X3) tptp.bot_bo8194388402131092736T_VEBT)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X3)) (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.int)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X3)) (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real N) X3)) (@ (@ tptp.insert_real X3) tptp.bot_bot_set_real)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.one_one_complex)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.real tptp.complex)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups713298508707869441omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.one_one_complex)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.int tptp.complex)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups7440179247065528705omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G A5) tptp.one_one_complex)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups3708469109370488835omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (= (@ G A5) tptp.one_one_complex)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.real tptp.real)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1681761925125756287l_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.int tptp.real)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups2316167850115554303t_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.complex tptp.real)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups766887009212190081x_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups73079841787564623at_rat G) A2) tptp.one_one_rat)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.one_one_rat)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.real tptp.rat)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups4061424788464935467al_rat G) A2) tptp.one_one_rat)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.one_one_rat)))))))
% 6.44/6.80 (assert (forall ((C5 tptp.set_nat) (D4 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.ord_less_eq_set_nat C5) D4) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C5)) (@ _let_1 D4))))))
% 6.44/6.80 (assert (forall ((C5 tptp.set_real) (D4 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ tptp.insert_real A))) (=> (@ (@ tptp.ord_less_eq_set_real C5) D4) (@ (@ tptp.ord_less_eq_set_real (@ _let_1 C5)) (@ _let_1 D4))))))
% 6.44/6.80 (assert (forall ((C5 tptp.set_int) (D4 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.ord_less_eq_set_int C5) D4) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C5)) (@ _let_1 D4))))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (not (@ (@ tptp.member_nat X3) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X3) B3)) (@ _let_1 B3))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (not (@ (@ tptp.member_real X3) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X3) B3)) (@ _let_1 B3))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.ord_le211207098394363844omplex A2))) (=> (not (@ (@ tptp.member_complex X3) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X3) B3)) (@ _let_1 B3))))))
% 6.44/6.80 (assert (forall ((X3 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X3) A2)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X3) B3)) (@ _let_1 B3))))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (not (@ (@ tptp.member_int X3) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X3) B3)) (@ _let_1 B3))))))
% 6.44/6.80 (assert (forall ((B3 tptp.set_nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.insert_nat A) B3))))
% 6.44/6.80 (assert (forall ((B3 tptp.set_real) (A tptp.real)) (@ (@ tptp.ord_less_eq_set_real B3) (@ (@ tptp.insert_real A) B3))))
% 6.44/6.80 (assert (forall ((B3 tptp.set_int) (A tptp.int)) (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.insert_int A) B3))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.insert_nat B) B3))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.insert_real B) B3))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.insert_int B) B3))))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A2)) N) (@ (@ tptp.groups705719431365010083at_int (lambda ((X2 tptp.nat)) (@ (@ tptp.power_power_int (@ F X2)) N))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) N) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.power_power_int (@ F X2)) N))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) N) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.power_power_nat (@ F X2)) N))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.modulo_modulo_int (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int F) A2)) A))))
% 6.44/6.80 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) A))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) A))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) (@ (@ tptp.groups73079841787564623at_rat G) A2)))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) (@ (@ tptp.groups4061424788464935467al_rat G) A2)))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) (@ (@ tptp.groups1072433553688619179nt_rat G) A2)))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) (@ (@ tptp.groups225925009352817453ex_rat G) A2)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) A2)))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) A2)))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) A2)))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) A2)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_complex))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_real))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_rat))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_int))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_nat))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat) (X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (or (= A2 tptp.bot_bot_set_nat) (= A2 _let_1))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_real) (X3 tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real X3) tptp.bot_bot_set_real))) (=> (@ (@ tptp.ord_less_eq_set_real A2) _let_1) (or (= A2 tptp.bot_bot_set_real) (= A2 _let_1))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_int) (X3 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))) (=> (@ (@ tptp.ord_less_eq_set_int A2) _let_1) (or (= A2 tptp.bot_bot_set_int) (= A2 _let_1))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A B) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)))))
% 6.44/6.80 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A B) (= (@ (@ tptp.set_or1266510415728281911st_int A) B) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)))))
% 6.44/6.80 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= A B) (= (@ (@ tptp.set_or1222579329274155063t_real A) B) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (X3 tptp.real) (C5 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real B3))) (let ((_let_2 (@ tptp.ord_less_eq_set_real A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_real X3) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_real X3) A2))))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (X3 tptp.complex) (C5 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex B3))) (let ((_let_2 (@ tptp.ord_le211207098394363844omplex A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_complex X3) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_complex X3) A2))))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (X3 tptp.product_prod_nat_nat) (C5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat B3))) (let ((_let_2 (@ tptp.ord_le3146513528884898305at_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X3) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member8440522571783428010at_nat X3) A2))))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (X3 tptp.nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B3))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X3) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_nat X3) A2))))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (X3 tptp.int) (C5 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B3))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X3) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_int X3) A2))))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.44/6.80 (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 ((A3 tptp.nat)) (@ (@ tptp.power_power_real C) (@ F A3)))) A2))))
% 6.44/6.80 (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 ((A3 tptp.nat)) (@ (@ tptp.power_power_complex C) (@ F A3)))) A2))))
% 6.44/6.80 (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 ((A3 tptp.nat)) (@ (@ tptp.power_power_int C) (@ F A3)))) A2))))
% 6.44/6.80 (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 ((A3 tptp.int)) (@ (@ tptp.power_power_int C) (@ F A3)))) A2))))
% 6.44/6.80 (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 ((A3 tptp.nat)) (@ (@ tptp.power_power_nat C) (@ F A3)))) A2))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_nat X5) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) tptp.one_one_rat))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_real X5) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) tptp.one_one_rat))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_int X5) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) tptp.one_one_rat))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X5 tptp.complex)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_complex X5) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) tptp.one_one_rat))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_real) (X3 tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X3))) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) B3) (@ (@ tptp.ord_less_eq_set_real A2) (@ _let_1 B3))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat) (X3 tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X3))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) B3) (@ (@ tptp.ord_less_eq_set_nat A2) (@ _let_1 B3))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_int) (X3 tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X3))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) B3) (@ (@ tptp.ord_less_eq_set_int A2) (@ _let_1 B3))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_complex) (X3 tptp.complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.ord_le211207098394363844omplex A2))) (let ((_let_2 (@ (@ tptp.member_complex X3) A2))) (let ((_let_3 (@ tptp.insert_complex X3))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_le211207098394363844omplex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X3 tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (let ((_let_2 (@ (@ tptp.member8440522571783428010at_nat X3) A2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X3))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_real) (X3 tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (let ((_let_2 (@ (@ tptp.member_real X3) A2))) (let ((_let_3 (@ tptp.insert_real X3))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat) (X3 tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (let ((_let_2 (@ (@ tptp.member_nat X3) A2))) (let ((_let_3 (@ tptp.insert_nat X3))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_int) (X3 tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (let ((_let_2 (@ (@ tptp.member_int X3) A2))) (let ((_let_3 (@ tptp.insert_int X3))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.44/6.80 (assert (forall ((Xs tptp.list_real) (I2 tptp.nat) (X3 tptp.real)) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) I2) X3))) (@ (@ tptp.insert_real X3) (@ tptp.set_real2 Xs)))))
% 6.44/6.80 (assert (forall ((Xs tptp.list_nat) (I2 tptp.nat) (X3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I2) X3))) (@ (@ tptp.insert_nat X3) (@ tptp.set_nat2 Xs)))))
% 6.44/6.80 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I2 tptp.nat) (X3 tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3))) (@ (@ tptp.insert_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)))))
% 6.44/6.80 (assert (forall ((Xs tptp.list_int) (I2 tptp.nat) (X3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I2) X3))) (@ (@ tptp.insert_int X3) (@ tptp.set_int2 Xs)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups705719431365010083at_int G) _let_1)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups708209901874060359at_nat G) _let_1)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I3)))) _let_1)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I3)))) _let_1)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G M)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G M)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G M)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G M)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_complex) (X3 tptp.complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex X3))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_complex X3))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_complex A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B3)) (=> (not _let_2) (@ (@ tptp.ord_le211207098394363844omplex A2) B3)))))))))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X3 tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X3))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X3))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_le7866589430770878221at_nat A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B3)) (=> (not _let_2) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3)))))))))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_real) (X3 tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real X3))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_real X3))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_real A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A2) B3)))))))))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_nat) (X3 tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X3))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_nat X3))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_nat A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A2) B3)))))))))))))
% 6.44/6.80 (assert (forall ((A2 tptp.set_int) (X3 tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X3))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_int X3))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_int A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A2) B3)))))))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.vEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N)) X3)) (@ (@ tptp.insert_VEBT_VEBT X3) tptp.bot_bo8194388402131092736T_VEBT))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat (@ tptp.suc N)) X3)) (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.int)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int (@ tptp.suc N)) X3)) (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.real)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real (@ tptp.suc N)) X3)) (@ (@ tptp.insert_real X3) tptp.bot_bot_set_real))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X3)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bo8194388402131092736T_VEBT)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_VEBT_VEBT X3) tptp.bot_bo8194388402131092736T_VEBT))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X3)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.int)) (let ((_let_1 (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X3)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.set_real2 (@ (@ tptp.replicate_real N) X3)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_real X3) tptp.bot_bot_set_real))))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.44/6.80 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N))) (=> (@ (@ tptp.ord_less_eq_int M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N))))))))
% 6.44/6.80 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I3)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I3) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups129246275422532515t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.44/6.80 (assert (forall ((X3 (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb3 tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X3))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb3) Xa2))) (=> (= (@ (@ (@ _let_1 Xa2) Xb3) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb3) (@ (@ X3 Xa2) Xc))))))))))
% 6.44/6.80 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B2 tptp.nat) (Acc2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B2) A3)) Acc2) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F3) (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) B2) (@ (@ F3 A3) Acc2))))))
% 6.44/6.80 (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 ((I3 tptp.real)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I6))))))
% 6.44/6.80 (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 ((I3 tptp.int)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I6))))))
% 6.44/6.80 (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 ((I3 tptp.complex)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I6))))))
% 6.44/6.80 (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 ((I3 tptp.product_prod_nat_nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I6))))))
% 6.44/6.80 (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 ((I3 tptp.real)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I6))))))
% 6.44/6.80 (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 ((I3 tptp.int)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I6))))))
% 6.44/6.80 (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 ((I3 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I6))))))
% 6.44/6.80 (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 ((I3 tptp.product_prod_nat_nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I6))))))
% 6.44/6.80 (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 ((I3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I6))))))
% 6.44/6.80 (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 ((I3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I6))))))
% 6.44/6.80 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.44/6.80 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A3 tptp.real) (N2 tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A3) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.44/6.80 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A3 tptp.rat) (N2 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.44/6.80 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A3 tptp.int) (N2 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.44/6.80 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A3 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A3) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups129246275422532515t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.44/6.80 (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 ((A3 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_complex))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_rat))))
% 6.44/6.80 (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 ((A3 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_int))))
% 6.44/6.80 (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 ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_nat))))
% 6.44/6.80 (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 ((A3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_real))))
% 6.44/6.80 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.44/6.80 (assert (forall ((X3 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 X3)) (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 X3) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X3) 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 X3) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))))
% 6.44/6.80 (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))))))))))))))))
% 6.44/6.80 (assert (forall ((X3 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 X3) 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 X3)) (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 X3) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X3) 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 X3) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))))
% 6.44/6.80 (assert (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.44/6.80 (assert (forall ((Z tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.44/6.80 (assert (forall ((R2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R2) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R2) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R2) _let_1))))))
% 6.44/6.80 (assert (forall ((R2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat R2) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat R2) _let_1))))))
% 6.44/6.80 (assert (forall ((R2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R2) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R2) _let_1))))))
% 6.44/6.80 (assert (forall ((X3 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) X3) (=> (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X3)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X3)))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) N)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) N)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)))
% 6.44/6.80 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 6.44/6.80 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)))
% 6.44/6.80 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 6.44/6.80 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 6.44/6.80 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.44/6.80 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 6.44/6.80 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 6.44/6.80 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.44/6.80 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.44/6.80 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.binomial N))) (= (@ (@ tptp.binomial (@ tptp.suc N)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)) (@ (@ tptp.ord_less_eq_nat K) N))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X3)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_eq_real X3) Y)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X3) tptp.one_one_real)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (= (@ _let_1 (@ tptp.ln_ln_real X3)) (@ (@ tptp.ord_less_real tptp.one_one_real) X3))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (= (@ tptp.ln_ln_real X3) tptp.zero_zero_real) (= X3 tptp.one_one_real)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X3)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real)))))
% 6.44/6.80 (assert (forall ((A (-> tptp.nat tptp.complex)) (X3 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) X3) (= (@ A tptp.zero_zero_nat) X3))))
% 6.44/6.80 (assert (forall ((A (-> tptp.nat tptp.real)) (X3 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ A N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) X3) (= (@ A tptp.zero_zero_nat) X3))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) K)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (R2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (let ((_let_2 (@ _let_1 R2))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K)))) (let ((_let_4 (@ _let_1 K))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K)) (@ (@ tptp.times_times_nat (@ _let_3 K)) (@ (@ tptp.binomial _let_2) M)))))))))
% 6.44/6.80 (assert (forall ((R2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) R2)) (@ (@ tptp.power_power_nat N) R2)))))
% 6.44/6.80 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X3)) X3))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X3)) (=> (@ _let_1 X3) (@ (@ tptp.ord_less_real tptp.one_one_real) X3))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X3)) tptp.zero_zero_real)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X3)))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.minus_minus_nat M) K)))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K))) _let_1))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (= (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) _let_1) (@ (@ tptp.plus_plus_rat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N)))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) J2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J2))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3)))))
% 6.44/6.80 (assert (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) (@ A tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ A N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) (@ A tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3))) X3))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X3) Y)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X3)) (@ tptp.ln_ln_real Y))))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) K))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (= (@ tptp.ln_ln_real X3) (@ (@ tptp.minus_minus_real X3) tptp.one_one_real)) (= X3 tptp.one_one_real)))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_rat A) _let_2) (@ (@ tptp.plus_plus_rat (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ _let_1 tptp.one_one_rat)) K))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat K))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) _let_1)) K)) (@ (@ tptp.gbinomial_rat A) K))))))
% 6.44/6.80 (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)))))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat _let_3) A) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 6.44/6.80 (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)))))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat A) _let_3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 6.44/6.80 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) J2))) (= (@ (@ 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)))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real K))) K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri681578069525770553at_rat K))) K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 N)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.44/6.80 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X3)) (@ (@ tptp.minus_minus_real X3) tptp.one_one_real)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X3)) (@ tptp.ln_ln_real Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X3) Y)) Y)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3))) X3))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ln_ln_real X3))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_2)) (@ (@ tptp.gbinomial_rat _let_1) _let_2)) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.gbinomial_rat A) K)))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ (@ tptp.gbinomial_rat A) _let_1)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) K))))))
% 6.44/6.80 (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))))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M)) K)) (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 (@ tptp.suc K)))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N) _let_1))) (let ((_let_3 (@ tptp.binomial N))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ _let_3 (@ tptp.suc _let_2)) (@ _let_3 _let_2))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.binomial N) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X3))) (@ tptp.uminus_uminus_real X3))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))) (@ (@ tptp.gbinomial_rat A) K)))))))
% 6.44/6.80 (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))))))))
% 6.44/6.80 (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))))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))))))))
% 6.44/6.80 (assert (= tptp.gbinomial_complex (lambda ((A3 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)) A3)) tptp.one_one_complex)) K3)))))
% 6.44/6.80 (assert (= tptp.gbinomial_real (lambda ((A3 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)) A3)) tptp.one_one_real)) K3)))))
% 6.44/6.80 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat K3)) A3)) tptp.one_one_rat)) K3)))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (= (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) K)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) N))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (= (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) K)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) N))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) K)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) Z)) (@ (@ tptp.insert_nat N) _let_1))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) _let_1)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (K tptp.nat)) (= (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (X3 tptp.real)) (=> (@ (@ tptp.sums_real G) X3) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_1)))))) X3))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (X3 tptp.real) (F (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (@ (@ tptp.sums_real G) X3) (=> (@ (@ tptp.sums_real F) Y) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (@ F (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X3) Y))))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3)))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((K tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N2)))) tptp.one_one_real))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real) (N tptp.nat)) (=> (@ (@ tptp.sums_real F) S) (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) (@ (@ tptp.minus_minus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) (@ (@ tptp.minus_minus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.sums_real F) S))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S tptp.real) (T tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_real F) S) (=> (@ (@ tptp.sums_real G) T) (@ (@ tptp.ord_less_eq_real S) T))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S tptp.nat) (T tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_nat F) S) (=> (@ (@ tptp.sums_nat G) T) (@ (@ tptp.ord_less_eq_nat S) T))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S tptp.int) (T tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_int F) S) (=> (@ (@ tptp.sums_int G) T) (@ (@ tptp.ord_less_eq_int S) T))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) A)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))) (@ (@ tptp.times_times_real A) C)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (G (-> tptp.nat tptp.real)) (B tptp.real)) (=> (@ (@ tptp.sums_real F) A) (=> (@ (@ tptp.sums_real G) B) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_real A) B))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (G (-> tptp.nat tptp.nat)) (B tptp.nat)) (=> (@ (@ tptp.sums_nat F) A) (=> (@ (@ tptp.sums_nat G) B) (@ (@ tptp.sums_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_nat A) B))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (G (-> tptp.nat tptp.int)) (B tptp.int)) (=> (@ (@ tptp.sums_int F) A) (=> (@ (@ tptp.sums_int G) B) (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_int A) B))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (@ (@ tptp.divide1717551699836669952omplex A) C)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (@ (@ tptp.divide_divide_real A) C)))))
% 6.44/6.80 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (@ (@ tptp.times_times_complex C) D)) (@ (@ tptp.sums_complex F) D)))))
% 6.44/6.80 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) D)) (@ (@ tptp.sums_real F) D)))))
% 6.44/6.80 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) C))) (@ (@ tptp.times_times_complex D) C)) (@ (@ tptp.sums_complex F) D)))))
% 6.44/6.80 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))) (@ (@ tptp.times_times_real D) C)) (@ (@ tptp.sums_real F) D)))))
% 6.44/6.80 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) A) (=> (not (= C tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A) C))))))
% 6.44/6.80 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) A) (=> (not (= C tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A) C))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (S tptp.complex)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S) (@ (@ tptp.sums_complex F) S)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S) (@ (@ tptp.sums_real F) S)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L2) (@ F tptp.zero_zero_nat))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (L2 tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L2) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L2) (@ F tptp.zero_zero_nat))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (L2 tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L2) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L2) (@ F tptp.zero_zero_nat))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ F tptp.zero_zero_nat))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.complex)) (S tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (= (@ F I4) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) S) (@ (@ tptp.sums_complex F) S)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (S tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (= (@ F I4) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) S) (@ (@ tptp.sums_real F) S)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (Z tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N2 M)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.power_power_complex Z) M))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (Z tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N2 M)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.power_power_real Z) M))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (Z tptp.int)) (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N2 M)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z) N2)))) (@ (@ tptp.power_power_int Z) M))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X3) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X3) tptp.one_one_real)) (@ tptp.suc N2))))))))))
% 6.44/6.80 (assert (forall ((X3 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))) X3) (=> (@ (@ tptp.ord_less_eq_real X3) 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) X3))) X3))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.44/6.80 (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) (J tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I4) J)) (=> (=> (@ (@ tptp.ord_less_eq_int I4) J) (@ (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J)) (@ (@ P I4) J)))) (@ (@ P A0) A12)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_atMost_nat X3) (@ tptp.set_ord_atMost_nat Y)) (= X3 Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (= (@ tptp.set_ord_atMost_int X3) (@ tptp.set_ord_atMost_int Y)) (= X3 Y))))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.44/6.80 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.times_3573771949741848930nteger A) A)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.times_times_rat A) A)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.44/6.80 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.44/6.80 (assert (forall ((M tptp.real) (K tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real M))) (= (@ _let_1 (@ tptp.abs_abs_real K)) (@ _let_1 K)))))
% 6.44/6.80 (assert (forall ((M tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int M))) (= (@ _let_1 (@ tptp.abs_abs_int K)) (@ _let_1 K)))))
% 6.44/6.80 (assert (forall ((M tptp.code_integer) (K tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer M))) (= (@ _let_1 (@ tptp.abs_abs_Code_integer K)) (@ _let_1 K)))))
% 6.44/6.80 (assert (forall ((M tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M)) K) (@ (@ tptp.dvd_dvd_real M) K))))
% 6.44/6.80 (assert (forall ((M tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M)) K) (@ (@ tptp.dvd_dvd_int M) K))))
% 6.44/6.80 (assert (forall ((M tptp.code_integer) (K tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.abs_abs_Code_integer M)) K) (@ (@ tptp.dvd_dvd_Code_integer M) K))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((I2 tptp.set_int) (K tptp.set_int)) (= (@ (@ tptp.member_set_int I2) (@ tptp.set_or58775011639299419et_int K)) (@ (@ tptp.ord_less_eq_set_int I2) K))))
% 6.44/6.80 (assert (forall ((I2 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_atMost_rat K)) (@ (@ tptp.ord_less_eq_rat I2) K))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X3)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_eq_real X3) Y))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.44/6.80 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat _let_1)) _let_1))))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N)) (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)))))
% 6.44/6.80 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N)) (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N)) (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N)))))
% 6.44/6.80 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ tptp.set_or58775011639299419et_int X3)) (@ tptp.set_or58775011639299419et_int Y)) (@ (@ tptp.ord_less_eq_set_int X3) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat X3)) (@ tptp.set_ord_atMost_rat Y)) (@ (@ tptp.ord_less_eq_rat X3) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X3)) (@ tptp.set_ord_atMost_num Y)) (@ (@ tptp.ord_less_eq_num X3) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X3)) (@ tptp.set_ord_atMost_nat Y)) (@ (@ tptp.ord_less_eq_nat X3) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X3)) (@ tptp.set_ord_atMost_int Y)) (@ (@ tptp.ord_less_eq_int X3) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X3)) (@ _let_1 X3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real))))
% 6.44/6.80 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A2))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ tptp.abs_abs_int (@ F I3)))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.abs_abs_real (@ F I3)))) A2))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) (or (@ _let_1 A) (= B tptp.zero_zero_rat))))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((L2 tptp.set_int) (H2 tptp.set_int) (H3 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int L2) H2)) (@ tptp.set_or58775011639299419et_int H3)) (or (not (@ (@ tptp.ord_less_eq_set_int L2) H2)) (@ (@ tptp.ord_less_eq_set_int H2) H3)))))
% 6.44/6.80 (assert (forall ((L2 tptp.rat) (H2 tptp.rat) (H3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat L2) H2)) (@ tptp.set_ord_atMost_rat H3)) (or (not (@ (@ tptp.ord_less_eq_rat L2) H2)) (@ (@ tptp.ord_less_eq_rat H2) H3)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X3)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X3))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ tptp.abs_abs_int (@ F I3)))) A2))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.abs_abs_real (@ F I3)))) A2))))
% 6.44/6.80 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N)) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) (or (not (= A tptp.zero_zero_real)) (= N tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N)) (or (not (= A tptp.zero_zero_rat)) (= N tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N)) (or (not (= A tptp.zero_zero_int)) (= N tptp.zero_zero_nat)))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) (@ F tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) (@ F tptp.zero_zero_nat))))
% 6.44/6.80 (assert (forall ((W tptp.num) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (= (@ tptp.abs_abs_int X3) (@ tptp.abs_abs_int Y)) (or (= X3 Y) (= X3 (@ tptp.uminus_uminus_int Y))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X3) (@ tptp.abs_abs_real Y)) (or (= X3 Y) (= X3 (@ tptp.uminus_uminus_real Y))))))
% 6.44/6.80 (assert (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer X3) (@ tptp.abs_abs_Code_integer Y)) (or (= X3 Y) (= X3 (@ tptp.uminus1351360451143612070nteger Y))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (= (= (@ tptp.abs_abs_rat X3) (@ tptp.abs_abs_rat Y)) (or (= X3 Y) (= X3 (@ tptp.uminus_uminus_rat Y))))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))))
% 6.44/6.80 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))))
% 6.44/6.80 (assert (forall ((L2 tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L2) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L2) K))))
% 6.44/6.80 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L2) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L2) K))))
% 6.44/6.80 (assert (forall ((L2 tptp.code_integer) (K tptp.code_integer)) (=> (= (@ tptp.abs_abs_Code_integer L2) (@ tptp.abs_abs_Code_integer K)) (@ (@ tptp.dvd_dvd_Code_integer L2) K))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.44/6.80 (assert (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))))
% 6.44/6.80 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 6.44/6.80 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.44/6.80 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((H2 tptp.real)) (not (= tptp.bot_bot_set_real (@ tptp.set_ord_atMost_real H2)))))
% 6.44/6.80 (assert (forall ((H2 tptp.nat)) (not (= tptp.bot_bot_set_nat (@ tptp.set_ord_atMost_nat H2)))))
% 6.44/6.80 (assert (forall ((H2 tptp.int)) (not (= tptp.bot_bot_set_int (@ tptp.set_ord_atMost_int H2)))))
% 6.44/6.80 (assert (forall ((H3 tptp.int) (L2 tptp.int) (H2 tptp.int)) (not (= (@ tptp.set_ord_atMost_int H3) (@ (@ tptp.set_or1266510415728281911st_int L2) H2)))))
% 6.44/6.80 (assert (forall ((H3 tptp.real) (L2 tptp.real) (H2 tptp.real)) (not (= (@ tptp.set_ord_atMost_real H3) (@ (@ tptp.set_or1222579329274155063t_real L2) H2)))))
% 6.44/6.80 (assert (= tptp.set_ord_atMost_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) U2))))))
% 6.44/6.80 (assert (= tptp.set_or58775011639299419et_int (lambda ((U2 tptp.set_int)) (@ tptp.collect_set_int (lambda ((X2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X2) U2))))))
% 6.44/6.80 (assert (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) U2))))))
% 6.44/6.80 (assert (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_eq_num X2) U2))))))
% 6.44/6.80 (assert (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) U2))))))
% 6.44/6.80 (assert (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) U2))))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer B))) (let ((_let_2 (@ tptp.abs_abs_Code_integer A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) C) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C) D))))))))
% 6.44/6.80 (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))))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat B))) (let ((_let_2 (@ tptp.abs_abs_rat A))) (=> (@ (@ tptp.ord_less_rat _let_2) C) (=> (@ (@ tptp.ord_less_rat _let_1) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C) D))))))))
% 6.44/6.80 (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))))))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 6.44/6.80 (assert (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)))
% 6.44/6.80 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X3)) tptp.one_one_real)))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) E2))) (= X3 tptp.zero_zero_real))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X3)) E2))) (= X3 tptp.zero_zero_rat))))
% 6.44/6.80 (assert (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X3) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y)) X3) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y) X3))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X3) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X3))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X3) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y)) X3) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y) X3))))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X3) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X3))))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (or (@ _let_1 B) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.44/6.80 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.abs_abs_rat B)) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (or (= B A) (= B (@ tptp.uminus_uminus_rat A)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.abs_abs_rat A) B) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (or (= A B) (= A (@ tptp.uminus_uminus_rat B)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X3)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X3) Y))))))
% 6.44/6.80 (assert (forall ((Y tptp.rat) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X3)) Y) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X3) Y))))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))))
% 6.44/6.80 (assert (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N))))
% 6.44/6.80 (assert (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))))
% 6.44/6.80 (assert (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))))
% 6.44/6.80 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.44/6.80 (assert (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))))
% 6.44/6.80 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.44/6.80 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.44/6.80 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.44/6.80 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.44/6.80 (assert (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))))
% 6.44/6.80 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.44/6.80 (assert (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))))
% 6.44/6.80 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger C) D)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) C))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) D))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat C) D)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((X3 tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X3) A))) R2) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X3) (@ (@ tptp.ord_le3102999989581377725nteger X3) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) A))) R2) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R2)) X3) (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.plus_plus_real A) R2))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X3) A))) R2) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R2)) X3) (@ (@ tptp.ord_less_eq_rat X3) (@ (@ tptp.plus_plus_rat A) R2))))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X3) A))) R2) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R2)) X3) (@ (@ tptp.ord_less_eq_int X3) (@ (@ tptp.plus_plus_int A) R2))))))
% 6.44/6.80 (assert (forall ((X3 tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X3) A))) R2) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X3) (@ (@ tptp.ord_le6747313008572928689nteger X3) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) A))) R2) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R2)) X3) (@ (@ tptp.ord_less_real X3) (@ (@ tptp.plus_plus_real A) R2))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X3) A))) R2) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R2)) X3) (@ (@ tptp.ord_less_rat X3) (@ (@ tptp.plus_plus_rat A) R2))))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X3) A))) R2) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R2)) X3) (@ (@ tptp.ord_less_int X3) (@ (@ tptp.plus_plus_int A) R2))))))
% 6.44/6.80 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X3 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 X3) U)) Y))) V)))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat A)) (@ tptp.set_ord_lessThan_rat B)) (@ (@ tptp.ord_less_rat A) B))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial K3) M))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc N)) (@ tptp.suc M)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X3))))
% 6.44/6.80 (assert (forall ((X3 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X3)))))
% 6.44/6.80 (assert (forall ((N tptp.int) (X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X3)))))
% 6.44/6.80 (assert (forall ((N tptp.int) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3)))))
% 6.44/6.80 (assert (forall ((N tptp.int) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X3)))))
% 6.44/6.80 (assert (forall ((N tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X3)))))
% 6.44/6.80 (assert (forall ((N tptp.int) (X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X3)))))
% 6.44/6.80 (assert (forall ((N tptp.int) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X3)))))
% 6.44/6.80 (assert (forall ((N tptp.int) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X3)))))
% 6.44/6.80 (assert (forall ((N tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X3)))))
% 6.44/6.80 (assert (forall ((A tptp.real) (X3 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y4))) D3) (and (@ (@ tptp.ord_less_eq_real A) Y4) (@ (@ tptp.ord_less_eq_real Y4) B))))))))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((Z tptp.rat) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_rat Z))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat Z))))) (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat M)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I3)) (@ F (@ tptp.suc I3))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I3)) (@ F (@ tptp.suc I3))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (I2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I3)) (@ F (@ tptp.suc I3))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (D (-> tptp.nat tptp.complex))) (= (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X2) I3)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ D I3)) (@ (@ tptp.power_power_complex X2) I3)))) _let_1)))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ C I3) (@ D I3)))))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (D (-> tptp.nat tptp.real))) (= (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X2) I3)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ D I3)) (@ (@ tptp.power_power_real X2) I3)))) _let_1)))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ C I3) (@ D I3)))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.44/6.80 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.44/6.80 (assert (forall ((A (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.44/6.80 (assert (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.44/6.80 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.44/6.80 (assert (forall ((R2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R2) K3)) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R2) N))) N))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N) M)) tptp.one_one_nat)) M))))
% 6.44/6.80 (assert (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X3)) (@ tptp.abs_abs_Code_integer Y)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X3) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))))))
% 6.44/6.80 (assert (forall ((X3 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 X3)) (@ tptp.abs_abs_real Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X3)) (@ tptp.abs_abs_rat Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 6.44/6.80 (assert (forall ((X3 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 X3)) (@ tptp.abs_abs_int Y)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.44/6.80 (assert (forall ((X3 tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X3) tptp.one_one_Code_integer))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat)) (= (= (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X3) tptp.one_one_rat))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (= (= (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X3) tptp.one_one_real))))
% 6.44/6.80 (assert (forall ((X3 tptp.int)) (= (= (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X3) tptp.one_one_int))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N) (@ (@ tptp.power_power_real A) N)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N) (@ (@ tptp.power_power_int A) N)))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex W2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ C K) tptp.zero_zero_complex)))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real W2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ C K) tptp.zero_zero_real)))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (forall ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ C I3) tptp.zero_zero_complex))))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat)) (= (forall ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ C I3) tptp.zero_zero_real))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.44/6.80 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K3))) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) N))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K3))) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) N))))
% 6.44/6.80 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K3))) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) N))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K3)) (@ (@ tptp.minus_minus_nat M) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N)) M)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (R2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K3)) (@ (@ tptp.binomial N) (@ (@ tptp.minus_minus_nat R2) K3))))) (@ tptp.set_ord_atMost_nat R2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N)) R2))))
% 6.44/6.80 (assert (forall ((Y tptp.code_integer) (X3 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X3) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X3)) Y))))))
% 6.44/6.80 (assert (forall ((Y tptp.real) (X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) Y))))))
% 6.44/6.80 (assert (forall ((Y tptp.rat) (X3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X3)) Y))))))
% 6.44/6.80 (assert (forall ((Y tptp.int) (X3 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 X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X3)) Y))))))
% 6.44/6.80 (assert (forall ((X3 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X3)) tptp.one_one_Code_integer))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X3)) tptp.one_one_rat))))
% 6.44/6.80 (assert (forall ((X3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X3)) tptp.one_one_int))))
% 6.44/6.80 (assert (forall ((X3 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X3)) tptp.one_one_Code_integer))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) tptp.one_one_real))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X3)) tptp.one_one_rat))))
% 6.44/6.80 (assert (forall ((X3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X3)) tptp.one_one_int))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.44/6.80 (assert (forall ((I6 tptp.set_nat) (X3 (-> tptp.nat tptp.code_integer)) (A (-> tptp.nat tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X3 I4)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X3) I6) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))))
% 6.44/6.80 (assert (forall ((I6 tptp.set_real) (X3 (-> tptp.real tptp.code_integer)) (A (-> tptp.real tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X3 I4)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X3) I6) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7713935264441627589nteger (lambda ((I3 tptp.real)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))))
% 6.44/6.80 (assert (forall ((I6 tptp.set_int) (X3 (-> tptp.int tptp.code_integer)) (A (-> tptp.int tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X3 I4)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X3) I6) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I3 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))))
% 6.44/6.80 (assert (forall ((I6 tptp.set_complex) (X3 (-> tptp.complex tptp.code_integer)) (A (-> tptp.complex tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X3 I4)))) (=> (= (@ (@ tptp.groups6621422865394947399nteger X3) I6) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups6621422865394947399nteger (lambda ((I3 tptp.complex)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))))
% 6.44/6.80 (assert (forall ((I6 tptp.set_real) (X3 (-> 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) (@ X3 I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X3) 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 ((I3 tptp.real)) (@ (@ tptp.times_times_real (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))))
% 6.44/6.80 (assert (forall ((I6 tptp.set_int) (X3 (-> 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) (@ X3 I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X3) 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 ((I3 tptp.int)) (@ (@ tptp.times_times_real (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))))
% 6.44/6.80 (assert (forall ((I6 tptp.set_complex) (X3 (-> 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) (@ X3 I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X3) 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 ((I3 tptp.complex)) (@ (@ tptp.times_times_real (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))))
% 6.44/6.80 (assert (forall ((I6 tptp.set_nat) (X3 (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X3 I4)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X3) I6) tptp.one_one_rat) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))))
% 6.44/6.80 (assert (forall ((I6 tptp.set_real) (X3 (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X3 I4)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X3) I6) tptp.one_one_rat) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups1300246762558778688al_rat (lambda ((I3 tptp.real)) (@ (@ tptp.times_times_rat (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))))
% 6.44/6.80 (assert (forall ((I6 tptp.set_int) (X3 (-> tptp.int tptp.rat)) (A (-> tptp.int tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X3 I4)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat X3) I6) tptp.one_one_rat) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((I3 tptp.int)) (@ (@ tptp.times_times_rat (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X3))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ (@ tptp.times_times_complex (@ _let_2 X3)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ (@ tptp.times_times_rat (@ _let_2 X3)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X3))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ (@ tptp.times_times_int (@ _let_2 X3)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X3))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ (@ tptp.times_times_real (@ _let_2 X3)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.complex)) (A tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex A) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex) (not (forall ((B5 (-> tptp.nat tptp.complex))) (not (forall ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z4) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B5 I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.rat)) (A tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat A) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat) (not (forall ((B5 (-> tptp.nat tptp.rat))) (not (forall ((Z4 tptp.rat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat Z4) I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z4) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B5 I3)) (@ (@ tptp.power_power_rat Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.int)) (A tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int A) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int) (not (forall ((B5 (-> tptp.nat tptp.int))) (not (forall ((Z4 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int Z4) I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z4) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ B5 I3)) (@ (@ tptp.power_power_int Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.real)) (A tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real A) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real) (not (forall ((B5 (-> tptp.nat tptp.real))) (not (forall ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z4) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ B5 I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (A tptp.complex)) (exists ((B5 (-> tptp.nat tptp.complex))) (forall ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z4) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B5 I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex A) I3)))) _let_1))))))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.rat)) (N tptp.nat) (A tptp.rat)) (exists ((B5 (-> tptp.nat tptp.rat))) (forall ((Z4 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z4) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B5 I3)) (@ (@ tptp.power_power_rat Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat A) I3)))) _let_1))))))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.int)) (N tptp.nat) (A tptp.int)) (exists ((B5 (-> tptp.nat tptp.int))) (forall ((Z4 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z4) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ B5 I3)) (@ (@ tptp.power_power_int Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int A) I3)))) _let_1))))))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (A tptp.real)) (exists ((B5 (-> tptp.nat tptp.real))) (forall ((Z4 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z4) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ B5 I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real A) I3)))) _let_1))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X3))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X3))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X3))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial N)) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.complex)) (N tptp.nat) (B (-> tptp.nat tptp.complex)) (X3 tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_complex))) (=> (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J) (= (@ B J) tptp.zero_zero_complex))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X3) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B J3)) (@ (@ tptp.power_power_complex X3) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_complex X3) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.rat)) (N tptp.nat) (B (-> tptp.nat tptp.rat)) (X3 tptp.rat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_rat))) (=> (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J) (= (@ B J) tptp.zero_zero_rat))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat X3) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B J3)) (@ (@ tptp.power_power_rat X3) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_rat X3) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.int)) (N tptp.nat) (B (-> tptp.nat tptp.int)) (X3 tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_int))) (=> (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J) (= (@ B J) tptp.zero_zero_int))) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X3) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ B J3)) (@ (@ tptp.power_power_int X3) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_int X3) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.real)) (N tptp.nat) (B (-> tptp.nat tptp.real)) (X3 tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_real))) (=> (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J) (= (@ B J) tptp.zero_zero_real))) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X3) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ B J3)) (@ (@ tptp.power_power_real X3) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_real X3) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (K tptp.complex)) (= (forall ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X2) I3)))) (@ tptp.set_ord_atMost_nat N)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)) (= (@ C X2) tptp.zero_zero_complex)))))))
% 6.44/6.80 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (K tptp.real)) (= (forall ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X2) I3)))) (@ tptp.set_ord_atMost_nat N)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)) (= (@ C X2) tptp.zero_zero_real)))))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) M)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) M)))))
% 6.44/6.80 (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)))))
% 6.44/6.80 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex A) B)) N) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_complex A) K3))) (@ (@ tptp.power_power_complex B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) N) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_int A) K3))) (@ (@ tptp.power_power_int B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat A) B)) N) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_rat A) K3))) (@ (@ tptp.power_power_rat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) B)) N) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_real A) K3))) (@ (@ tptp.power_power_real B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) B)) N) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s4660882817536571857er_int A) K3))) (@ (@ tptp.comm_s4660882817536571857er_int B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) B)) N) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat A) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) B)) N) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s7457072308508201937r_real A) K3))) (@ (@ tptp.comm_s7457072308508201937r_real B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X3 tptp.nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_nat))) (=> (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J) (= (@ B J) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I3)) (@ (@ tptp.power_power_nat X3) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X3) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X3) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N) K3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) N))))
% 6.44/6.80 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.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 P2)) (@ (@ 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 P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.44/6.80 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.rat)) (H2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_rat (= J3 K)) tptp.zero_zero_rat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.44/6.80 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.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 P2)) (@ (@ 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 P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.44/6.80 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.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 P2)) (@ (@ 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 P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.44/6.80 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.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 P2)) (@ (@ 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 P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.44/6.80 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_complex (= J3 K)) tptp.one_one_complex) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.44/6.80 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_real (= J3 K)) tptp.one_one_real) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.44/6.80 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.rat)) (H2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_rat (= J3 K)) tptp.one_one_rat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.44/6.80 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_int (= J3 K)) tptp.one_one_int) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.44/6.80 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_nat (= J3 K)) tptp.one_one_nat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A tptp.complex) (X3 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 X3) 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 X3)) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X3) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) A)) K3)) (@ (@ tptp.power_power_rat X3) K3))) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X3)) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X3) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A tptp.real) (X3 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 X3) 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 X3)) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X3))) X3))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X3))) X3))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) (@ tptp.ring_1_of_int_real N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X3) N))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (N tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X3) (@ tptp.ring_1_of_int_rat N)))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim7778729529865785530nd_rat X3) N))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (Z tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_int Z) N) A) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= I3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int A)) (@ (@ (@ tptp.if_int (= I3 N)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.power_power_int Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (Z tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_complex Z) N) A) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= I3 tptp.zero_zero_nat)) (@ tptp.uminus1482373934393186551omplex A)) (@ (@ (@ tptp.if_complex (= I3 N)) tptp.one_one_complex) tptp.zero_zero_complex))) (@ (@ tptp.power_power_complex Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (Z tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_8256067586552552935nteger Z) N) A) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ (@ tptp.if_Code_integer (= I3 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ (@ tptp.if_Code_integer (= I3 N)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.power_8256067586552552935nteger Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (Z tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_rat Z) N) A) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ (@ tptp.if_rat (= I3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_rat A)) (@ (@ (@ tptp.if_rat (= I3 N)) tptp.one_one_rat) tptp.zero_zero_rat))) (@ (@ tptp.power_power_rat Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (Z tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_real Z) N) A) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= I3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_real A)) (@ (@ (@ tptp.if_real (= I3 N)) tptp.one_one_real) tptp.zero_zero_real))) (@ (@ tptp.power_power_real Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))))
% 6.44/6.80 (assert (forall ((X3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X3))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X3 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X3)))))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X3))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X3 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X3)))))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X3))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X3 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X3)))))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I3)) (@ tptp.semiri8010041392384452111omplex I3))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I3)) (@ tptp.semiri4939895301339042750nteger I3))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I3)) (@ tptp.semiri1314217659103216013at_int I3))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I3)) (@ tptp.semiri681578069525770553at_rat I3))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ tptp.semiri5074537144036343181t_real I3))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) K3))) K3)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) M))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A tptp.complex) (X3 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 X3) 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 X3) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X3) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) A)) K3)) (@ (@ tptp.power_power_rat X3) K3))) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat K3)) A)) tptp.one_one_rat)) K3)) (@ (@ tptp.power_power_rat X3) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X3) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.44/6.80 (assert (forall ((M tptp.nat) (A tptp.real) (X3 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 X3) 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 X3) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.complex)) (X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X3) I3)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex Y) I3)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X3) 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 X3) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.rat)) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat X3) I3)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat Y) I3)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X3) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_rat Y) K3))) (@ (@ tptp.power_power_rat X3) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.int)) (X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X3) I3)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int Y) I3)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X3) 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 X3) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.real)) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X3) I3)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real Y) I3)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X3) 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 X3) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat I3) (@ (@ tptp.binomial N) I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I3)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I3)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I3)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I3)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))
% 6.44/6.80 (assert (forall ((E tptp.real) (C (-> tptp.nat tptp.complex)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.real)) (forall ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z4))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_atMost_nat N)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N)))))))))))
% 6.44/6.80 (assert (forall ((E tptp.real) (C (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.real)) (forall ((Z4 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z4))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_atMost_nat N)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N)))))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) 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) X3))) X3))) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.complex)) (X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X3) I3)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex Y) I3)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X3) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I3) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_complex X3) J3)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.rat)) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat X3) I3)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat Y) I3)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X3) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I3) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_rat X3) J3)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.int)) (X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X3) I3)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int Y) I3)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X3) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I3) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_int X3) J3)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.real)) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X3) I3)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real Y) I3)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X3) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I3) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_real X3) J3)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (= (@ (@ tptp.groups2906978787729119204at_rat (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat _let_2) (@ tptp.semiri681578069525770553at_rat M))) tptp.one_one_rat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_rat _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((X3 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 X3)) (@ (@ 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) X3))) X3))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_complex (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I3))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_int (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I3))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_rat (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I3))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_real (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I3))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I3))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I3))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I3))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))))
% 6.44/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I3))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))))
% 6.44/6.80 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X3 tptp.code_integer)) (=> (forall ((X5 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X5) (@ (@ P X5) (@ (@ tptp.power_8256067586552552935nteger X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_Code_integer X3)) (@ (@ tptp.power_8256067586552552935nteger X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.44/6.80 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X3 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 X3)) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.44/6.80 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X3 tptp.rat)) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X5) (@ (@ P X5) (@ (@ tptp.power_power_rat X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_rat X3)) (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.44/6.80 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X3 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 X3)) (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X3) _let_1))))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (= (@ tptp.arctan X3) (@ 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 X3) _let_1))))))))))
% 6.44/6.80 (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)))))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) 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 X3) _let_1)))))))))
% 6.44/6.80 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) N2)))
% 6.44/6.80 (assert (forall ((X3 tptp.int)) (= (@ (@ tptp.dvd_dvd_int X3) tptp.one_one_int) (= (@ tptp.abs_abs_int X3) tptp.one_one_int))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K)))) (@ tptp.summable_real F))))
% 6.44/6.80 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X3)) (@ _let_1 X3)))))
% 6.44/6.80 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real))))
% 6.44/6.80 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.44/6.80 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.44/6.80 (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))))
% 6.44/6.80 (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))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X3)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_eq_real X3) Y))))
% 6.44/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X3)) (@ tptp.arctan Y)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N5 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3)))) (@ tptp.summable_real F)))))
% 6.44/6.80 (assert (forall ((G (-> tptp.nat tptp.real)) (N5 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3)))) (@ tptp.summable_complex F)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N6 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N6 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2))))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ tptp.summable_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2))))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ tptp.summable_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2))))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) (@ tptp.summable_real F))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K)))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (X3 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X3) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (X3 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex X3) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)))))))
% 6.44/6.80 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (=> (not (= C tptp.zero_zero_complex)) (@ tptp.summable_complex F)))))
% 6.44/6.80 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))))
% 6.44/6.80 (assert (forall ((M tptp.int) (N tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M) N)) tptp.one_one_int) (= (@ tptp.abs_abs_int M) tptp.one_one_int))))
% 6.44/6.80 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 6.44/6.80 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 6.44/6.80 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 6.44/6.80 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 6.44/6.80 (assert (forall ((Y tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y) X3) (= (@ tptp.abs_abs_int (@ (@ tptp.divide_divide_int X3) Y)) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int X3)) (@ tptp.abs_abs_int Y))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real F)) C) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C)))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) (@ tptp.suminf_real F))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (= (@ (@ tptp.plus_plus_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2)))))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (= (@ (@ tptp.plus_plus_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)) (@ tptp.suminf_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2)))))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (= (@ (@ tptp.plus_plus_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)) (@ tptp.suminf_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2)))))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.suminf_complex F)) C)))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (@ (@ tptp.divide_divide_real (@ tptp.suminf_real F)) C)))))
% 6.44/6.80 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (@ tptp.summable_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3))))))))
% 6.44/6.80 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3))))))))
% 6.44/6.80 (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))))))
% 6.44/6.80 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (= (= (@ tptp.suminf_real F) tptp.zero_zero_real) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_real)))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (= (= (@ tptp.suminf_nat F) tptp.zero_zero_nat) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_nat)))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (= (= (@ tptp.suminf_int F) tptp.zero_zero_int) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_int)))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F N3))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F N3))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F N3))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))))))
% 6.44/6.80 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_int (@ F N2)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N2))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))))))
% 6.48/6.80 (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))))
% 6.48/6.80 (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))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))))
% 6.48/6.80 (assert (forall ((I2 tptp.int) (D tptp.int)) (=> (not (= I2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int D) I2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int D)) (@ tptp.abs_abs_int I2))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N6 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2))))))))
% 6.48/6.80 (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)))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N6 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_real F))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_nat F))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_int F))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F)) (exists ((I3 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F)) (exists ((I3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F)) (exists ((I3 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I3))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (X3 tptp.int)) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N3))) X3)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X3)))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (X3 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N3))) X3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X3)))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (X3 tptp.real)) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N3))) X3)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X3)))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (X3 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X3) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (X3 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex X3) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (X3 tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N3))) X3)) (@ tptp.summable_int F)))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (X3 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N3))) X3)) (@ tptp.summable_nat F)))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (X3 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N3))) X3)) (@ tptp.summable_real F)))))
% 6.48/6.80 (assert (forall ((A (-> tptp.nat tptp.int)) (B3 tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int A) (@ tptp.set_ord_atMost_nat N3))) B3)) (@ tptp.summable_int A)))))
% 6.48/6.80 (assert (forall ((A (-> tptp.nat tptp.nat)) (B3 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat A) (@ tptp.set_ord_atMost_nat N3))) B3)) (@ tptp.summable_nat A)))))
% 6.48/6.80 (assert (forall ((A (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real A) (@ tptp.set_ord_atMost_nat N3))) B3)) (@ tptp.summable_real A)))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X3)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X3)))))
% 6.48/6.80 (assert (forall ((X3 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X3)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X3)))))
% 6.48/6.80 (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)))))
% 6.48/6.80 (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)))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ F tptp.zero_zero_nat))))))
% 6.48/6.80 (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)))))))
% 6.48/6.80 (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))))))))))))))))
% 6.48/6.80 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.48/6.80 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 6.48/6.80 (assert (forall ((M tptp.int) (N tptp.int)) (=> (not (= M tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M) N)) M) (= (@ tptp.abs_abs_int N) tptp.one_one_int)))))
% 6.48/6.80 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N2))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real F) (@ (@ tptp.plus_plus_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K))))) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.48/6.80 (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))))))
% 6.48/6.80 (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)))))))
% 6.48/6.80 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.48/6.80 (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)))
% 6.48/6.80 (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)))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2))))) Z))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2))))) Z))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2))))) Z) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2))))) (@ F tptp.zero_zero_nat))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2))))) Z) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2))))) (@ F tptp.zero_zero_nat))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X3))))))
% 6.48/6.80 (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 ((N7 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) M2) (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N8)))) E)))))))))))
% 6.48/6.80 (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 ((N7 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) M2) (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N8)))) E)))))))))))
% 6.48/6.80 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_real F) (exists ((N7 tptp.nat)) (forall ((N8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N8) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N8)))))) R2))))))))
% 6.48/6.80 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_complex F) (exists ((N7 tptp.nat)) (forall ((N8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N8) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N8)))))) R2))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I4)) tptp.one_one_real)) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I3)) (@ (@ tptp.power_power_real Z) I3))))))))))
% 6.48/6.80 (assert (forall ((R2 tptp.real) (R0 tptp.real) (A (-> tptp.nat tptp.complex)) (M7 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_real R2) R0) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N3))) (@ (@ tptp.power_power_real R0) N3))) M7)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N2))) (@ (@ tptp.power_power_real R2) N2)))))))))
% 6.48/6.80 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_nat I4) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ F I4) K)))))))))
% 6.48/6.80 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex A)) (@ tptp.suminf_complex B)) (@ tptp.suminf_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3)))))))))
% 6.48/6.80 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real A)) (@ tptp.suminf_real B)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3)))))))))
% 6.48/6.80 (assert (forall ((D tptp.int) (Z tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X3) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X3) Z))) tptp.one_one_int)) D))))))
% 6.48/6.80 (assert (forall ((D tptp.int) (X3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))))
% 6.48/6.80 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.48/6.80 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.48/6.80 (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))
% 6.48/6.80 (assert (forall ((C tptp.real) (N5 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V7735802525324610683m_real (@ F N3)))))) (@ tptp.summable_real F)))))
% 6.48/6.80 (assert (forall ((C tptp.real) (N5 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V1022390504157884413omplex (@ F N3)))))) (@ tptp.summable_complex F)))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N) I2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I2)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N) I2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))))))
% 6.48/6.80 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N) I2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))))))
% 6.48/6.80 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ F I4) K))))))))
% 6.48/6.80 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (@ (@ tptp.sums_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3)))) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex A)) (@ tptp.suminf_complex B)))))))
% 6.48/6.80 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (@ (@ tptp.sums_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3)))) (@ (@ tptp.times_times_real (@ tptp.suminf_real A)) (@ tptp.suminf_real B)))))))
% 6.48/6.80 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X3))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.48/6.80 (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))
% 6.48/6.80 (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))))
% 6.48/6.80 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ F I4) K))))))))
% 6.48/6.80 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 6.48/6.80 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))) tptp.zero_zero_complex))))
% 6.48/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X3)) (@ tptp.arctan Y)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X3) Y)))))))))
% 6.48/6.80 (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))))))
% 6.48/6.80 (assert (forall ((X3 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 X3)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X3)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X3)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.48/6.80 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))))
% 6.48/6.80 (assert (forall ((C (-> tptp.nat tptp.complex)) (X3 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X3) N2)))) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ C N2))) (@ (@ tptp.power_power_complex X3) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X3) N2))))))))
% 6.48/6.80 (assert (forall ((C (-> tptp.nat tptp.real)) (X3 tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X3) N2)))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ C N2))) (@ (@ tptp.power_power_real X3) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X3) N2))))))))
% 6.48/6.80 (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))))
% 6.48/6.80 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X4 (-> tptp.nat tptp.real))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_real (@ X4 M6)) (@ X4 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_real (@ X4 N2)) (@ X4 M6))))))))
% 6.48/6.80 (assert (= tptp.topolo3100542954746470799et_int (lambda ((X4 (-> tptp.nat tptp.set_int))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_set_int (@ X4 M6)) (@ X4 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_set_int (@ X4 N2)) (@ X4 M6))))))))
% 6.48/6.80 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X4 (-> tptp.nat tptp.rat))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_rat (@ X4 M6)) (@ X4 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_rat (@ X4 N2)) (@ X4 M6))))))))
% 6.48/6.80 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X4 (-> tptp.nat tptp.num))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_num (@ X4 M6)) (@ X4 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_num (@ X4 N2)) (@ X4 M6))))))))
% 6.48/6.80 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X4 (-> tptp.nat tptp.nat))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_nat (@ X4 M6)) (@ X4 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_nat (@ X4 N2)) (@ X4 M6))))))))
% 6.48/6.80 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X4 (-> tptp.nat tptp.int))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_int (@ X4 M6)) (@ X4 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_int (@ X4 N2)) (@ X4 M6))))))))
% 6.48/6.80 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_real (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.48/6.80 (assert (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_set_int (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo3100542954746470799et_int X8))))
% 6.48/6.80 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_rat (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.48/6.80 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_num (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.48/6.80 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_nat (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.48/6.80 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_int (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.48/6.80 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.48/6.80 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 6.48/6.80 (assert (= (@ tptp.cos_real tptp.pi) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X3)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X3)))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X3) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X3)))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X3) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X3)))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X3)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X3)))))
% 6.48/6.80 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X3))) (let ((_let_2 (@ tptp.cos_complex X3))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.sin_real X3))) (let ((_let_2 (@ tptp.cos_real X3))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.48/6.80 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.48/6.80 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)))
% 6.48/6.80 (assert (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)))
% 6.48/6.80 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.48/6.80 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.48/6.80 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.48/6.80 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X3))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X3))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X3)) (@ tptp.cos_real X3))))
% 6.48/6.80 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))))
% 6.48/6.80 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X3)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X3)) _let_1)) tptp.one_one_real))))
% 6.48/6.80 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X3)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X3)) _let_1)) tptp.one_one_complex))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X3)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X3)) _let_1)) tptp.one_one_real))))
% 6.48/6.80 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X3)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X3)) _let_1)) tptp.one_one_complex))))
% 6.48/6.80 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.zero_zero_real)))
% 6.48/6.80 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.one_one_real)))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X3)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X3)))))
% 6.48/6.80 (assert (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)))
% 6.48/6.80 (assert (forall ((N tptp.int)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.one_one_real)))
% 6.48/6.80 (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))
% 6.48/6.80 (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)))
% 6.48/6.80 (assert (forall ((N tptp.int)) (let ((_let_1 (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))))) (let ((_let_2 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X3) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X3)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X3)) (@ tptp.sin_real Y))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (exists ((R3 tptp.real) (A5 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (and (= X3 (@ _let_1 (@ tptp.cos_real A5))) (= Y (@ _let_1 (@ tptp.sin_real A5))))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X3)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X3)) (@ tptp.sin_real Y))))))
% 6.48/6.80 (assert (forall ((X3 tptp.complex)) (=> (= (@ tptp.cos_complex X3) tptp.one_one_complex) (= (@ tptp.sin_complex X3) tptp.zero_zero_complex))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (=> (= (@ tptp.cos_real X3) tptp.one_one_real) (= (@ tptp.sin_real X3) tptp.zero_zero_real))))
% 6.48/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X3)) (@ tptp.sin_real Y))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X3) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X3)) (@ tptp.sin_real Y))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (=> (= (@ tptp.sin_real X3) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X3)) tptp.one_one_real))))
% 6.48/6.80 (assert (forall ((X3 tptp.complex)) (=> (= (@ tptp.sin_complex X3) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X3)) tptp.one_one_real))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (=> (= (@ tptp.sin_real X3) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X3)) tptp.one_one_real))))
% 6.48/6.80 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X3)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X3))) (@ tptp.cos_complex X3))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X3)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X3))) (@ tptp.cos_real X3))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (exists ((Y3 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ tptp.sin_real Y3) (@ tptp.sin_real X3)) (= (@ tptp.cos_real Y3) (@ tptp.cos_real X3))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X3)) X3))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X3)) tptp.one_one_real)))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X3)) tptp.one_one_real)))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X3))) (@ tptp.abs_abs_real X3))))
% 6.48/6.80 (assert (forall ((X3 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 X3)) (@ tptp.sin_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y))))) tptp.one_one_real)))
% 6.48/6.80 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X3)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X3)) _let_1))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X3)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X3)) _let_1))))))
% 6.48/6.80 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X3)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X3)) _let_1))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X3)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X3)) _let_1))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X3)) (@ tptp.sin_real X3)))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (@ _let_1 (@ tptp.sin_real X3)))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X3))))
% 6.48/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (=> (= (@ tptp.cos_real X3) (@ tptp.cos_real Y)) (= X3 Y)))))))))
% 6.48/6.80 (assert (forall ((X3 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 X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (=> (@ _let_2 Y) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y)) (@ _let_1 X3))))))))))
% 6.48/6.80 (assert (forall ((Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y)))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X3))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X3))) tptp.one_one_real)))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X3))) tptp.one_one_real)))
% 6.48/6.80 (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))))))
% 6.48/6.80 (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))))))
% 6.48/6.80 (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))))))
% 6.48/6.80 (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))))))
% 6.48/6.80 (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))))))
% 6.48/6.80 (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))))))
% 6.48/6.80 (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)))))))
% 6.48/6.80 (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)))))))
% 6.48/6.80 (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)))))))
% 6.48/6.80 (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)))))))
% 6.48/6.80 (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)))))))
% 6.48/6.80 (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)))))))
% 6.48/6.80 (assert (forall ((X3 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)) X3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X3)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X3)) _let_2)))))))
% 6.48/6.80 (assert (forall ((X3 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)) X3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X3)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X3)) _let_2)))))))
% 6.48/6.80 (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)))))))))
% 6.48/6.80 (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)))))))))
% 6.48/6.80 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.48/6.80 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y)) (@ (@ tptp.ord_less_real Y) X3)))))))))
% 6.48/6.80 (assert (forall ((Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real Y) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y)))))))
% 6.48/6.80 (assert (forall ((Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y)) (@ tptp.cos_real X3)))))))
% 6.48/6.80 (assert (forall ((X3 tptp.real)) (= (= (@ tptp.sin_real X3) tptp.zero_zero_real) (exists ((I3 tptp.int)) (= X3 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) tptp.pi))))))
% 6.48/6.80 (assert (= tptp.diffs_int (lambda ((C2 (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C2 _let_1))))))
% 6.48/6.81 (assert (= tptp.diffs_real (lambda ((C2 (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C2 _let_1))))))
% 6.48/6.81 (assert (= tptp.diffs_rat (lambda ((C2 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ C2 _let_1))))))
% 6.48/6.81 (assert (forall ((Y tptp.real) (X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) tptp.pi) (= X3 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X3))) (= (@ 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))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X3))) (= (@ 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)))))))))
% 6.48/6.81 (assert (forall ((C (-> tptp.nat tptp.complex)) (X3 tptp.complex)) (=> (forall ((X5 tptp.complex)) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N2)) (@ (@ tptp.power_power_complex X5) N2))))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X3) N2)))))))
% 6.48/6.81 (assert (forall ((C (-> tptp.nat tptp.real)) (X3 tptp.real)) (=> (forall ((X5 tptp.real)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ C N2)) (@ (@ tptp.power_power_real X5) N2))))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X3) N2)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X3)))))))
% 6.48/6.81 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.48/6.81 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.48/6.81 (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 ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y4) tptp.zero_zero_real)) (= Y4 X5))))))
% 6.48/6.81 (assert (forall ((Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_real Y) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y)) (@ tptp.cos_real X3)))))))
% 6.48/6.81 (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 ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) tptp.pi) (= (@ tptp.cos_real Y4) Y)) (= Y4 X5)))))))))
% 6.48/6.81 (assert (forall ((X3 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 X3) (=> (@ _let_2 Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X3 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X3 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (=> (@ (@ tptp.ord_less_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X3 (@ tptp.cos_real T3)) (not (= Y (@ tptp.sin_real T3))))))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X3)) tptp.zero_zero_real)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X3))) tptp.one_one_real))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X3)))))))
% 6.48/6.81 (assert (forall ((Y tptp.real) (X3 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) X3) (=> (@ (@ tptp.ord_less_eq_real X3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) (@ tptp.sin_real X3))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X3))) (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 X3) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X3)) (@ tptp.sin_real Y)) (@ _let_1 Y)))))))))))
% 6.48/6.81 (assert (forall ((X3 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 X3) (=> (@ (@ tptp.ord_less_eq_real X3) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (=> (= (@ tptp.sin_real X3) (@ tptp.sin_real Y)) (= X3 Y))))))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (= (@ tptp.cos_real X3) tptp.one_one_real) (exists ((X2 tptp.int)) (= X3 (@ (@ 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))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X3))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X3)) (@ (@ 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))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.cos_real X3))) (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 X3)) (@ (@ 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))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (K5 tptp.real) (C (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X3)) K5) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X5)) K5) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ C N2)) (@ (@ tptp.power_power_real X5) N2)))))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X3) N2))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (K5 tptp.real) (C (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X3)) K5) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X5)) K5) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N2)) (@ (@ tptp.power_power_complex X5) N2)))))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X3) N2))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X3)) tptp.zero_zero_real)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X3)) tptp.zero_zero_real)))))
% 6.48/6.81 (assert (forall ((Y tptp.real) (X3 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) X3) (=> (@ (@ tptp.ord_less_eq_real X3) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y)) (@ tptp.sin_real X3))))))))
% 6.48/6.81 (assert (forall ((X3 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 X3) (=> (@ (@ tptp.ord_less_eq_real X3) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X3)) (@ tptp.sin_real Y)) (@ (@ tptp.ord_less_real X3) Y))))))))))
% 6.48/6.81 (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 ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_eq_real Y4) _let_1) (= (@ tptp.sin_real Y4) Y)) (= Y4 X5)))))))))))
% 6.48/6.81 (assert (forall ((X3 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)) X3) (=> (@ (@ tptp.ord_less_real X3) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X3)))))))
% 6.48/6.81 (assert (forall ((X3 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)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (= (@ tptp.cos_real X3) tptp.one_one_real) (or (exists ((X2 tptp.nat)) (= X3 (@ (@ 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)) (= X3 (@ 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))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (= (@ tptp.sin_real X3) tptp.zero_zero_real) (exists ((I3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I3) (= X3 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (= (@ tptp.cos_real X3) tptp.zero_zero_real) (exists ((I3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I3)) (= X3 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (= (@ tptp.sin_real X3) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3) (= X3 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (= (@ tptp.sin_real X3) tptp.zero_zero_real) (or (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2) (= X3 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2) (= X3 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (= (@ tptp.cos_real X3) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3)) (= X3 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (= (@ tptp.cos_real X3) tptp.zero_zero_real) (or (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= X3 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= X3 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo3100542954746470799et_int X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo3100542954746470799et_int X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.48/6.81 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X4 (-> tptp.nat tptp.real))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X4 N2)) (@ X4 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X4 (@ tptp.suc N2))) (@ X4 N2)))))))
% 6.48/6.81 (assert (= tptp.topolo3100542954746470799et_int (lambda ((X4 (-> tptp.nat tptp.set_int))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X4 N2)) (@ X4 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X4 (@ tptp.suc N2))) (@ X4 N2)))))))
% 6.48/6.81 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X4 (-> tptp.nat tptp.rat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X4 N2)) (@ X4 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X4 (@ tptp.suc N2))) (@ X4 N2)))))))
% 6.48/6.81 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X4 (-> tptp.nat tptp.num))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X4 N2)) (@ X4 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X4 (@ tptp.suc N2))) (@ X4 N2)))))))
% 6.48/6.81 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X4 (-> tptp.nat tptp.nat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X4 N2)) (@ X4 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X4 (@ tptp.suc N2))) (@ X4 N2)))))))
% 6.48/6.81 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X4 (-> tptp.nat tptp.int))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X4 N2)) (@ X4 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X4 (@ tptp.suc N2))) (@ X4 N2)))))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_real (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_set_int (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo3100542954746470799et_int X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_rat (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_num (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_nat (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_int (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real X3) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ tptp.cos_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X3) (= (@ tptp.cos_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X3)) (= (@ tptp.cos_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X3) _let_1))))) (@ tptp.sin_real X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X3))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X3))) (=> (not (= (@ tptp.cos_complex X3) 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)))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X3))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X3))) (=> (not (= (@ tptp.cos_real X3) 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)))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X3) tptp.pi)) (@ tptp.tan_real X3))))
% 6.48/6.81 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 6.48/6.81 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 6.48/6.81 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 6.48/6.81 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 6.48/6.81 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.48/6.81 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.48/6.81 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.48/6.81 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 6.48/6.81 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 6.48/6.81 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.48/6.81 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 6.48/6.81 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 6.48/6.81 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.48/6.81 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 6.48/6.81 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri773545260158071498ct_rat _let_1) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N)) tptp.pi))) (@ tptp.tan_real X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi))) (@ tptp.tan_real X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (I2 tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) tptp.pi))) (@ tptp.tan_real X3))))
% 6.48/6.81 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 6.48/6.81 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_rat _let_1))))
% 6.48/6.81 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 6.48/6.81 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 6.48/6.81 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X3))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N)))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N)))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N)))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri3624122377584611663nteger N)) (@ tptp.semiri3624122377584611663nteger M)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real M)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M)))))
% 6.48/6.81 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 6.48/6.81 (assert (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))
% 6.48/6.81 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 6.48/6.81 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 6.48/6.81 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger N))) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.plus_plus_nat K) N)))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat N))) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.plus_plus_nat K) N)))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int N))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K) N)))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real N))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K) N)))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat N))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K) N)))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri3624122377584611663nteger N)) (@ tptp.semiri3624122377584611663nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))))
% 6.48/6.81 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))))
% 6.48/6.81 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((N2 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))))
% 6.48/6.81 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N2 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))))
% 6.48/6.81 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N2 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))))
% 6.48/6.81 (assert (= tptp.tan_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex X2)))))
% 6.48/6.81 (assert (= tptp.tan_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X2)) (@ tptp.cos_real X2)))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri3624122377584611663nteger N)))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri773545260158071498ct_rat N)))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri1406184849735516958ct_int N)))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri2265585572941072030t_real N)))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((K tptp.num)) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ tptp.pred_numeral K))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real _let_1) _let_1)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.48/6.81 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M6)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))))
% 6.48/6.81 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((N2 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))))
% 6.48/6.81 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N2 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))))
% 6.48/6.81 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N2 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1406184849735516958ct_int N) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri773545260158071498ct_rat N) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri2265585572941072030t_real N) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1408675320244567234ct_nat N) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ tptp.semiri5044797733671781792omplex N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ tptp.semiri3624122377584611663nteger N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ tptp.semiri1406184849735516958ct_int N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ tptp.semiri773545260158071498ct_rat N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real N)))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N)) (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) K))))))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K))))))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N)) (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K))))))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X3)))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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 ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_real Y4) _let_1) (= (@ tptp.tan_real Y4) Y)) (= Y4 X5)))))))))
% 6.48/6.81 (assert (forall ((Y tptp.real) (X3 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) X3) (=> (@ (@ tptp.ord_less_real X3) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X3))))))))
% 6.48/6.81 (assert (forall ((Y tptp.real) (X3 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 X3) (=> (@ (@ tptp.ord_less_real X3) _let_2) (= (@ _let_1 X3) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X3))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X3))) (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 X3) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_real Y) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X3)) (@ tptp.tan_real Y)) (@ _let_1 Y)))))))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X3))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X3)) (@ tptp.tan_complex Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X3) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X3))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X3)) (@ tptp.tan_real Y)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X3) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.48/6.81 (assert (= tptp.gbinomial_complex (lambda ((A3 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 A3)) K3))) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.48/6.81 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat A3)) K3))) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 6.48/6.81 (assert (= tptp.gbinomial_real (lambda ((A3 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 A3)) K3))) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.48/6.81 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex K3))) tptp.one_one_complex)) K3)) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.48/6.81 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A3) (@ tptp.semiri681578069525770553at_rat K3))) tptp.one_one_rat)) K3)) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 6.48/6.81 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real K3))) tptp.one_one_real)) K3)) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X3)) tptp.zero_zero_real)))))
% 6.48/6.81 (assert (forall ((X3 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)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X3)) (@ tptp.tan_real Y))))))))
% 6.48/6.81 (assert (forall ((X3 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 X3) (=> (@ (@ tptp.ord_less_real X3) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X3)) (@ tptp.tan_real Y)) (@ (@ tptp.ord_less_eq_real X3) Y))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) (@ (@ 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 X3))) tptp.one_one_real))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((X3 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)) X3) (=> (@ (@ tptp.ord_less_real X3) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X3)) X3))))))
% 6.48/6.81 (assert (forall ((X3 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)) X3) (=> (@ (@ tptp.ord_less_real X3) _let_1) (=> (= (@ tptp.tan_real X3) Y) (= (@ tptp.arctan Y) X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X3 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X3 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.rat tptp.real))) (=> (= X3 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_rat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X3 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X3 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))))
% 6.48/6.81 (assert (forall ((H2 tptp.real) (F (-> tptp.real tptp.real)) (J2 (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (exists ((B8 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J2 M6)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B8) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X3))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X3) Y))) (=> (not (= (@ tptp.cos_complex X3) 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))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X3))) (let ((_let_3 (@ (@ tptp.plus_plus_real X3) Y))) (=> (not (= (@ tptp.cos_real X3) 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))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X3))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X3) Y))) (=> (not (= (@ tptp.cos_complex X3) 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))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X3))) (let ((_let_3 (@ (@ tptp.minus_minus_real X3) Y))) (=> (not (= (@ tptp.cos_real X3) 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))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X3))) (=> (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 X3)) (@ tptp.tan_complex Y))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X3) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X3))) (=> (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 X3)) (@ tptp.tan_real Y))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X3) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (exists ((Z2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z2) (@ (@ tptp.ord_less_real Z2) _let_1) (= (@ tptp.tan_real Z2) X3)))))))
% 6.48/6.81 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_complex A) _let_1) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri5044797733671781792omplex _let_1))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_rat A) _let_1) (@ (@ tptp.divide_divide_rat (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri773545260158071498ct_rat _let_1))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A) _let_1) (@ (@ tptp.divide_divide_real (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri2265585572941072030t_real _let_1))))))
% 6.48/6.81 (assert (forall ((A tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_int A) _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1406184849735516958ct_int _let_1))))))
% 6.48/6.81 (assert (forall ((A tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_nat A) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri5044797733671781792omplex _let_3) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex _let_2) _let_3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2)) N))) (@ tptp.semiri5044797733671781792omplex N))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri773545260158071498ct_rat _let_3) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat _let_2) _let_3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2)) N))) (@ tptp.semiri773545260158071498ct_rat N))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri2265585572941072030t_real _let_3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real _let_2) _let_3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) N))) (@ tptp.semiri2265585572941072030t_real N))))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (= tptp.cos_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ tptp.semiri2265585572941072030t_real N2))) tptp.zero_zero_real)))))
% 6.48/6.81 (assert (= tptp.gbinomial_complex (lambda ((A3 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 A3) (@ 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))))))
% 6.48/6.81 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.divide_divide_rat (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((L tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A3) (@ tptp.semiri681578069525770553at_rat L))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K3))))))
% 6.48/6.81 (assert (= tptp.gbinomial_real (lambda ((A3 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 A3) (@ 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))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X3) _let_1))))) (@ tptp.cos_real X3))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X3) (= (@ tptp.sin_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) X3) (= (@ tptp.sin_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N)))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X3)) (= (@ tptp.sin_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_real (and (@ _let_2 P4) (not (@ _let_2 N2)))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4)))) (@ (@ tptp.power_power_real X3) N2))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_real (@ tptp.sin_real X3)) (@ tptp.sin_real Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_complex (and (@ _let_2 P4) (not (@ _let_2 N2)))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4)))) (@ (@ tptp.power_power_complex X3) N2))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X3)) (@ tptp.sin_complex Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) P4)) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real X3) N2))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_real)))) (@ tptp.set_ord_atMost_nat P4)))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X3) Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat _let_1) P4)) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_complex X3) N2))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_complex)))) (@ tptp.set_ord_atMost_nat P4)))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X3) Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (A tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real X3))) (let ((_let_2 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ _let_2 Y)) (@ _let_2 (@ _let_1 Y)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (A tptp.real) (Y tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X3))) (let ((_let_2 (@ tptp.real_V2046097035970521341omplex A))) (= (@ _let_1 (@ _let_2 Y)) (@ _let_2 (@ _let_1 Y)))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 X3)) Y) (@ _let_1 (@ (@ tptp.times_times_real X3) Y))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 X3)) Y) (@ _let_1 (@ (@ tptp.times_times_complex X3) Y))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real tptp.one_one_real) X3) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex tptp.one_one_real) X3) X3)))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real) (X3 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real A) (@ (@ tptp.real_V1485227260804924795R_real B) X3)) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.times_times_real A) B)) X3))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real) (X3 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex A) (@ (@ tptp.real_V2046097035970521341omplex B) X3)) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.times_times_real A) B)) X3))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.real_V1485227260804924795R_real X3) Y)) N) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.power_power_real Y) N)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.real_V2046097035970521341omplex X3) Y)) N) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.power_power_complex Y) N)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (@ tptp.uminus_uminus_real X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (@ tptp.uminus1482373934393186551omplex X3))))
% 6.48/6.81 (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)))
% 6.48/6.81 (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)))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.real_V7735802525324610683m_real X3)))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex A) X3)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.real_V1022390504157884413omplex X3)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))
% 6.48/6.81 (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)))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.48/6.81 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X3)) (@ _let_1 Y))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X3) Y)) (@ (@ tptp.plus_plus_complex (@ _let_1 X3)) (@ _let_1 Y))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_real X3) N2)))) (@ tptp.sin_real X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_complex X3) N2)))) (@ tptp.sin_complex X3))))
% 6.48/6.81 (assert (= tptp.sin_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_real X2) N2)))))))
% 6.48/6.81 (assert (= tptp.sin_complex (lambda ((X2 tptp.complex)) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_complex X2) N2)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real) (Xa2 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real X3) Y)) Xa2) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real X3) Xa2)) (@ (@ tptp.real_V1485227260804924795R_real Y) Xa2)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real) (Xa2 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.plus_plus_real X3) Y)) Xa2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex X3) Xa2)) (@ (@ tptp.real_V2046097035970521341omplex Y) Xa2)))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real) (X3 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real A) B)) X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) (@ (@ tptp.real_V1485227260804924795R_real B) X3)))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real) (X3 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.plus_plus_real A) B)) X3) (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex A) X3)) (@ (@ tptp.real_V2046097035970521341omplex B) X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_real X3) N2)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_complex X3) N2)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X3)) N2))))) (@ tptp.sin_real X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X3)) N2))))) (@ tptp.sin_complex X3))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) (@ (@ tptp.real_V1485227260804924795R_real B) X3))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 X3)) (@ _let_1 Y)))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N)))))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real) (X3 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 X3) Y) (=> (@ _let_1 B) (=> (@ _let_1 X3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) (@ (@ tptp.real_V1485227260804924795R_real B) Y)))))))))
% 6.48/6.81 (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)))))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 X3))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) tptp.zero_zero_real)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) X3)))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) tptp.zero_zero_real)))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) tptp.zero_zero_real)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) X3)))))
% 6.48/6.81 (assert (forall ((R2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) R2)))) (@ (@ tptp.power_power_nat N) R2)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X3) (@ (@ tptp.plus_plus_real X3) X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X3) (@ (@ tptp.plus_plus_complex X3) X3))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.binomial N) K)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_real X3) N2)))) (@ tptp.cos_real X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_complex X3) N2)))) (@ tptp.cos_complex X3))))
% 6.48/6.81 (assert (= tptp.cos_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_real X2) N2)))))))
% 6.48/6.81 (assert (= tptp.cos_complex (lambda ((X2 tptp.complex)) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_complex X2) N2)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_real X3) N2)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_complex X3) N2)))))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X3)) N2)))) (@ tptp.cos_real X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X3)) N2)))) (@ tptp.cos_complex X3))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N)) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N))) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.48/6.81 (assert (= tptp.binomial (lambda ((N2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K3))) (let ((_let_2 (@ tptp.ord_less_nat N2))) (@ (@ (@ tptp.if_nat (@ _let_2 K3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K3))) (@ (@ tptp.binomial N2) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N2) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))))
% 6.48/6.81 (assert (= tptp.sin_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) tptp.zero_zero_real) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N2)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_real (and (@ _let_2 P4) (@ _let_2 N2))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real X3) N2))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_complex (and (@ _let_2 P4) (@ _let_2 N2))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_complex X3) N2))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X3)) (@ tptp.cos_complex Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (= (@ tptp.sin_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X3))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X3) (@ (@ 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)))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X3) (@ (@ 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 X3)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.48/6.81 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (=> (@ (@ tptp.ord_less_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T3)) (@ tptp.sin_real T3)))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat)) (=> (not (= X3 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T3))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X3)) (= (@ tptp.exp_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X3) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N)))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X3)) N)))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (= A B))))
% 6.48/6.81 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (= A B))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (= A B))))
% 6.48/6.81 (assert (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A)))
% 6.48/6.81 (assert (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A)))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A)))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (= (@ tptp.sqrt X3) (@ tptp.sqrt Y)) (= X3 Y))))
% 6.48/6.81 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.48/6.81 (assert (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.48/6.81 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.48/6.81 (assert (forall ((A tptp.real)) (= (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.48/6.81 (assert (forall ((A tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)))))
% 6.48/6.81 (assert (= (@ tptp.inverse_inverse_real tptp.one_one_real) tptp.one_one_real))
% 6.48/6.81 (assert (= (@ tptp.invers8013647133539491842omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.48/6.81 (assert (= (@ tptp.inverse_inverse_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (= (@ tptp.inverse_inverse_real X3) tptp.one_one_real) (= X3 tptp.one_one_real))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex X3) tptp.one_one_complex) (= X3 tptp.one_one_complex))))
% 6.48/6.81 (assert (forall ((X3 tptp.rat)) (= (= (@ tptp.inverse_inverse_rat X3) tptp.one_one_rat) (= X3 tptp.one_one_rat))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real B) A))))
% 6.48/6.81 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex B) A))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat B) A))))
% 6.48/6.81 (assert (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real A)))))
% 6.48/6.81 (assert (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A)))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat A)))))
% 6.48/6.81 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.abs_abs_real A)))))
% 6.48/6.81 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex (@ tptp.abs_abs_complex A)))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.abs_abs_rat A)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (= (@ tptp.sqrt X3) tptp.zero_zero_real) (= X3 tptp.zero_zero_real))))
% 6.48/6.81 (assert (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X3)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_real X3) Y))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X3)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real X3) Y))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (= (@ tptp.sqrt X3) tptp.one_one_real) (= X3 tptp.one_one_real))))
% 6.48/6.81 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X3)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_eq_real X3) Y))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.inverse_inverse_rat A)) (@ _let_1 A)))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ _let_1 A)))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.inverse_inverse_rat A)) (@ _let_1 A)))))
% 6.48/6.81 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.48/6.81 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real))))
% 6.48/6.81 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X3)) tptp.one_one_real) (@ (@ tptp.ord_less_real X3) tptp.one_one_real))))
% 6.48/6.81 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X3)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (= (@ tptp.exp_real X3) tptp.one_one_real) (= X3 tptp.zero_zero_real))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X3) X3)) (@ tptp.abs_abs_real X3))))
% 6.48/6.81 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.invers8013647133539491842omplex A)) tptp.one_one_complex))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.inverse_inverse_rat A)) tptp.one_one_rat))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) A) tptp.one_one_rat))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 6.48/6.81 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ tptp.inverse_inverse_rat _let_1) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_1)))))
% 6.48/6.81 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X3)) tptp.one_one_real) (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X3)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X3)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X3)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ tptp.inverse_inverse_rat _let_1) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_1)))))
% 6.48/6.81 (assert (forall ((T tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T)) (@ tptp.sin_real T))) tptp.one_one_real)))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X3))))
% 6.48/6.81 (assert (forall ((X3 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 X3) _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)))))
% 6.48/6.81 (assert (forall ((R2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.real_V2046097035970521341omplex R2) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ _let_1 A)) (@ _let_1 B))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X3) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X3)) K))))
% 6.48/6.81 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real A)) N) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real A) N)))))
% 6.48/6.81 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex A)) N) (@ tptp.invers8013647133539491842omplex (@ (@ tptp.power_power_complex A) N)))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat A)) N) (@ tptp.inverse_inverse_rat (@ (@ tptp.power_power_rat A) N)))))
% 6.48/6.81 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.48/6.81 (assert (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.48/6.81 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.48/6.81 (assert (forall ((A tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.48/6.81 (assert (forall ((A tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= A B))))))
% 6.48/6.81 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= A B))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= A B))))))
% 6.48/6.81 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A))))
% 6.48/6.81 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A))))
% 6.48/6.81 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real)))))
% 6.48/6.81 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex)))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X3))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X3))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X3)))))
% 6.48/6.81 (assert (forall ((Y tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real Y))) (let ((_let_2 (@ tptp.times_times_real X3))) (=> (= (@ (@ tptp.times_times_real Y) X3) (@ _let_2 Y)) (= (@ (@ tptp.times_times_real _let_1) X3) (@ _let_2 _let_1)))))))
% 6.48/6.81 (assert (forall ((Y tptp.complex) (X3 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex Y))) (let ((_let_2 (@ tptp.times_times_complex X3))) (=> (= (@ (@ tptp.times_times_complex Y) X3) (@ _let_2 Y)) (= (@ (@ tptp.times_times_complex _let_1) X3) (@ _let_2 _let_1)))))))
% 6.48/6.81 (assert (forall ((Y tptp.rat) (X3 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat Y))) (let ((_let_2 (@ tptp.times_times_rat X3))) (=> (= (@ (@ tptp.times_times_rat Y) X3) (@ _let_2 Y)) (= (@ (@ tptp.times_times_rat _let_1) X3) (@ _let_2 _let_1)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt X3)) (@ tptp.sqrt Y)))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (= A B))))
% 6.48/6.81 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (= A B))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (= A B))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ tptp.sqrt (@ tptp.inverse_inverse_real X3)) (@ tptp.inverse_inverse_real (@ tptp.sqrt X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X3) Y)) (@ (@ tptp.times_times_real (@ tptp.sqrt X3)) (@ tptp.sqrt Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X3) Y)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X3)) (@ tptp.sqrt Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X3)) (@ tptp.sqrt Y)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X3)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.sqrt X3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.divide_divide_real _let_1) X3) (@ tptp.inverse_inverse_real _let_1))))))
% 6.48/6.81 (assert (forall ((R2 tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real R2) (@ tptp.real_V7735802525324610683m_real X3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.inverse_inverse_real X3))) (@ tptp.inverse_inverse_real R2))))))
% 6.48/6.81 (assert (forall ((R2 tptp.real) (X3 tptp.complex)) (=> (@ (@ tptp.ord_less_eq_real R2) (@ tptp.real_V1022390504157884413omplex X3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.invers8013647133539491842omplex X3))) (@ tptp.inverse_inverse_real R2))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ _let_1 tptp.zero_zero_rat) (@ _let_1 A))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (=> (not (= A tptp.zero_zero_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ tptp.inverse_inverse_rat A)) (=> (not (= A tptp.zero_zero_rat)) (@ _let_1 A))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.inverse_inverse_rat A))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A)))))))
% 6.48/6.81 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real A))))))
% 6.48/6.81 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A))))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat A))))))
% 6.48/6.81 (assert (let ((_let_1 (@ tptp.numeral_numeral_real tptp.one))) (= (@ tptp.inverse_inverse_real _let_1) _let_1)))
% 6.48/6.81 (assert (let ((_let_1 (@ tptp.numera6690914467698888265omplex tptp.one))) (= (@ tptp.invers8013647133539491842omplex _let_1) _let_1)))
% 6.48/6.81 (assert (let ((_let_1 (@ tptp.numeral_numeral_rat tptp.one))) (= (@ tptp.inverse_inverse_rat _let_1) _let_1)))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.one_one_real) (= (@ tptp.inverse_inverse_real A) B))))
% 6.48/6.81 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.one_one_complex) (= (@ tptp.invers8013647133539491842omplex A) B))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.one_one_rat) (= (@ tptp.inverse_inverse_rat A) B))))
% 6.48/6.81 (assert (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real A3) (@ tptp.inverse_inverse_real B2)))))
% 6.48/6.81 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex A3) (@ tptp.invers8013647133539491842omplex B2)))))
% 6.48/6.81 (assert (= tptp.divide_divide_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat A3) (@ tptp.inverse_inverse_rat B2)))))
% 6.48/6.81 (assert (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real A3) (@ tptp.inverse_inverse_real B2)))))
% 6.48/6.81 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex A3) (@ tptp.invers8013647133539491842omplex B2)))))
% 6.48/6.81 (assert (= tptp.divide_divide_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat A3) (@ tptp.inverse_inverse_rat B2)))))
% 6.48/6.81 (assert (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B2)) A3))))
% 6.48/6.81 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B2)) A3))))
% 6.48/6.81 (assert (= tptp.divide_divide_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B2)) A3))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (@ _let_1 (@ tptp.sqrt X3))))))
% 6.48/6.81 (assert (= tptp.inverse_inverse_real (@ tptp.divide_divide_real tptp.one_one_real)))
% 6.48/6.81 (assert (= tptp.invers8013647133539491842omplex (@ tptp.divide1717551699836669952omplex tptp.one_one_complex)))
% 6.48/6.81 (assert (= tptp.inverse_inverse_rat (@ tptp.divide_divide_rat tptp.one_one_rat)))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X3) M))) (let ((_let_2 (@ tptp.inverse_inverse_real X3))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X3) M))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex X3))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.48/6.81 (assert (forall ((X3 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X3) M))) (let ((_let_2 (@ tptp.inverse_inverse_rat X3))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X3) M))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X3)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X3) M))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X3)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.48/6.81 (assert (forall ((X3 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X3) M))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X3)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (= (@ tptp.sqrt X3) tptp.zero_zero_real) (= X3 tptp.zero_zero_real)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (@ _let_1 (@ tptp.sqrt X3))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X3)) tptp.zero_zero_real))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X3))))
% 6.48/6.81 (assert (forall ((Xa2 tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real Xa2)))) (= (@ (@ tptp.times_times_real _let_1) X3) (@ (@ tptp.times_times_real X3) _let_1)))))
% 6.48/6.81 (assert (forall ((Xa2 tptp.nat) (X3 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.semiri8010041392384452111omplex Xa2)))) (= (@ (@ tptp.times_times_complex _let_1) X3) (@ (@ tptp.times_times_complex X3) _let_1)))))
% 6.48/6.81 (assert (forall ((Xa2 tptp.nat) (X3 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat Xa2)))) (= (@ (@ tptp.times_times_rat _let_1) X3) (@ (@ tptp.times_times_rat X3) _let_1)))))
% 6.48/6.81 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.abs_abs_real A))))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.abs_abs_rat A))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X3) (@ _let_1 (@ tptp.sqrt X3))))))
% 6.48/6.81 (assert (forall ((Xa2 tptp.int) (X3 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.ring_1_of_int_real Xa2)))) (= (@ (@ tptp.times_times_real _let_1) X3) (@ (@ tptp.times_times_real X3) _let_1)))))
% 6.48/6.81 (assert (forall ((Xa2 tptp.int) (X3 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.ring_17405671764205052669omplex Xa2)))) (= (@ (@ tptp.times_times_complex _let_1) X3) (@ (@ tptp.times_times_complex X3) _let_1)))))
% 6.48/6.81 (assert (forall ((Xa2 tptp.int) (X3 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.ring_1_of_int_rat Xa2)))) (= (@ (@ tptp.times_times_rat _let_1) X3) (@ (@ tptp.times_times_rat X3) _let_1)))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X3)) (@ tptp.exp_complex Y)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X3) Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X3)) (@ tptp.exp_real Y)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X3) Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X3) Y) (@ (@ tptp.times_times_complex Y) X3)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X3) Y)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X3)) (@ tptp.exp_complex Y))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (= (@ (@ tptp.times_times_real X3) Y) (@ (@ tptp.times_times_real Y) X3)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.times_times_real (@ tptp.exp_real X3)) (@ tptp.exp_real Y))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X3) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X3)) (@ tptp.exp_complex Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X3) Y)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X3)) (@ tptp.exp_real Y)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (= tptp.divide_divide_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (@ (@ tptp.times_times_real X2) (@ tptp.inverse_inverse_real Y6)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X3) N2)))) (@ tptp.exp_real X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_complex X3) N2)))) (@ tptp.exp_complex X3))))
% 6.48/6.81 (assert (= tptp.exp_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2)))))))
% 6.48/6.81 (assert (= tptp.exp_complex (lambda ((X2 tptp.complex)) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_complex X2) N2)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.exp_real X3))) (@ (@ 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))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X3)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real X3)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat X3)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real X3)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_real X3) tptp.one_one_real)))))
% 6.48/6.81 (assert (forall ((X3 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X3)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X3) (@ (@ tptp.ord_less_rat X3) tptp.one_one_rat)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat A))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) A) tptp.one_one_rat))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_2)) _let_1))))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.plus_plus_rat A) B))) _let_1))))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.minus_minus_rat B) A))) _let_1))))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex A) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 6.48/6.81 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat A) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X3) Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.sqrt X3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.divide_divide_real X3) _let_1) _let_1)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X3) Y))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X3)) (@ tptp.sqrt Y))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3)) (@ tptp.exp_real X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) X3)) (@ (@ tptp.times_times_real Y) Y))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X3)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X3))) tptp.one_one_real)))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X3)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X3))) tptp.one_one_complex)))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (N tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X3) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X3)) N))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X3) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.exp_real X3)) N))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) X3)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X3)) N))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X3)) (@ (@ tptp.power_power_real (@ tptp.exp_real X3)) N))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.exp_real X3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.exp_real X3))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) (@ 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))))))))
% 6.48/6.81 (assert (= tptp.exp_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))))))
% 6.48/6.81 (assert (= tptp.exp_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X2) _let_1)))))))))
% 6.48/6.81 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.times_times_rat A) B))) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat B) A)) (=> (@ (@ tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) B)))))))
% 6.48/6.81 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3)) (@ tptp.exp_real X3)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real Y) (@ tptp.ln_ln_real X3)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y)) X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y)) Y)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X3)) X3))))))
% 6.48/6.81 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.48/6.81 (assert (forall ((E tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2)))) (and (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E)))))))
% 6.48/6.81 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_real X3) (@ tptp.sqrt Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.sqrt Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X3)) Y) (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.48/6.81 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.48/6.81 (assert (forall ((Y tptp.real) (X3 tptp.real)) (=> (= (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X3) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ tptp.sqrt X3) Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X3)) Y)))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) Y) (= X3 tptp.zero_zero_real)))))
% 6.48/6.81 (assert (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) X3) (= Y tptp.zero_zero_real)))))
% 6.48/6.81 (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)))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (assert (forall ((Y tptp.real) (X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X3)) Y)))))))
% 6.48/6.81 (assert (forall ((X3 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 X3) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real X3) Y))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.power_power_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) N) (= (@ tptp.sqrt (@ _let_3 N)) (@ _let_3 (@ (@ tptp.divide_divide_nat N) _let_2)))))))))
% 6.48/6.81 (assert (forall ((X3 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 X3)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.48/6.81 (assert (forall ((Y tptp.real) (X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.48/6.81 (assert (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X3)) (@ tptp.abs_abs_real Y))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ tptp.ln_ln_real (@ tptp.sqrt X3)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X3) (@ tptp.inverse_inverse_real X3))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3)) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.48/6.81 (assert (forall ((X3 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 X3) _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))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X3)) N) (@ (@ tptp.power_power_real X3) (@ (@ tptp.divide_divide_nat N) _let_1))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X3) Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X3)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X3))))))))
% 6.48/6.81 (assert (forall ((X3 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 X3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) tptp.one_one_real))))
% 6.48/6.81 (assert (forall ((X3 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 X3)) _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 X3) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3) (= (@ tptp.arcosh_real X3) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X3) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X3) _let_1))) N)) (@ tptp.exp_real X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real X3) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X3) _let_1))) N)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X3))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X3)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X3)) (@ (@ tptp.divide_divide_real X3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X3)) (= (@ tptp.exp_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X3) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))))
% 6.48/6.81 (assert (forall ((X3 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 X3) _let_4) (=> (@ (@ tptp.ord_less_real Y) _let_4) (=> (@ _let_3 X3) (=> (@ _let_3 Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U)))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X3))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.sin_real X3))) (=> (@ (@ 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 X3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.48/6.81 (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)))))))))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X3)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.48/6.81 (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)))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X3)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_eq_real X3) Y))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X3)) (@ _let_1 X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real))))
% 6.48/6.81 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 6.48/6.81 (assert (= (@ tptp.arccos (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.pi))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.48/6.81 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (@ (@ tptp.times_times_complex X2) (@ tptp.invers8013647133539491842omplex Y6)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X3)) (@ tptp.cosh_real X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X3)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_eq_real X3) Y)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X3)) (@ tptp.cosh_real Y)) (@ _let_1 X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ tptp.arcosh_real (@ tptp.cosh_real X3)) X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X3)) (@ tptp.cosh_real Y))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X3)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real X3) Y)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X3)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real Y) X3))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ tptp.arccos X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) 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 X3)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_eq_real Y) X3))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (@ tptp.arccos X3) (@ tptp.arccos Y)) (= X3 Y)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X3)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X3)) (@ tptp.arcsin Y)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) 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 X3)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_eq_real X3) Y))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (= (@ tptp.arcsin X3) (@ tptp.arcsin Y)) (= X3 Y))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y)) (@ tptp.arccos X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X3)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_real Y) X3))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X3)) X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X3)) (@ tptp.arcsin Y)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X3)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_real X3) Y))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X3)) tptp.zero_zero_real))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X3) (= (@ tptp.arccos (@ tptp.cos_real X3)) (@ tptp.uminus_uminus_real X3))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X3)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X3)) tptp.zero_zero_real))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X3)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X3))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) (@ tptp.inverse_inverse_real X3))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (assert (forall ((X3 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)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X3)) X3))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X3) (@ tptp.inverse_inverse_real X3))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X3))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ _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 X3)) Y) (@ _let_1 (@ tptp.sin_real Y)))))))))))
% 6.48/6.81 (assert (forall ((X3 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)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) 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 X3)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) X3))))))))))
% 6.48/6.81 (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))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X3)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X3)) tptp.zero_zero_real)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))))
% 6.48/6.81 (assert (forall ((X3 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) X3) (= (@ (@ tptp.log _let_1) X3) (@ (@ 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 X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X3))))
% 6.48/6.81 (assert (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)))
% 6.48/6.81 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (@ _let_1 (@ _let_1 X3)) (@ tptp.uminus1482373934393186551omplex X3)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 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 X3) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_real (@ _let_1 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X3) Y)))))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X3)) tptp.one_one_real) (@ (@ tptp.ord_less_real X3) A))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ _let_1 (@ (@ tptp.log A) X3)) (@ (@ tptp.ord_less_real A) X3)))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X3) tptp.one_one_real))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 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 X3) (= (@ _let_2 (@ (@ tptp.log A) X3)) (@ _let_1 X3))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X3) tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X3))))
% 6.48/6.81 (assert (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X3)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X3)) (@ (@ tptp.ord_less_eq_real A) X3))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X3)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X3) A))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 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 X3) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X3) Y)))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.48/6.81 (assert (forall ((Z tptp.complex) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ (@ tptp.divide1717551699836669952omplex Z) (@ (@ tptp.times_times_complex _let_1) tptp.imaginary_unit)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z))) _let_1)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.48/6.81 (assert (not (= tptp.imaginary_unit tptp.one_one_complex)))
% 6.48/6.81 (assert (forall ((W tptp.num)) (not (= tptp.imaginary_unit (@ tptp.numera6690914467698888265omplex W)))))
% 6.48/6.81 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (= (@ _let_1 W) Z) (= W (@ tptp.uminus1482373934393186551omplex (@ _let_1 Z)))))))
% 6.48/6.81 (assert (forall ((W tptp.num)) (not (= tptp.imaginary_unit (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))))))
% 6.48/6.81 (assert (= tptp.ln_ln_real (@ tptp.log (@ tptp.exp_real tptp.one_one_real))))
% 6.48/6.81 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.complex2 X3) Y) tptp.imaginary_unit) (and (= X3 tptp.zero_zero_real) (= Y tptp.one_one_real)))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) tptp.imaginary_unit) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real) (X3 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) X3) (@ (@ tptp.divide_divide_real (@ _let_1 X3)) (@ _let_1 B))))))))
% 6.48/6.81 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log B) _let_1)))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 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 X3) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.times_times_real X3) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X3)) (@ _let_1 Y)))))))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 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 X3) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.divide_divide_real X3) Y)) (@ (@ tptp.minus_minus_real (@ _let_1 X3)) (@ _let_1 Y)))))))))))
% 6.48/6.81 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N)) X3) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X3)) (@ tptp.semiri5074537144036343181t_real N))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ _let_1 (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_1 X3)))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 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 X3) (= (@ _let_1 (@ tptp.inverse_inverse_real X3)) (@ tptp.uminus_uminus_real (@ _let_1 X3))))))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real) (X3 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 X3) (= (@ (@ tptp.log A) X3) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X3)))))))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X3)))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.48/6.81 (assert (forall ((X3 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) X3) (= (@ _let_1 X3) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3)) (@ tptp.cot_real X3))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 6.48/6.81 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.48/6.81 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))))
% 6.48/6.81 (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)))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X3)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X3) (@ (@ tptp.ord_less_eq_real X3) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 6.48/6.81 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 6.48/6.81 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X3)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X3))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.48/6.81 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)))
% 6.48/6.81 (assert (= (@ tptp.cis tptp.zero_zero_real) tptp.one_one_complex))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X3) tptp.one_one_real) (= X3 tptp.zero_zero_real)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (= (@ (@ tptp.powr_real X3) tptp.one_one_real) X3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.powr_real X3) tptp.one_one_real) X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X3))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N))))))
% 6.48/6.81 (assert (= (@ tptp.cis tptp.pi) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X3) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X3)) X3)))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.powr_real X3) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat N))))))
% 6.48/6.81 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X3)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X3))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X3) Y))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X3) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X3))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ tptp.ord_less_real A) B))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.powr_real X3))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.powr_real X3))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X3) A)) (@ (@ tptp.powr_real Y) A)))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X3) A)))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 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 X3) (@ _let_1 Y)) (= X3 Y)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.powr_real X3) Y)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X3) A)))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real) (X3 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) X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X3) A)) (@ (@ tptp.powr_real Y) B))))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X3) A)) tptp.one_one_real)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X3) Y)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X3) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X3) Y)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X3) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (not (= X3 tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X3) Y)) (@ (@ tptp.times_times_real Y) (@ tptp.ln_ln_real X3))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (B tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X3 tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X3) Y)) (@ (@ tptp.times_times_real Y) (@ _let_1 X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X3)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X3) (@ (@ tptp.ord_less_real X3) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.powr_real X3) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X3) N)))))
% 6.48/6.81 (assert (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X3) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X3)))))))
% 6.48/6.81 (assert (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_real X3) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X3)) Y))))))
% 6.48/6.81 (assert (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X3)) Y) (@ (@ tptp.ord_less_real X3) (@ (@ tptp.powr_real B) Y)))))))
% 6.48/6.81 (assert (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X3)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X3))))))
% 6.48/6.81 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_real R2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2))) tptp.one_one_real))))
% 6.48/6.81 (assert (forall ((N tptp.int) (X3 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X3) N))))))
% 6.48/6.81 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real R2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2))) tptp.one_one_real))))
% 6.48/6.81 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2)))))
% 6.48/6.81 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2)))))
% 6.48/6.81 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.cis A)) N) (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.powr_real X3) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real X3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.times_times_real X3) (@ _let_1 Y)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y)))))))
% 6.48/6.81 (assert (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X3))))))
% 6.48/6.81 (assert (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X3)) Y) (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.powr_real B) Y)))))))
% 6.48/6.81 (assert (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X3)) Y))))))
% 6.48/6.81 (assert (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X3) (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X3)))))))
% 6.48/6.81 (assert (forall ((N tptp.int) (X3 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X3) N))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X3) A)) A))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X3)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X3))))))
% 6.48/6.81 (assert (forall ((B tptp.real) (X3 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 X3) (= (@ (@ tptp.plus_plus_real (@ _let_1 X3)) Y) (@ _let_1 (@ (@ tptp.times_times_real X3) (@ (@ tptp.powr_real B) Y)))))))))))
% 6.48/6.81 (assert (forall ((B tptp.real) (X3 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 X3) (= (@ (@ tptp.plus_plus_real Y) (@ _let_1 X3)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y)) X3))))))))))
% 6.48/6.81 (assert (forall ((B tptp.real) (X3 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 X3) (= (@ (@ tptp.minus_minus_real Y) (@ _let_1 X3)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y)) X3))))))))))
% 6.48/6.81 (assert (forall ((B tptp.real) (X3 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 X3) (= (@ (@ tptp.minus_minus_real (@ _let_1 X3)) Y) (@ _let_1 (@ (@ tptp.times_times_real X3) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.powr_real X3) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.powr_real X3) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat N)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) _let_2))))) tptp.one_one_int))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K3 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K3))) (@ tptp.semiri5074537144036343181t_real N))))) (@ tptp.set_ord_lessThan_nat N)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))))))
% 6.48/6.81 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.imaginary_unit)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.48/6.81 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex tptp.pi))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.48/6.81 (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))
% 6.48/6.81 (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))
% 6.48/6.81 (assert (forall ((Z tptp.complex)) (exists ((A5 tptp.complex) (R3 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ tptp.exp_complex A5))))))
% 6.48/6.81 (assert (forall ((R2 tptp.real) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X3) Y)) (@ (@ tptp.complex2 (@ _let_1 X3)) (@ _let_1 Y))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real) (R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X3) Y)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X3) R2)) (@ (@ tptp.times_times_real Y) R2)))))
% 6.48/6.81 (assert (forall ((R2 tptp.real) (X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X3) Y)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R2) X3)) Y))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real) (R2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X3) Y)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X3) R2)) Y))))
% 6.48/6.81 (assert (= tptp.cis (lambda ((B2 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B2))))))
% 6.48/6.81 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.48/6.81 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.48/6.81 (assert (= tptp.complex2 (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex A3)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B2))))))
% 6.48/6.81 (assert (forall ((Z tptp.complex)) (exists ((R3 tptp.real) (A5 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A5))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A5)))))))))
% 6.48/6.81 (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)))
% 6.48/6.81 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A)))))) (@ tptp.abs_abs_real R2))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (= tptp.arctan (lambda ((Y6 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) Y6))))))))
% 6.48/6.81 (assert (= tptp.arcsin (lambda ((Y6 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) Y6))))))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ tptp.sgn_sgn_int L2))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (and (=> _let_7 (= _let_6 (@ _let_3 _let_1))) (=> (not _let_7) (= _let_6 (@ _let_3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat N) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))) _let_1)))))))))))))))))
% 6.48/6.81 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.csqrt Z) tptp.one_one_complex) (= Z tptp.one_one_complex))))
% 6.48/6.81 (assert (= (@ tptp.csqrt tptp.one_one_complex) tptp.one_one_complex))
% 6.48/6.81 (assert (forall ((R2 tptp.int) (L2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) L2)) K) (and (@ (@ tptp.dvd_dvd_int L2) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (R2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int L2) (@ tptp.sgn_sgn_int R2))) K) (and (@ (@ tptp.dvd_dvd_int L2) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (R2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) K)) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (K tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L2))) (= (@ _let_1 (@ (@ tptp.times_times_int K) (@ tptp.sgn_sgn_int R2))) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))))
% 6.48/6.81 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 6.48/6.81 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat) (L4 tptp.int)) (not (= K (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L4)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 6.48/6.81 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L2)) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X3) (@ tptp.the_real (lambda ((X2 tptp.real)) false))))))
% 6.48/6.81 (assert (= tptp.sgn_sgn_int (lambda ((I3 tptp.int)) (@ (@ (@ tptp.if_int (= I3 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I3)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.48/6.81 (assert (forall ((V tptp.int) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.abs_abs_int K))) (let ((_let_3 (@ tptp.times_times_int (@ tptp.sgn_sgn_int V)))) (=> (not (= V tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) (@ _let_3 _let_1)) (@ (@ tptp.divide_divide_int _let_2) _let_1))))))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.dvd_dvd_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int K)) (@ tptp.sgn_sgn_int L2))) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt X3)) (@ tptp.csqrt (@ tptp.real_V4546457046886955230omplex X3))))))
% 6.48/6.81 (assert (= tptp.arccos (lambda ((Y6 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) Y6)))))))
% 6.48/6.81 (assert (forall ((R2 tptp.int) (L2 tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R2) (@ tptp.sgn_sgn_int L2)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R2)) (@ tptp.abs_abs_int L2)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) L2)) R2)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R2)))))))
% 6.48/6.81 (assert (= tptp.eucl_rel_int (lambda ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A1 K3) (= A22 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A1 K3) (= A22 L) (= A32 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (not (= L tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q4) L)))) (exists ((R5 tptp.int) (L tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A1 K3) (= A22 L) (= A32 (@ (@ tptp.product_Pair_int_int Q4) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) L)) R5))))))))
% 6.48/6.81 (assert (forall ((A12 tptp.int) (A23 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A12) A23) A33) (=> (=> (= A23 tptp.zero_zero_int) (not (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A12)))) (=> (forall ((Q3 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int)) (=> (not (= A23 tptp.zero_zero_int)) (not (= A12 (@ (@ tptp.times_times_int Q3) A23)))))) (not (forall ((R3 tptp.int) (Q3 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q3) R3)) (=> (= (@ tptp.sgn_sgn_int R3) (@ tptp.sgn_sgn_int A23)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int A23)) (not (= A12 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q3) A23)) R3)))))))))))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (=> (not (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L2))) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2)))) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K)))))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M) N))) (let ((_let_2 (@ tptp.sgn_sgn_int L2))) (let ((_let_3 (@ tptp.sgn_sgn_int K))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (@ tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))))))))))))))))
% 6.48/6.81 (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)))))))))))
% 6.48/6.81 (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))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (I2 tptp.int)) (let ((_let_1 (@ tptp.power_power_real X3))) (let ((_let_2 (@ (@ tptp.powr_real X3) (@ 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) X3) (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)))))))))))))
% 6.48/6.81 (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))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X3)) (@ _let_1 X3)))))
% 6.48/6.81 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 6.48/6.81 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))))
% 6.48/6.81 (assert (forall ((I2 tptp.int)) (= (= (@ tptp.nat2 I2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 6.48/6.81 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))))
% 6.48/6.81 (assert (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N) (@ tptp.nat2 Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N) Y))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X3))) A) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.semiri5074537144036343181t_real A)))))
% 6.48/6.81 (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))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))))
% 6.48/6.81 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)) A))))
% 6.48/6.81 (assert (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))))
% 6.48/6.81 (assert (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)) A))))
% 6.48/6.81 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X3) Y)))))))
% 6.48/6.81 (assert (= tptp.numeral_numeral_nat (lambda ((I3 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X3)) (@ tptp.nat2 Y)))))
% 6.48/6.81 (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 Z) (@ tptp.nat2 Z6)) (= Z Z6)))))))
% 6.48/6.81 (assert (= (lambda ((P5 (-> tptp.nat Bool))) (forall ((X7 tptp.nat)) (@ P5 X7))) (lambda ((P6 (-> tptp.nat Bool))) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ P6 (@ tptp.nat2 X2)))))))
% 6.48/6.81 (assert (= (lambda ((P5 (-> tptp.nat Bool))) (exists ((X7 tptp.nat)) (@ P5 X7))) (lambda ((P6 (-> tptp.nat Bool))) (exists ((X2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ P6 (@ tptp.nat2 X2)))))))
% 6.48/6.81 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X3) Y)) (@ (@ tptp.bit_se1409905431419307370or_int X3) Y)) (@ (@ tptp.plus_plus_int X3) Y))))
% 6.48/6.81 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M6) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X3)) N) (@ (@ tptp.ord_less_eq_int X3) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (= (@ tptp.semiri1314217659103216013at_int M) Z) (and (= M (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)))))
% 6.48/6.81 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))))
% 6.48/6.81 (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))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.48/6.81 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.48/6.81 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X3))))))
% 6.48/6.81 (assert (= tptp.divide_divide_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.48/6.81 (assert (= tptp.modulo_modulo_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.48/6.81 (assert (= tptp.sgn_sgn_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (= A3 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A3)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (W tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= M (@ tptp.nat2 W)) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.48/6.81 (assert (forall ((W tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= (@ tptp.nat2 W) M) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.48/6.81 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) K)))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (= tptp.suc (lambda ((A3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) tptp.one_one_int)))))
% 6.48/6.81 (assert (forall ((Z6 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z6) (=> (@ (@ tptp.ord_less_eq_int Z6) Z) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z) Z6)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X3) Y)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X3)) (@ tptp.nat2 Y))))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X3) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X3)) (@ tptp.nat2 Y))))))
% 6.48/6.81 (assert (forall ((Y tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X3) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X3)) (@ tptp.nat2 Y))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X3)) tptp.zero_zero_nat))))
% 6.48/6.81 (assert (forall ((Z tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N)))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X3) Y)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X3)) (@ tptp.nat2 Y))))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) X3) (=> (@ (@ tptp.ord_less_real X3) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X3)) N)))))
% 6.48/6.81 (assert (forall ((X3 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X3)) A) (@ (@ tptp.ord_less_eq_nat X3) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 6.48/6.81 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.modulo_modulo_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 6.48/6.81 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K))))))
% 6.48/6.81 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K))))))
% 6.48/6.81 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.48/6.81 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.48/6.81 (assert (forall ((A tptp.real) (N tptp.nat) (X3 tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) X3) (=> (= X3 (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) X3) (=> (@ (@ tptp.ord_less_real X3) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X3)) N)))))
% 6.48/6.81 (assert (forall ((Z tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z)) M) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z) (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.48/6.81 (assert (forall ((Z tptp.complex) (X3 tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X3)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (= (@ tptp.arg Z) X3))))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (=> (@ (@ tptp.ord_less_int X3) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X3) Y)) _let_1)))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.int)) (let ((_let_1 (@ tptp.power_power_real X3))) (let ((_let_2 (@ (@ tptp.powr_real X3) (@ tptp.ring_1_of_int_real N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N)))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (not (= X3 tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X3)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X3))))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 6.48/6.81 (assert (= tptp.arg (lambda ((Z5 tptp.complex)) (@ (@ (@ tptp.if_real (= Z5 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A3 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z5) (@ tptp.cis A3)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A3) (@ (@ tptp.ord_less_eq_real A3) tptp.pi))))))))
% 6.48/6.81 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cis (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_complex))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X3))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3)))))
% 6.48/6.81 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))))
% 6.48/6.81 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))))
% 6.48/6.81 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) tptp.one) (@ tptp.bit0 tptp.one))))
% 6.48/6.81 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit1 M)) (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.48/6.81 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) tptp.one) tptp.one)))
% 6.48/6.81 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.48/6.81 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.48/6.81 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.48/6.81 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 6.48/6.81 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (= (@ tptp.sin_real (@ (@ tptp.times_times_real X3) tptp.pi)) tptp.zero_zero_real) (@ (@ tptp.member_real X3) tptp.ring_1_Ints_real))))
% 6.48/6.81 (assert (forall ((X3 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 (= X3 tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X3) 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 ((N3 tptp.num)) (= X3 (@ tptp.bit0 N3))) (=> _let_1 (not (= Y (@ tptp.bit0 tptp.one))))) (=> (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (=> (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M5)) (not (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (=> (=> (exists ((N3 tptp.num)) (= X3 (@ tptp.bit1 N3))) _let_2) (=> (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (not (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))))))))))))))))))
% 6.48/6.81 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.zero_zero_real))))
% 6.48/6.81 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_real))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.48/6.81 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M6)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.48/6.81 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X3))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 6.48/6.81 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M6)) (not (@ _let_2 N2)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.48/6.81 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.48/6.81 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.48/6.81 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 6.48/6.81 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ _let_1 K)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) tptp.zero_zero_int) L2) (@ (@ tptp.bit_se545348938243370406it_int N) L2))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.48/6.81 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)))))
% 6.48/6.81 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) N) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N) K)))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X3) Y)))))))
% 6.48/6.81 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 6.48/6.81 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 6.48/6.81 (assert (forall ((Uu2 Bool) (Uv2 Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D) (= D tptp.one_one_nat))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N) M))))))
% 6.48/6.81 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q2)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1148574629649215175it_nat Q2) (@ (@ tptp.minus_minus_nat N) M))))))
% 6.48/6.81 (assert (= tptp.bit_concat_bit (lambda ((N2 tptp.nat) (K3 tptp.int) (L tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K3)) (@ (@ tptp.bit_se545348938243370406it_int N2) L)))))
% 6.48/6.81 (assert (= tptp.bit_concat_bit (lambda ((N2 tptp.nat) (K3 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K3)) (@ (@ tptp.bit_se545348938243370406it_int N2) L)))))
% 6.48/6.81 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)))))
% 6.48/6.81 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.48/6.81 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (=> (@ (@ tptp.ord_less_int X3) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X3) Y)) _let_1)))))))
% 6.48/6.81 (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)))))))))
% 6.48/6.81 (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)))))))))))))
% 6.48/6.81 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A2)))))))
% 6.48/6.81 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.48/6.81 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or1269000886237332187st_nat L2) U))))
% 6.48/6.81 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_lessThan_nat K))))
% 6.48/6.81 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_atMost_nat K))))
% 6.48/6.81 (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))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 6.48/6.81 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N3) (@ F N3))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) U)))))))
% 6.48/6.81 (assert (= tptp.finite_finite_nat (lambda ((N9 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N9) (@ (@ tptp.ord_less_eq_nat X2) M6)))))))
% 6.48/6.81 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.48/6.81 (assert (= tptp.finite_finite_nat (lambda ((N9 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N9) (@ (@ tptp.ord_less_nat X2) M6)))))))
% 6.48/6.81 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) N5) (@ (@ tptp.ord_less_nat X5) N))) (@ tptp.finite_finite_nat N5))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))
% 6.48/6.81 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.48/6.81 (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)))
% 6.48/6.81 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N5))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int)))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.48/6.81 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N) M))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.zero_zero_int)))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) K))))))
% 6.48/6.81 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) K))))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or1266510415728281911st_int L2) U))))
% 6.48/6.81 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I3) (@ (@ tptp.ord_less_eq_int I3) B)))))))
% 6.48/6.81 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.ord_less_int A) I3) (@ (@ tptp.ord_less_eq_int I3) B)))))))
% 6.48/6.81 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I3) (@ (@ tptp.ord_less_int I3) B)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))))))
% 6.48/6.81 (assert (= tptp.finite_finite_nat (lambda ((S4 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S4) (@ tptp.set_ord_atMost_nat K3))))))
% 6.48/6.81 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N)))))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C))))))))
% 6.48/6.81 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S3) (@ tptp.set_ord_lessThan_nat K2))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.root N) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X3) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X3) tptp.zero_zero_real)))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X3) (@ _let_1 Y)) (= X3 Y))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X3) tptp.zero_zero_real) (= X3 tptp.zero_zero_real)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X3) Y))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X3) Y))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X3) tptp.one_one_real) (= X3 tptp.one_one_real)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) tptp.one_one_real) tptp.one_one_real))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real)))))
% 6.48/6.81 (assert (forall ((N 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) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X3)) tptp.one_one_real) (@ (@ tptp.ord_less_real X3) tptp.one_one_real)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X3)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real)))))
% 6.48/6.81 (assert (forall ((N 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) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X3)) N) X3)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.uminus_uminus_real X3)) (@ tptp.uminus_uminus_real (@ _let_1 X3))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.inverse_inverse_real X3)) (@ tptp.inverse_inverse_real (@ _let_1 X3))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X3) Y)) (@ (@ tptp.divide_divide_real (@ _let_1 X3)) (@ _let_1 Y))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.root M))) (let ((_let_2 (@ tptp.root N))) (= (@ _let_1 (@ _let_2 X3)) (@ _let_2 (@ _let_1 X3)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.times_times_real X3) Y)) (@ (@ tptp.times_times_real (@ _let_1 X3)) (@ _let_1 Y))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N)) X3) (@ (@ tptp.root M) (@ (@ tptp.root N) X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.root N) X3))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_real (@ _let_1 X3)) (@ _let_1 Y)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X3)) (@ _let_1 Y)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.power_power_real X3) K)) (@ (@ tptp.power_power_real (@ _let_1 X3)) K))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ tptp.abs_abs_real X3)) (@ tptp.abs_abs_real (@ _let_1 X3)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N) X3)) (@ tptp.sgn_sgn_real X3)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.root N) X3)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ tptp.ord_less_real (@ (@ tptp.root N5) X3)) (@ (@ tptp.root N) X3)))))))
% 6.48/6.81 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y) N))) (@ tptp.abs_abs_real Y)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N) X3))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X3)) (@ (@ tptp.root N5) X3))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N5) X3)) (@ (@ tptp.root N) X3)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X3)) N) X3)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N) X3) (= (@ (@ tptp.root N) X3) Y))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X3) N)) X3)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X3)) N) X3))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (Y tptp.real) (X3 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (= (@ (@ tptp.power_power_real Y) N) X3) (= (@ (@ tptp.root N) X3) Y)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X3) N)) X3))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X3)) (@ (@ tptp.root N5) X3))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N))) Y))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ (@ tptp.root N) X3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N)) X3)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (B tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N) B)) X3) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) X3)))))))
% 6.48/6.81 (assert (forall ((P (-> tptp.real Bool)) (N tptp.nat) (X3 tptp.real)) (= (@ P (@ (@ tptp.root N) X3)) (and (=> (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (forall ((Y6 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N)) X3) (@ P Y6))))))))
% 6.48/6.81 (assert (forall ((S3 tptp.set_int)) (= (not (@ tptp.finite_finite_int S3)) (forall ((M6 tptp.int)) (exists ((N2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int M6) (@ tptp.abs_abs_int N2)) (@ (@ tptp.member_int N2) S3)))))))
% 6.48/6.81 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M6 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N2) (@ (@ tptp.member_nat N2) S3)))))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (S3 tptp.set_nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M5) (exists ((N8 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N8) (@ (@ tptp.member_nat N8) S3))))) (not (@ tptp.finite_finite_nat S3)))))
% 6.48/6.81 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M6 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.member_nat N2) S3)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.root N) X3) (@ (@ tptp.powr_real X3) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.48/6.81 (assert (= tptp.finite_finite_nat (lambda ((S4 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S4) (@ tptp.set_ord_lessThan_nat K3))))))
% 6.48/6.81 (assert (forall ((X3 tptp.num) (Xa2 tptp.num) (Y tptp.num)) (let ((_let_1 (= X3 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (@ (@ tptp.bit_or_not_num_neg X3) Xa2) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X3) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y tptp.one) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bit1 M5)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.bit0 tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y tptp.one) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))) (not (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))))))))))))))))))
% 6.48/6.81 (assert (= tptp.int_ge_less_than (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z7) (@ (@ tptp.ord_less_int Z7) Z5))))))))
% 6.48/6.81 (assert (= tptp.int_ge_less_than2 (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z5) (@ (@ tptp.ord_less_int Z7) Z5))))))))
% 6.48/6.81 (assert (forall ((X3 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 X3) Y) (=> (@ _let_2 X3) (=> (=> (= X3 _let_1) (=> Y (not (@ _let_2 _let_1)))) (=> (forall ((Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv))) (=> (= X3 _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) true))) (=> (= X3 _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy2))) (=> (= X3 _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))) (=> (= X3 _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.48/6.81 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or4665077453230672383an_nat L2) U))))
% 6.48/6.81 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N) (@ P M6))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N) (@ P M6))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.48/6.81 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L2) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L2) U))))
% 6.48/6.81 (assert (= tptp.set_ord_lessThan_nat (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat)))
% 6.48/6.81 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat N) (@ _let_1 N))))))
% 6.48/6.81 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N5))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.suc N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N) (@ _let_1 N)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.48/6.81 (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)))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.48/6.81 (assert (forall ((X3 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X3)) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X3) (=> (forall ((Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv))) (=> (= X3 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (=> (forall ((Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) true))) (=> (= X3 _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))) (=> (= X3 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))
% 6.48/6.81 (assert (forall ((X3 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 X3) (=> (@ _let_2 X3) (=> (=> (= X3 _let_1) (not (@ _let_2 _let_1))) (not (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy2))) (=> (= X3 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I4 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J) (=> (@ (@ tptp.ord_less_nat J) N) (@ (@ tptp.ord_less_eq_nat (@ A I4)) (@ A J))))) (=> (forall ((I4 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J) (=> (@ (@ tptp.ord_less_nat J) N) (@ (@ tptp.ord_less_eq_nat (@ B J)) (@ B I4))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I3)) (@ B I3)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int L2) U))))
% 6.48/6.81 (assert (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L2) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L2) U))))
% 6.48/6.81 (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 ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N2) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X4 M6)) (@ X4 N2)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 6.48/6.81 (assert (= tptp.code_Target_positive tptp.numeral_numeral_int))
% 6.48/6.81 (assert (= tptp.unique4921790084139445826nteger (lambda ((L tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((V tptp.num)) (= (@ tptp.re (@ tptp.numera6690914467698888265omplex V)) (@ tptp.numeral_numeral_real V))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (= tptp.sgn_sgn_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))
% 6.48/6.81 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.48/6.81 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.48/6.81 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 6.48/6.81 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L2) L2)))
% 6.48/6.81 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.48/6.81 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L2) tptp.zero_z3403309356797280102nteger)))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X3)) (@ tptp.real_V1022390504157884413omplex X3))))
% 6.48/6.81 (assert (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.plus_plus_complex X3) Y)) (@ (@ tptp.plus_plus_real (@ tptp.re X3)) (@ tptp.re Y)))))
% 6.48/6.81 (assert (forall ((R2 tptp.real) (X3 tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R2) X3)) (@ (@ tptp.times_times_real R2) (@ tptp.re X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X3))) (@ tptp.real_V1022390504157884413omplex X3))))
% 6.48/6.81 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 6.48/6.81 (assert (= tptp.one_one_int tptp.one_one_int))
% 6.48/6.81 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.re (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))))
% 6.48/6.81 (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)))))))))))
% 6.48/6.81 (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)))))))))
% 6.48/6.81 (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))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X3) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.power_power_complex X3) N)) tptp.zero_zero_real))))
% 6.48/6.81 (assert (forall ((V tptp.num)) (= (@ tptp.im (@ tptp.numera6690914467698888265omplex V)) tptp.zero_zero_real)))
% 6.48/6.81 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.re Z))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X3) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.power_power_real (@ tptp.re X3)) N)))))
% 6.48/6.81 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.uminus_uminus_real (@ tptp.im Z)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.re X3))) (=> (= (@ tptp.im X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= (@ tptp.csqrt X3) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt _let_1))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.im X3))) (=> (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 X3)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X3)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.re X3))) (=> (= (@ tptp.im X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X3) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))))
% 6.48/6.81 (assert (forall ((Xa2 tptp.int) (X3 tptp.int)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X3)) (@ tptp.code_integer_of_int (@ (@ tptp.modulo_modulo_int Xa2) X3)))))
% 6.48/6.81 (assert (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real))
% 6.48/6.81 (assert (= (@ tptp.im tptp.one_one_complex) tptp.zero_zero_real))
% 6.48/6.81 (assert (forall ((Xa2 tptp.int) (X3 tptp.int)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X3)) (@ tptp.code_integer_of_int (@ (@ tptp.plus_plus_int Xa2) X3)))))
% 6.48/6.81 (assert (forall ((Xa2 tptp.int) (X3 tptp.int)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X3)) (@ tptp.code_integer_of_int (@ (@ tptp.times_times_int Xa2) X3)))))
% 6.48/6.81 (assert (= tptp.one_one_Code_integer (@ tptp.code_integer_of_int tptp.one_one_int)))
% 6.48/6.81 (assert (forall ((Xa2 tptp.int) (X3 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X3)) (@ (@ tptp.ord_less_eq_int Xa2) X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.plus_plus_complex X3) Y)) (@ (@ tptp.plus_plus_real (@ tptp.im X3)) (@ tptp.im Y)))))
% 6.48/6.81 (assert (forall ((R2 tptp.real) (X3 tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R2) X3)) (@ (@ tptp.times_times_real R2) (@ tptp.im X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X3))) (@ tptp.real_V1022390504157884413omplex X3))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X3) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X3)) (@ tptp.im Y))) (@ (@ tptp.times_times_real (@ tptp.im X3)) (@ tptp.re Y))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.im X3) (@ tptp.im Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X3))) (@ tptp.abs_abs_real (@ tptp.re Y)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.re X3) (@ tptp.re Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X3))) (@ tptp.abs_abs_real (@ tptp.im Y)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X3) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X3)) (@ tptp.re Y))) (@ (@ tptp.times_times_real (@ tptp.im X3)) (@ tptp.im Y))))))
% 6.48/6.81 (assert (= tptp.plus_plus_complex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real (@ tptp.re X2)) (@ tptp.re Y6))) (@ (@ tptp.plus_plus_real (@ tptp.im X2)) (@ tptp.im Y6))))))
% 6.48/6.81 (assert (= tptp.real_V2046097035970521341omplex (lambda ((R5 tptp.real) (X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R5))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X2))) (@ _let_1 (@ tptp.im X2)))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.im (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((A tptp.complex)) (= A (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.re A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.im A)))))))
% 6.48/6.81 (assert (= tptp.times_times_complex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (let ((_let_1 (@ tptp.re Y6))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X2)))) (let ((_let_3 (@ tptp.im Y6))) (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))))))))))
% 6.48/6.81 (assert (= tptp.exp_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.exp_real (@ tptp.re Z5)))) (@ tptp.cis (@ tptp.im Z5))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X3) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X3))) (@ tptp.im X3))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X3) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X3)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X3)) _let_1))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X3))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X3)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X3)) _let_1))))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((X3 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 X3) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X3)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X3)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X3))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X3)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X3)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))))
% 6.48/6.81 (assert (forall ((X3 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 X3) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X3)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X3)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))))))
% 6.48/6.81 (assert (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y6))) (let ((_let_3 (@ tptp.re Y6))) (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)))))))))))
% 6.48/6.81 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R2))) (@ tptp.im Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.48/6.81 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R2)) (@ tptp.re Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.48/6.81 (assert (= tptp.code_positive tptp.numera6620942414471956472nteger))
% 6.48/6.81 (assert (forall ((Y tptp.complex) (X3 tptp.complex)) (=> (@ (@ tptp.member_complex Y) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X3) tptp.real_V2521375963428798218omplex) (= (= X3 (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y)) (and (= X3 tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))))
% 6.48/6.81 (assert (forall ((Y tptp.complex) (X3 tptp.complex)) (=> (@ (@ tptp.member_complex Y) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X3) tptp.real_V2521375963428798218omplex) (= (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y) X3) (and (= X3 tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit1 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.times_times_complex X3) Y)) (@ (@ tptp.times_times_complex (@ tptp.cnj X3)) (@ tptp.cnj Y)))))
% 6.48/6.81 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.cnj Z) tptp.one_one_complex) (= Z tptp.one_one_complex))))
% 6.48/6.81 (assert (= (@ tptp.cnj tptp.one_one_complex) tptp.one_one_complex))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (N tptp.nat)) (= (@ tptp.cnj (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.power_power_complex (@ tptp.cnj X3)) N))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.plus_plus_complex X3) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.cnj X3)) (@ tptp.cnj Y)))))
% 6.48/6.81 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.cnj _let_1) _let_1))))
% 6.48/6.81 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (= (@ tptp.cnj _let_1) _let_1))))
% 6.48/6.81 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) tptp.zero_zero_real)))
% 6.48/6.81 (assert (= tptp.code_integer_of_num tptp.numera6620942414471956472nteger))
% 6.48/6.81 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))) tptp.zero_zero_real))))
% 6.48/6.81 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))) tptp.zero_zero_real))))
% 6.48/6.81 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z5 tptp.complex)) (@ tptp.sqrt (@ tptp.re (@ (@ tptp.times_times_complex Z5) (@ tptp.cnj Z5)))))))
% 6.48/6.81 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (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))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (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))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit0 N)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))))))
% 6.48/6.81 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A3) (@ tptp.cnj B2))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K3) L)) (@ (@ tptp.modulo364778990260209775nteger K3) L)))))
% 6.48/6.81 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_lessThan_nat U)) U)))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.ord_less_nat I3) N)))) N)))
% 6.48/6.81 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 6.48/6.81 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L2) U)) (@ (@ tptp.minus_minus_nat U) L2))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I3) N)))) (@ tptp.suc N))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L2)))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L2) U)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U) L2)) tptp.one_one_int)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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))))))))))
% 6.48/6.81 (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))))))))))
% 6.48/6.81 (assert (forall ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N5)) N))))
% 6.48/6.81 (assert (forall ((S3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S3)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) S3))))
% 6.48/6.81 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))) N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) N))))
% 6.48/6.81 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K3 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S5 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S5))) (= S5 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.48/6.81 (assert (= tptp.code_divmod_abs (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.48/6.81 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K3)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L) S5)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L)) S5)))))) _let_1))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.nat)) (= (@ (@ tptp.bezw X3) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))))
% 6.48/6.81 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 6.48/6.81 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M3)))) M)))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M3) N)))) M)))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K3 tptp.nat)) K3)) (@ _let_1 N))))))
% 6.48/6.81 (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)))))))))
% 6.48/6.81 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X2 tptp.rat)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z5)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))))
% 6.48/6.81 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (not (forall ((S2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S2) (forall ((T3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T3) (not (= R2 (@ (@ tptp.plus_plus_rat S2) T3)))))))))))
% 6.48/6.81 (assert (= tptp.sgn_sgn_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (= A3 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A3)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.48/6.81 (assert (= tptp.ord_less_eq_rat (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y6) (= X2 Y6)))))
% 6.48/6.81 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 6.48/6.81 (assert (forall ((P2 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A3)) B2)) (@ tptp.abs_abs_int A3))))) (@ tptp.quotient_of P2)))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X3))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X3))) (=> (= (@ (@ tptp.nat_prod_decode_aux X3) Xa2) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X3) Xa2)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 6.48/6.81 (assert (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int))))
% 6.48/6.81 (assert (= (@ tptp.quotient_of tptp.one_one_rat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)))
% 6.48/6.81 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.48/6.81 (assert (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K))) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))))
% 6.48/6.81 (assert (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int)))
% 6.48/6.81 (assert (= tptp.minus_minus_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.plus_plus_rat Q4) (@ tptp.uminus_uminus_rat R5)))))
% 6.48/6.81 (assert (= tptp.divide_divide_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.times_times_rat Q4) (@ tptp.inverse_inverse_rat R5)))))
% 6.48/6.81 (assert (= tptp.ord_less_rat (lambda ((P4 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B2 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int C2) B2)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P4)))))
% 6.48/6.81 (assert (= tptp.ord_less_eq_rat (lambda ((P4 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B2 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int C2) B2)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P4)))))
% 6.48/6.81 (assert (forall ((X3 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 X3) Xa2)))) (let ((_let_2 (@ tptp.suc X3))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X3))) (=> (= (@ (@ tptp.nat_prod_decode_aux X3) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X3) Xa2)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 6.48/6.81 (assert (forall ((A tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A)) (@ (@ tptp.product_Pair_int_int A) tptp.one_one_int))))
% 6.48/6.81 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int B2) C2))) (@ (@ tptp.times_times_int C2) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))))
% 6.48/6.81 (assert (forall ((P2 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 6.48/6.81 (assert (forall ((Q2 tptp.int) (S tptp.int) (P2 tptp.int) (R2 tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S))) (= (@ (@ tptp.times_times_int P2) S) (@ (@ tptp.times_times_int R2) Q2)))))))
% 6.48/6.81 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) B2)) (@ (@ tptp.times_times_int C2) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))))
% 6.48/6.81 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int C2) B2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))))
% 6.48/6.81 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int B2) C2))) (@ (@ tptp.times_times_int C2) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))))
% 6.48/6.81 (assert (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) (@ tptp.numeral_numeral_int K))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat K)))))
% 6.48/6.81 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int L2))) (@ (@ tptp.divide_divide_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat L2)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.divide_divide_nat M) N))))
% 6.48/6.81 (assert (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 6.48/6.81 (assert (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int)) (@ tptp.numeral_numeral_rat K))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R3) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S3))) (forall ((N8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N8) (@ tptp.finite_card_nat S3)) (@ (@ tptp.member_nat (@ R3 N8)) S3))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N) K)) (@ _let_1 K)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se8568078237143864401it_int N) _let_1) _let_1))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.modulo_modulo_nat M) N))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N) M)) K)))))
% 6.48/6.81 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.48/6.81 (assert (forall ((P2 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.sgn_sgn_rat P2)) (@ (@ tptp.product_Pair_int_int (@ tptp.sgn_sgn_int (@ tptp.product_fst_int_int (@ tptp.quotient_of P2)))) tptp.one_one_int))))
% 6.48/6.81 (assert (forall ((X3 tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X3) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X3) 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 X3) Xa2))))))))))))))
% 6.48/6.81 (assert (= tptp.bezw (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y6) (@ (@ tptp.modulo_modulo_nat X2) Y6)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y6 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) Y6)))))))))))
% 6.48/6.81 (assert (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_integer K) L2)) (@ (@ tptp.modulo364778990260209775nteger K) L2))))
% 6.48/6.81 (assert (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_abs K) L2)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K)) (@ tptp.abs_abs_Code_integer L2)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N) K)))))
% 6.48/6.81 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.48/6.81 (assert (forall ((Y tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X3) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X3) 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 X3) Y)))))))))))
% 6.48/6.81 (assert (forall ((X3 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 X3) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X3) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X3) 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 X3) Xa2)))))))) (not _let_1)))))))))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N)))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N))))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N)))))))
% 6.48/6.81 (assert (= tptp.adjust_mod (lambda ((L tptp.int) (R5 tptp.int)) (@ (@ (@ tptp.if_int (= R5 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L) R5)))))
% 6.48/6.81 (assert (= tptp.normalize (lambda ((P4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P4))) (let ((_let_2 (@ tptp.product_fst_int_int P4))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))
% 6.48/6.81 (assert (forall ((M tptp.int)) (= (@ (@ tptp.gcd_gcd_int M) tptp.one_one_int) tptp.one_one_int)))
% 6.48/6.81 (assert (forall ((N tptp.num) (X3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int _let_1)) X3) (@ (@ tptp.gcd_gcd_int _let_1) X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.gcd_gcd_int X3))) (= (@ _let_2 (@ tptp.uminus_uminus_int _let_1)) (@ _let_2 _let_1))))))
% 6.48/6.81 (assert (= tptp.gcd_gcd_int (lambda ((X2 tptp.int) (Y6 tptp.int)) (@ (@ tptp.gcd_gcd_int Y6) (@ (@ tptp.modulo_modulo_int X2) Y6)))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X3) Y))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (Y tptp.int)) (exists ((U3 tptp.int) (V2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U3) X3)) (@ (@ tptp.times_times_int V2) Y)) (@ (@ tptp.gcd_gcd_int X3) Y)))))
% 6.48/6.81 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int K)) (@ (@ tptp.gcd_gcd_int M) N)) (@ (@ tptp.gcd_gcd_int (@ _let_1 M)) (@ _let_1 N))))))
% 6.48/6.81 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) B))))
% 6.48/6.81 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) A))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (Y tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X3))) (let ((_let_2 (@ P (@ _let_1 Y)))) (let ((_let_3 (@ tptp.uminus_uminus_int Y))) (let ((_let_4 (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int X3)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X3) tptp.zero_zero_int))) (let ((_let_7 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (@ _let_7 Y))) (let ((_let_9 (@ _let_7 X3))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (@ P (@ _let_1 _let_3)))) (=> (=> _let_6 (=> _let_8 (@ P (@ _let_4 Y)))) (=> (=> _let_6 (=> _let_5 (@ P (@ _let_4 _let_3)))) _let_2)))))))))))))))
% 6.48/6.81 (assert (forall ((D tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) D) (@ _let_1 A) (@ _let_1 B) (forall ((E3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int E3))) (=> (and (@ _let_1 A) (@ _let_1 B)) (@ _let_1 D))))) (= D (@ (@ tptp.gcd_gcd_int A) B))))))
% 6.48/6.81 (assert (forall ((Y tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y) (= (@ (@ tptp.gcd_gcd_int X3) Y) (@ (@ tptp.gcd_gcd_int Y) (@ (@ tptp.modulo_modulo_int X3) Y))))))
% 6.48/6.81 (assert (= tptp.gcd_gcd_int (lambda ((K3 tptp.int) (L tptp.int)) (@ tptp.abs_abs_int (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K3) (@ (@ tptp.gcd_gcd_int L) (@ (@ tptp.modulo_modulo_int (@ tptp.abs_abs_int K3)) (@ tptp.abs_abs_int L))))))))
% 6.48/6.81 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K3) (@ tptp.sgn_sgn_Code_integer L))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer L)) S5)))))) _let_1))))))))))
% 6.48/6.81 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)))
% 6.48/6.81 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M) N)) (or (not (= M tptp.zero_zero_nat)) (not (= N tptp.zero_zero_nat))))))
% 6.48/6.81 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.gcd_gcd_nat M) N)) (@ (@ tptp.gcd_gcd_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.48/6.81 (assert (= tptp.gcd_gcd_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.gcd_gcd_nat Y6) (@ (@ tptp.modulo_modulo_nat X2) Y6)))))
% 6.48/6.81 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) B))))
% 6.48/6.81 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) A))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N) M)) N) (@ (@ tptp.gcd_gcd_nat M) N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M) N)) N) (@ (@ tptp.gcd_gcd_nat M) N)))))
% 6.48/6.81 (assert (forall ((X3 tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X3) Xa2) Y) (and (=> _let_1 (= Y X3)) (=> (not _let_1) (= Y (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X3) Xa2)))))))))
% 6.48/6.81 (assert (= tptp.gcd_gcd_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ (@ tptp.if_nat (= Y6 tptp.zero_zero_nat)) X2) (@ (@ tptp.gcd_gcd_nat Y6) (@ (@ tptp.modulo_modulo_nat X2) Y6))))))
% 6.48/6.81 (assert (forall ((Y tptp.nat) (X3 tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (= (@ (@ tptp.gcd_gcd_nat X3) Y) (@ (@ tptp.gcd_gcd_nat Y) (@ (@ tptp.modulo_modulo_nat X3) Y))))))
% 6.48/6.81 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X5 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 6.48/6.81 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y3))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X5))) (let ((_let_6 (@ _let_4 Y3))) (let ((_let_7 (@ _let_2 X5))) (or (and (@ (@ tptp.ord_less_eq_nat _let_6) _let_7) (= (@ (@ tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (@ (@ tptp.ord_less_eq_nat _let_3) _let_5) (= (@ (@ tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))))
% 6.48/6.81 (assert (= tptp.gcd_gcd_Code_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (@ tptp.abs_abs_Code_integer (@ (@ (@ tptp.if_Code_integer (= L tptp.zero_z3403309356797280102nteger)) K3) (@ (@ tptp.gcd_gcd_Code_integer L) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K3)) (@ tptp.abs_abs_Code_integer L))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X3) Y))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X3) Y)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int X3))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int Y)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I) (@ P I))) (@ P K2)))) (@ P M)))))
% 6.48/6.81 (assert (forall ((X3 tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X3) Xa2)))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X3) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X3)) (=> (not _let_2) (= Y (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X3) Xa2))))) (not _let_1)))))))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) (@ (@ tptp.plus_plus_int L2) tptp.one_one_int))))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or5832277885323065728an_int L2) U))))
% 6.48/6.81 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L2) tptp.one_one_int)) U) (@ (@ tptp.set_or5832277885323065728an_int L2) U))))
% 6.48/6.81 (assert (= tptp.code_negative (@ (@ tptp.comp_C3531382070062128313er_num tptp.uminus1351360451143612070nteger) tptp.numera6620942414471956472nteger)))
% 6.48/6.81 (assert (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)))
% 6.48/6.81 (assert (forall ((K tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int K))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 (@ (@ tptp.neg_numeral_sub_int N) tptp.one)))))))
% 6.48/6.81 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or5834768355832116004an_nat L2) U))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((N tptp.num) (K tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) K) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.neg_numeral_sub_int N) tptp.one)) K)))))
% 6.48/6.81 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or5834768355832116004an_nat L2) U))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X3)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ (@ tptp.neg_numeral_sub_int (@ tptp.bitM N)) tptp.one) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.neg_numeral_sub_int N) tptp.one)))))
% 6.48/6.81 (assert (forall ((K tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K) tptp.zero_zero_nat))))
% 6.48/6.81 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y6) X2))) (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.ord_less_nat Y6) X2))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 6.48/6.81 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 6.48/6.81 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (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)))))))))
% 6.48/6.81 (assert (forall ((K tptp.num)) (= (@ tptp.code_int_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_int K))))
% 6.48/6.81 (assert (forall ((X3 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.plus_p5714425477246183910nteger X3) Xa2)) (@ (@ tptp.plus_plus_int (@ tptp.code_int_of_integer X3)) (@ tptp.code_int_of_integer Xa2)))))
% 6.48/6.81 (assert (forall ((X3 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.times_3573771949741848930nteger X3) Xa2)) (@ (@ tptp.times_times_int (@ tptp.code_int_of_integer X3)) (@ tptp.code_int_of_integer Xa2)))))
% 6.48/6.81 (assert (= (@ tptp.code_int_of_integer tptp.one_one_Code_integer) tptp.one_one_int))
% 6.48/6.81 (assert (forall ((X3 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.modulo364778990260209775nteger X3) Xa2)) (@ (@ tptp.modulo_modulo_int (@ tptp.code_int_of_integer X3)) (@ tptp.code_int_of_integer Xa2)))))
% 6.48/6.81 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((X2 tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa4)))))
% 6.48/6.81 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L)))))
% 6.48/6.81 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X3 tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X3)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 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 Y6))) (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) X3)))))
% 6.48/6.81 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.48/6.81 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X3 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X3)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y6 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) Y6)))) __flatten_var_0))) Xa2) X3))))
% 6.48/6.81 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X3 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X3)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y6 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) Y6)))) __flatten_var_0))) Xa2) X3))))
% 6.48/6.81 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X3 tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X3)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 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 Y6) V4)))) __flatten_var_0))) Xa2) X3)))))
% 6.48/6.81 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X3 tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X3)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 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 Y6) U2)))) __flatten_var_0))) Xa2) X3)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N)))) (=> (not _let_2) (= _let_1 tptp.one)))))))
% 6.48/6.81 (assert (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)))
% 6.48/6.81 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N) N)) (@ tptp.bit0 (@ tptp.num_of_nat N))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N))))))))
% 6.48/6.81 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y6 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 Y6) V4)) (@ (@ tptp.plus_plus_nat U2) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa4)))))
% 6.48/6.81 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y6 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 Y6) V4)) (@ (@ tptp.plus_plus_nat U2) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa4)))))
% 6.48/6.81 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M6 tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M6)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X3))) (= (@ _let_1 (@ tptp.bit1 Y)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y))) X3)))))
% 6.48/6.81 (assert (forall ((C tptp.nat) (Y tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X3) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X3) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat I3) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X3) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat I3) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat I3) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.48/6.81 (assert (forall ((M7 tptp.set_nat) (N5 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N5) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N5))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I2) J2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I2)) (@ tptp.suc J2)))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I2) J2)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I2)) (@ tptp.suc J2)))))
% 6.48/6.81 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))))
% 6.48/6.81 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.48/6.81 (assert (= tptp.sqr (lambda ((X2 tptp.num)) (@ (@ tptp.times_times_num X2) X2))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N))))))
% 6.48/6.81 (assert (forall ((X3 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X3))) (= (@ _let_1 (@ tptp.bit0 Y)) (@ tptp.sqr (@ _let_1 Y))))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc I2))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J2))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.48/6.81 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.48/6.81 (assert (= tptp.finite_finite_int (lambda ((S4 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S4)) (@ tptp.set_ord_atMost_int K3))))))
% 6.48/6.81 (assert (= tptp.finite_finite_int (lambda ((S4 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S4)) (@ tptp.set_ord_lessThan_int K3))))))
% 6.48/6.81 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.48/6.81 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or4665077453230672383an_nat A) B)) (@ (@ tptp.set_or4662586982721622107an_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X8 I4))) (= (@ tptp.suminf_real X8) (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_nat_real (lambda ((I3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X8) (@ tptp.set_ord_lessThan_nat I3)))) tptp.top_top_set_nat)))))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) L2))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L2))) (@ (@ tptp.set_or4662586982721622107an_int L2) U))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 6.48/6.81 (assert (forall ((U tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) U) (= (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U) (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ tptp.set_ord_lessThan_nat (@ tptp.nat2 U)))))))
% 6.48/6.81 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 6.48/6.81 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 6.48/6.81 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (= tptp.root (lambda ((N2 tptp.nat) (X2 tptp.real)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y6 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N2)))) X2)))))
% 6.48/6.81 (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)))))))))))
% 6.48/6.81 (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)))))))))))))
% 6.48/6.81 (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))))))))))))
% 6.48/6.81 (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))))))))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_nat _let_1) J2) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J2)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J2))))))))
% 6.48/6.81 (assert (= tptp.upto_aux (lambda ((I3 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I3)) Js) (@ (@ (@ tptp.upto_aux I3) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 6.48/6.81 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 6.48/6.81 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J2) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J2)) (@ (@ tptp.set_or4665077453230672383an_nat J2) _let_1))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X3) Xa2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X3) Xa2))) (=> (= (@ (@ tptp.upto X3) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X3) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X3) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))))
% 6.48/6.81 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I2) J2))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I2) J2)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J2)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 6.48/6.81 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (= (= (@ (@ tptp.upto I2) J2) tptp.nil_int) (@ (@ tptp.ord_less_int J2) I2))))
% 6.48/6.81 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I2) J2)) (@ (@ tptp.ord_less_int J2) I2))))
% 6.48/6.81 (assert (forall ((J2 tptp.int) (I2 tptp.int)) (=> (@ (@ tptp.ord_less_int J2) I2) (= (@ (@ tptp.upto I2) J2) tptp.nil_int))))
% 6.48/6.81 (assert (forall ((I2 tptp.int)) (= (@ (@ tptp.upto I2) I2) (@ (@ tptp.cons_int I2) tptp.nil_int))))
% 6.48/6.81 (assert (forall ((I2 tptp.int) (K tptp.nat) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I2) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J2) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I2) J2)) K) _let_1)))))
% 6.48/6.81 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I2) J2)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J2) I2)) tptp.one_one_int)))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.48/6.81 (assert (= tptp.upto_aux (lambda ((I3 tptp.int) (J3 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I3) J3)) __flatten_var_0))))
% 6.48/6.81 (assert (= tptp.upto (lambda ((I3 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.upto_aux I3) J3) tptp.nil_int))))
% 6.48/6.81 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I2) J2))))
% 6.48/6.81 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) J3)))))
% 6.48/6.81 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (=> (@ (@ tptp.ord_less_eq_int J2) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J2)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J2) tptp.one_one_int)) K))))))))
% 6.48/6.81 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (=> (@ (@ tptp.ord_less_eq_int J2) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))) (@ (@ tptp.upto J2) K))))))))
% 6.48/6.81 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.48/6.81 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (= (@ (@ tptp.upto I2) J2) (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J2))))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X3) Xa2))) (=> (= (@ (@ tptp.upto X3) Xa2) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X3) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X3) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y tptp.nil_int)))))))
% 6.48/6.81 (assert (= tptp.upto (lambda ((I3 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I3) J3)) (@ (@ tptp.cons_int I3) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3))) tptp.nil_int))))
% 6.48/6.81 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (= (@ _let_1 J2) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))) (@ (@ tptp.cons_int J2) tptp.nil_int)))))))
% 6.48/6.81 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.48/6.81 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (=> (@ (@ tptp.ord_less_eq_int J2) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))) (@ (@ tptp.cons_int J2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J2) tptp.one_one_int)) K)))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ _let_1 X3)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))))))
% 6.48/6.81 (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 ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B))))))
% 6.48/6.81 (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 ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B)) (@ F A))))))
% 6.48/6.81 (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 ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B)) (@ F A))))))
% 6.48/6.81 (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 ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_eq_real (@ F A)) (@ F B))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X3 tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X3) S3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X3) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F _let_1)))))))))))))
% 6.48/6.81 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X3 tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X3) S3)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X3) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X3)))))))))))))
% 6.48/6.81 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X3 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X3) 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 X3)) (@ F (@ (@ tptp.plus_plus_real X3) H4))))))))))))
% 6.48/6.81 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X3 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X3) 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 X3) H4))) (@ F X3)))))))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F4 Z2)))))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X3 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y3)))) (= L2 tptp.zero_zero_real))))))
% 6.48/6.81 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X3 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F Y3)) (@ F X3)))) (= L2 tptp.zero_zero_real))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real X2) N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X3) S))))
% 6.48/6.81 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ G X2)) N))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ G X3)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M)) _let_1)))))
% 6.48/6.81 (assert (forall ((Z tptp.real) (R2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z5 tptp.real)) (@ (@ tptp.powr_real Z5) R2))) (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real Z) (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X3))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))))
% 6.48/6.81 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X3 tptp.real) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (let ((_let_2 (@ G X3))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.powr_real (@ G X2)) R2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M)) _let_1)))))))
% 6.48/6.81 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X3 tptp.real) (F (-> tptp.real tptp.real)) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (let ((_let_2 (@ G X3))) (let ((_let_3 (@ F X3))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R2) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.powr_real (@ G X2)) (@ F X2)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R2) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M) _let_3)) _let_2)))) _let_1)))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X3))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))))
% 6.48/6.81 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F4 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F4 X0))) (=> (forall ((N3 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ F X2) N3))) (@ (@ F4 X0) N3)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((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 ((N3 tptp.nat) (X5 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X5) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X5) N3)) (@ (@ F Y3) N3)))) (@ (@ tptp.times_times_real (@ L5 N3)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X5) Y3)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (@ F X2)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))
% 6.48/6.81 (assert (forall ((X3 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 X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X3) A2))))
% 6.48/6.81 (assert (forall ((X3 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 X3)))) (=> (not (= X3 tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X3) 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 X3) tptp.top_top_set_real)))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ (@ 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 X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X3) A2)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) 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 X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X3) A2)))))
% 6.48/6.81 (assert (forall ((R 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 R)) R)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X5) N2)))))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R)) R)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X2) (@ tptp.suc N2))))))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X0) N2))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X3)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) 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 X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) 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 X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))))
% 6.48/6.81 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X3 tptp.real) (N 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 ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X3)) (= (@ F X3) (@ (@ 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 X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N)))))))))
% 6.48/6.81 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X3 tptp.real) (N 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 ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X3)) (= (@ F X3) (@ (@ 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 X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (not (= X3 tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X3)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))))))
% 6.48/6.81 (assert (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 6.48/6.81 (assert (forall ((H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N)))))))))))
% 6.48/6.81 (assert (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real H2) T3) (@ (@ tptp.ord_less_eq_real T3) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 6.48/6.81 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X3 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X3 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 ((T3 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T3))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X3)) (= (@ F X3) (@ (@ 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 X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N)))))))))))))
% 6.48/6.81 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X3 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X3))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X3)) (= (@ F X3) (@ (@ 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 X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (=> (not (= X3 C)) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T3))) (let ((_let_2 (@ tptp.ord_less_real X3))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T3) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T3) (@ _let_1 X3))) (= (@ F X3) (@ (@ 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 X3) C)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X3) C)) N))))))))))))))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real C) T3) (@ (@ tptp.ord_less_real T3) B) (= (@ F B) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N)))))))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real A) T3) (@ (@ tptp.ord_less_real T3) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N)))))))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B3 tptp.real)) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M2 tptp.nat) (T4 tptp.real)) (let ((_let_1 (@ tptp.suc M2))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M2))) (@ (@ tptp.minus_minus_real (@ (@ Diff M2) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((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 B3) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U2) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T4)) (@ (@ 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 T4) P4)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B3) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T4) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) 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 X3) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (X3 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X3)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X3 tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X3) 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 X3) tptp.top_top_set_real)))))))))))))
% 6.48/6.81 (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 ((X tptp.real)) (let ((_let_1 (@ F X))) (=> (and (@ (@ tptp.ord_less_eq_real A) X) (@ (@ tptp.ord_less_eq_real X) B)) (and (@ (@ tptp.ord_less_eq_real L6) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M8))))) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L6) Y4) (@ (@ tptp.ord_less_eq_real Y4) M8)) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B) (= (@ F X5) Y4)))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) tptp.sqrt)))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.nat)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ tptp.root N))))
% 6.48/6.81 (assert (forall ((A tptp.real) (X3 tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (= (@ G (@ F Z2)) Z2)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X3)) tptp.top_top_set_real)) G)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) tptp.arcosh_real))))
% 6.48/6.81 (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)))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) tptp.arccos)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) tptp.arcsin)))))
% 6.48/6.81 (assert (forall ((B tptp.real) (X3 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real B) X3)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) tptp.artanh_real)))))
% 6.48/6.81 (assert (forall ((D tptp.real) (X3 tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X3))) D) (= (@ G (@ F Z2)) Z2))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X3))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X3)) tptp.top_top_set_real)) G))))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) G)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z2) (=> (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z2)) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z2) (=> (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 Z2)) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))) (exists ((C3 tptp.real)) (and (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G2 C3)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) (@ F4 C3))))))))))))
% 6.48/6.81 (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 ((N8 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 6.48/6.81 (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 ((N8 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 6.48/6.81 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 6.48/6.81 (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))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X8 I4))) B3)) (not (forall ((L6 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat))))))))
% 6.48/6.81 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.root N2) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))
% 6.48/6.81 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N3))) (@ G N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N8)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N8))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N6 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_real R3) (@ X8 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.48/6.81 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.48/6.81 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.root N2) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))))
% 6.48/6.81 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.48/6.81 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 6.48/6.81 (assert (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) L2)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real L2) (@ (@ tptp.plus_plus_real (@ F N8)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L2)) tptp.at_top_nat))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X3)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X3) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X3) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.48/6.81 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X3) (@ tptp.semiri5074537144036343181t_real N2)))) N2))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X3))) tptp.at_top_nat)))
% 6.48/6.81 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real R2) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 6.48/6.81 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ A N2))))))))
% 6.48/6.81 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ A N2)))))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X3) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.48/6.81 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat))))))
% 6.48/6.81 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))))))))
% 6.48/6.81 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) _let_1) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 6.48/6.81 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat)))))
% 6.48/6.81 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))))))
% 6.48/6.81 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat))))))
% 6.48/6.81 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F3 (-> tptp.real tptp.real))) (exists ((C2 tptp.real)) (= F3 (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C2)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X3) Y6))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y6)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X3))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.48/6.81 (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))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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))
% 6.48/6.81 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 6.48/6.81 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real tptp.one_one_real))) tptp.at_bot_real))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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 ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N))) tptp.at_bot_real) F5))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N))) tptp.at_top_real) F5))))))
% 6.48/6.81 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_bot_real) tptp.at_infinity_real))
% 6.48/6.81 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_top_real) tptp.at_infinity_real))
% 6.48/6.81 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real))
% 6.48/6.81 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_real))
% 6.48/6.81 (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))))
% 6.48/6.81 (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)))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X3) Y6))) Y6))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X3))) tptp.at_top_real)))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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 ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.48/6.81 (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))
% 6.48/6.81 (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))))))))))))
% 6.48/6.81 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I3 tptp.nat)) (@ P (@ tptp.suc I3)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.48/6.81 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N2 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N2) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.48/6.81 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I3 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I3) K)))) tptp.at_top_nat))))
% 6.48/6.81 (assert (forall ((F5 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F5) tptp.at_top_nat) (forall ((N9 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N9)) F5)))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N9 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N2) (@ P N2)))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.image_nat_real F) tptp.top_top_set_nat)) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X3)) tptp.at_top_nat)))))
% 6.48/6.81 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or6659071591806873216st_nat L2) U))))
% 6.48/6.81 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L2) U)) (@ (@ tptp.minus_minus_nat U) L2))))
% 6.48/6.81 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.48/6.81 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 6.48/6.81 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.48/6.81 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or6659071591806873216st_nat L2) U))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J2) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J2)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J2))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J2) I2)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J2))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N))))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or6656581121297822940st_int L2) U))))
% 6.48/6.81 (assert (= (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or6656581121297822940st_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L2)))))
% 6.48/6.81 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 6.48/6.81 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L2) tptp.one_one_int)) U) (@ (@ tptp.set_or6656581121297822940st_int L2) U))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real B3) (@ X8 I4))) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 6.48/6.81 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3)))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real B3) (@ 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)))))))))))
% 6.48/6.81 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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) (Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L4) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L4)))))))))
% 6.48/6.81 (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)))))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arccos))
% 6.48/6.81 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arcsin))
% 6.48/6.81 (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)))))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (X3 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) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (= (@ F X3) (@ F A)))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 6.48/6.81 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I4)) B3)) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 6.48/6.81 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I4)) B3)) (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))))))))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N) (@ F N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.inj_on_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N)))) tptp.top_top_set_real))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((N5 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N5)))
% 6.48/6.81 (assert (forall ((N5 tptp.set_nat) (K tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) N5) (@ (@ tptp.ord_less_eq_nat K) N3))) (@ (@ tptp.inj_on_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) K))) N5))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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)))))))
% 6.48/6.81 (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))))))))))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (or (not (= X3 tptp.zero_zero_real)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) N)) (= (@ (@ tptp.powr_real X3) (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.power_int_real X3) N))))))
% 6.48/6.81 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X3) Xa2) Y) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X3 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (= 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)))) (=> (= X3 (@ (@ (@ (@ 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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _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)))))))))))))
% 6.48/6.81 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList) Summary)) Deg4) (and (= Deg Deg4) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ 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 TreeList) (@ (@ 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 TreeList)) (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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> _let_2 (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)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) 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)) TreeList) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima2)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X3) Xa2)) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X3 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (= 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)))) (=> (= X3 (@ (@ (@ (@ 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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _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)))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X3) Xa2) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X3 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (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)))) (=> (= X3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (not (and (= Deg2 Xa2) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _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))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X3) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X3 _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)))) (=> (= X3 _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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _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)))))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X3) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X3 _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))) (=> (= X3 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _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)))))))))))))))
% 6.48/6.81 (assert (= tptp.complete_Sup_Sup_int (lambda ((X4 tptp.set_int)) (@ tptp.the_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) X4) (forall ((Y6 tptp.int)) (=> (@ (@ tptp.member_int Y6) X4) (@ (@ tptp.ord_less_eq_int Y6) X2)))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X3) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X3 _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))) (=> (= X3 _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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _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))))))))))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M) N))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.48/6.81 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I3 tptp.int) (N2 tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I3)) (@ tptp.semiri5074537144036343181t_real N2))) (not (= N2 tptp.zero_zero_nat))))))))
% 6.48/6.81 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int A) B))) (let ((_let_2 (@ (@ tptp.fract A) B))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) _let_2) (@ (@ tptp.ord_less_rat _let_2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (= (@ (@ tptp.member_real (@ tptp.abs_abs_real X3)) tptp.field_5140801741446780682s_real) (@ (@ tptp.member_real X3) tptp.field_5140801741446780682s_real))))
% 6.48/6.81 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))
% 6.48/6.81 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int B) C)))))
% 6.48/6.81 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.48/6.81 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D)))))))
% 6.48/6.81 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.48/6.81 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D)))))))
% 6.48/6.81 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.fract A) B)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B))))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X3) X5)))))
% 6.48/6.81 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract K) tptp.one_one_int) (@ tptp.ring_1_of_int_rat K))))
% 6.48/6.81 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.fract (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int) (@ tptp.semiri681578069525770553at_rat K))))
% 6.48/6.81 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.fract A) B))))))
% 6.48/6.81 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (= (@ (@ tptp.fract A) B) (@ (@ tptp.fract C) D)) (= (@ (@ tptp.times_times_int A) D) (@ (@ tptp.times_times_int C) B)))))))
% 6.48/6.81 (assert (forall ((A tptp.int)) (= (@ (@ tptp.fract A) tptp.zero_zero_int) (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int))))
% 6.48/6.81 (assert (forall ((X3 tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X5) X3)))))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X3) X5) (@ (@ tptp.ord_less_real X5) Y))))))
% 6.48/6.81 (assert (= tptp.one_one_rat (@ (@ tptp.fract tptp.one_one_int) tptp.one_one_int)))
% 6.48/6.81 (assert (= tptp.zero_zero_rat (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int)))
% 6.48/6.81 (assert (= tptp.numeral_numeral_rat (lambda ((K3 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K3)) tptp.one_one_int))))
% 6.48/6.81 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.numeral_numeral_int W)) tptp.one_one_int) (@ tptp.numeral_numeral_rat W))))
% 6.48/6.81 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_int A) B)))))
% 6.48/6.81 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int B) A)))))
% 6.48/6.81 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I3 tptp.int) (J3 tptp.int)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I3)) (@ tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int))))))))
% 6.48/6.81 (assert (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.48/6.81 (assert (forall ((N tptp.int) (M tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ (@ tptp.plus_plus_int M) N)) N) (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract M) N)) tptp.one_one_rat)))))
% 6.48/6.81 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 6.48/6.81 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A)))))
% 6.48/6.81 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int B) A)))))
% 6.48/6.81 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.48/6.81 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) tptp.one_one_int) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))))
% 6.48/6.81 (assert (forall ((K tptp.num)) (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) (lambda ((Q4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.numeral_numeral_int Q4)))))) (@ (@ tptp.bit_take_bit_num _let_1) N))))))
% 6.48/6.81 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.48/6.81 (assert (forall ((R2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ tptp.some_num tptp.one))) N))))
% 6.48/6.81 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.48/6.81 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N) M))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N) M)))))
% 6.48/6.81 (assert (forall ((R2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R2)) M))))))
% 6.48/6.81 (assert (forall ((R2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R2)) M)))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))))
% 6.48/6.81 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.48/6.81 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num tptp.one))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N)) tptp.none_num)))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N2) M)))) N))))
% 6.48/6.81 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) (@ tptp.some_num Q2)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int Q2)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit1 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N2) M))))) N))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) tptp.none_num) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N) M)))))
% 6.48/6.81 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.positive (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B)))))
% 6.48/6.81 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ tptp.positive X3) (=> (@ tptp.positive Y) (@ tptp.positive (@ (@ tptp.plus_plus_rat X3) Y))))))
% 6.48/6.81 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ tptp.positive X3) (=> (@ tptp.positive Y) (@ tptp.positive (@ (@ tptp.times_times_rat X3) Y))))))
% 6.48/6.81 (assert (= tptp.positive (lambda ((X2 tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X2))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.product_snd_int_int _let_1)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (let ((_let_2 (= X3 tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X3) Xa2) Y) (=> (=> _let_2 (=> (= Xa2 tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit0 N3))) (not (= Y (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit1 N3))) _let_1)) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num _let_1))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (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) N3)))))))) (not (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3))))))))))))))))))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.48/6.81 (assert (forall ((X3 tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X3 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (@ (@ tptp.bit_and_not_num X3) Xa2) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X3) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.some_num _let_1)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.some_num (@ tptp.bit0 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= 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) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))))
% 6.48/6.81 (assert (forall ((X3 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 (= X3 tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X3) Xa2) Y) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit0 N3))) _let_4)) (=> (=> _let_5 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit1 N3))) _let_1)) (=> (=> (exists ((M5 tptp.num)) (= X3 (@ tptp.bit0 M5))) (=> _let_2 _let_4)) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (=> (=> (exists ((M5 tptp.num)) (= X3 (@ tptp.bit1 M5))) _let_3) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (not (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (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) N3)))))))))))))))))))))))))
% 6.48/6.81 (assert (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.48/6.81 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num tptp.one))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N)) tptp.none_num)))
% 6.48/6.81 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.48/6.81 (assert (forall ((X3 tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X3 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X3) Xa2) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X3) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.some_num tptp.one)) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= 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) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X3 tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X3) Xa2) Y) (=> (=> _let_1 (=> (= Xa2 tptp.one) (not (= Y tptp.none_num)))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y (@ tptp.some_num (@ tptp.bit1 N3))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y (@ tptp.some_num (@ tptp.bit0 N3))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit1 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3))))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3))))))))) (not (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))))))))))))))))))))
% 6.48/6.81 (assert (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N)))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N)))))
% 6.48/6.81 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.48/6.81 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num (@ tptp.bit0 N)))))
% 6.48/6.81 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num (@ tptp.bit1 N)))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N))))))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N))))))
% 6.48/6.81 (assert (forall ((X3 tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X3 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X3) Xa2) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X3) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.some_num (@ tptp.bit1 N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.some_num (@ tptp.bit0 N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.some_num (@ tptp.bit1 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.some_num (@ tptp.bit0 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))))
% 6.48/6.81 (assert (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel))
% 6.48/6.81 (assert (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel))
% 6.48/6.81 (assert (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num))
% 6.48/6.81 (assert (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num))
% 6.48/6.81 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M6 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A3 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))) A3))) (@ (@ tptp.product_Pair_nat_num N2) M6)))))
% 6.48/6.81 (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))))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat M) N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.48/6.81 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.48/6.81 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat (@ tptp.pred_numeral K)) N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) (@ tptp.pred_numeral K))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L2 tptp.int) (R2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit M) (@ (@ (@ tptp.bit_concat_bit N) K) L2)) R2) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.minus_minus_nat M) N)) L2) R2)))))
% 6.48/6.81 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N) Q2)) (@ (@ tptp.ord_min_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M) N)) Q2) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N) Q2)))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (I2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M) I2)) (@ (@ tptp.minus_minus_nat N) I2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M) N)) I2))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ (@ (@ tptp.bit_concat_bit N) K) L2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N)) L2)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) M) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M3)))) M))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat M) (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M3) N)))) M))))
% 6.48/6.81 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q2) tptp.zero_z5237406670263579293d_enat)))
% 6.48/6.81 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q2) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.48/6.81 (assert (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))
% 6.48/6.81 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N))) (= (@ tptp.remdups_nat _let_1) _let_1))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (= (@ tptp.hd_nat (@ (@ tptp.upt I2) J2)) I2))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (I2 tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.drop_nat M) (@ (@ tptp.upt I2) J2)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) M)) J2))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I2) J2)) (@ (@ tptp.minus_minus_nat J2) I2))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) M))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ tptp.take_nat M) (@ _let_2 N)) (@ _let_2 _let_1)))))))
% 6.48/6.81 (assert (forall ((J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.upt I2) J2) tptp.nil_nat))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.upt M) N))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (= (@ (@ tptp.upt I2) J2) tptp.nil_nat) (or (= J2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J2) I2)))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (K tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J2) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I2) J2)) K) _let_1)))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat)) (= (@ (@ tptp.upt I2) tptp.zero_zero_nat) tptp.nil_nat)))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I2) J2))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N) Ns))) (= (= (@ (@ tptp.cons_nat M) _let_1) (@ (@ tptp.upt M) Q2)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M)) Q2))))))
% 6.48/6.81 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) (@ tptp.suc M6))))))
% 6.48/6.81 (assert (= tptp.set_ord_lessThan_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N2)))))
% 6.48/6.81 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) M6)))))
% 6.48/6.81 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N2) (@ tptp.suc M6))))))
% 6.48/6.81 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I3) J3)))))
% 6.48/6.81 (assert (= tptp.set_ord_atMost_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N2))))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (= (@ (@ tptp.upt I2) J2) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J2))))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J2) K))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J2)) (@ (@ tptp.upt J2) _let_1))))))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (X3 tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I2) J2) (@ (@ tptp.cons_nat X3) Xs)) (and (@ (@ tptp.ord_less_nat I2) J2) (= I2 X3) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) tptp.one_one_nat)) J2) Xs)))))
% 6.48/6.81 (assert (= tptp.upt (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I3) J3)) (@ (@ tptp.cons_nat I3) (@ (@ tptp.upt (@ tptp.suc I3)) J3))) tptp.nil_nat))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (let ((_let_2 (@ _let_1 (@ tptp.suc J2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I2) J2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J2)) (@ (@ tptp.cons_nat J2) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 6.48/6.81 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ _let_1 (@ tptp.suc J2)) (@ (@ tptp.append_nat (@ _let_1 J2)) (@ (@ tptp.cons_nat J2) tptp.nil_nat)))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N)))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat I3) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M) N)))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.upt M) N))))
% 6.48/6.81 (assert (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q4) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ tptp.groups4561878855575611511st_nat L) N5))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L) N5)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L)) tptp.one_one_nat) N5))))))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N5 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ tptp.groups4561878855575611511st_nat L) N5))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N5) M)) tptp.one_one_nat)) N5))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N))))
% 6.48/6.81 (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))))))
% 6.48/6.81 (assert (forall ((M tptp.int) (N tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M) N))))
% 6.48/6.81 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I2) J2))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) N))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (forall ((M tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J3)) M)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M)) (lambda ((R5 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) R5)))))))
% 6.48/6.81 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S3)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S3))))))
% 6.48/6.81 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N2)) M6))))))))
% 6.48/6.81 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.gcd_gcd_nat M) N) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_1 M) (@ _let_1 N))))))))))
% 6.48/6.81 (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))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (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)))))
% 6.48/6.81 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M6) N2))) M6)))))
% 6.48/6.81 (assert (forall ((X3 tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X3) Y) (=> (=> (= X3 tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X5 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X3 (@ (@ tptp.cons_nat X5) Xs3)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs3)))))))))))))
% 6.48/6.81 (assert (forall ((X3 tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X3) Xs)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs)))))))
% 6.48/6.81 (assert (forall ((X3 tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X3) Y) (=> (@ _let_1 X3) (=> (=> (= X3 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))) (=> (= X3 _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)))))))))))))
% 6.48/6.81 (assert (forall ((N5 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N5) (= (@ tptp.gcd_Gcd_nat N5) tptp.one_one_nat))))
% 6.48/6.81 (assert (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K5))))
% 6.48/6.81 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 6.48/6.81 (assert (= tptp.positive (@ (@ (@ tptp.map_fu898904425404107465nt_o_o tptp.rep_Rat) tptp.id_o) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2)))))))
% 6.48/6.81 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N))) (= (@ (@ tptp.linord738340561235409698at_nat (lambda ((X2 tptp.nat)) X2)) _let_1) _let_1))))
% 6.48/6.81 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J2))) (= (@ (@ tptp.linord1735203802627413978nt_int (lambda ((X2 tptp.int)) X2)) _let_1) _let_1))))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X4 tptp.real)) (@ P X4)))))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 (-> tptp.nat tptp.int tptp.int)) (Y (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 (-> tptp.nat tptp.int tptp.int)) (Y (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 (-> tptp.nat tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 (-> tptp.nat tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((X3 tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X3) Y) X3)))
% 6.48/6.81 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 6.48/6.81 (assert (forall ((X3 tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X3) Y) Y)))
% 6.48/6.81 (assert (forall ((X3 tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X3) Y) X3)))
% 6.48/6.81 (assert (not (and (not (= tptp.xa tptp.mi)) (not (= tptp.xa tptp.ma)))))
% 8.14/8.50 (set-info :filename cvc5---1.0.5_8919)
% 8.14/8.50 (check-sat-assuming ( true ))
% 8.14/8.50 ------- get file name : TPTP file name is ITP227^3
% 8.14/8.50 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_8919.smt2...
% 8.14/8.50 --- Run --ho-elim --full-saturate-quant at 10...
% 8.14/8.50 % SZS status Theorem for ITP227^3
% 8.14/8.50 % SZS output start Proof for ITP227^3
% 8.14/8.50 (
% 8.14/8.50 (let ((_let_1 (= tptp.xa tptp.ma))) (let ((_let_2 (= tptp.xa tptp.mi))) (let ((_let_3 (not (and (not _let_2) (not _let_1))))) (let ((_let_4 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_5 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_6 (@ tptp.bit0 tptp.one))) (let ((_let_7 (@ tptp.bit0 _let_6))) (let ((_let_8 (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_7))))))))) (let ((_let_9 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_10 (@ _let_9 _let_8))) (let ((_let_11 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_12 (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real _let_11) tptp.one_one_real)))) (let ((_let_13 (@ tptp.numeral_numeral_real _let_6))) (let ((_let_14 (@ tptp.divide_divide_real tptp.pi))) (let ((_let_15 (@ _let_14 _let_13))) (let ((_let_16 (@ tptp.filterlim_real_real tptp.arctan))) (let ((_let_17 (@ tptp.topolo2177554685111907308n_real _let_15))) (let ((_let_18 (@ tptp.filterlim_real_real tptp.tan_real))) (let ((_let_19 (@ tptp.topolo2177554685111907308n_real tptp.one_one_real))) (let ((_let_20 (@ tptp.filterlim_real_real tptp.artanh_real))) (let ((_let_21 (@ tptp.topolo2815343760600316023s_real tptp.one_one_real))) (let ((_let_22 (@ tptp.filterlim_real_real tptp.tanh_real))) (let ((_let_23 (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))) (let ((_let_24 (@ tptp.uminus_uminus_real _let_15))) (let ((_let_25 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (let ((_let_26 (@ tptp.numeral_numeral_nat _let_6))) (let ((_let_27 (@ tptp.insert_nat tptp.zero_zero_nat))) (let ((_let_28 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (let ((_let_29 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_30 (@ tptp.numera6620942414471956472nteger _let_6))) (let ((_let_31 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_32 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (let ((_let_33 (@ tptp.power_power_nat _let_26))) (let ((_let_34 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_35 (@ tptp.suc _let_34))) (let ((_let_36 (@ tptp.numeral_numeral_int _let_6))) (let ((_let_37 (@ tptp.nat2 tptp.one_one_int))) (let ((_let_38 (@ tptp.times_times_real _let_13))) (let ((_let_39 (@ tptp.sqrt _let_13))) (let ((_let_40 (@ tptp.plus_plus_complex tptp.one_one_complex))) (let ((_let_41 (@ tptp.real_V4546457046886955230omplex tptp.pi))) (let ((_let_42 (@ tptp.numera6690914467698888265omplex _let_6))) (let ((_let_43 (@ tptp.times_times_complex _let_41))) (let ((_let_44 (@ tptp.times_times_complex tptp.imaginary_unit))) (let ((_let_45 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_46 (@ _let_38 tptp.pi))) (let ((_let_47 (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit))) (let ((_let_48 (@ tptp.exp_real tptp.one_one_real))) (let ((_let_49 (@ tptp.bit1 tptp.one))) (let ((_let_50 (@ tptp.numeral_numeral_real _let_49))) (let ((_let_51 (@ tptp.sqrt _let_50))) (let ((_let_52 (@ tptp.divide_divide_real tptp.one_one_real))) (let ((_let_53 (@ _let_14 (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_49))))) (let ((_let_54 (@ (@ tptp.divide_divide_real _let_51) _let_13))) (let ((_let_55 (@ _let_14 _let_50))) (let ((_let_56 (@ (@ tptp.divide_divide_real _let_39) _let_13))) (let ((_let_57 (@ tptp.numeral_numeral_real _let_7))) (let ((_let_58 (@ _let_14 _let_57))) (let ((_let_59 (@ _let_52 _let_13))) (let ((_let_60 (@ tptp.numeral_numeral_rat tptp.one))) (let ((_let_61 (@ tptp.numera6690914467698888265omplex tptp.one))) (let ((_let_62 (@ tptp.numeral_numeral_real tptp.one))) (let ((_let_63 (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))) (let ((_let_64 (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))) (let ((_let_65 (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_66 (@ tptp.numeral_numeral_rat _let_6))) (let ((_let_67 (@ tptp.cos_real _let_13))) (let ((_let_68 (@ tptp.divide_divide_real _let_50))) (let ((_let_69 (@ (@ tptp.times_times_real (@ _let_68 _let_13)) tptp.pi))) (let ((_let_70 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_71 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_72 (@ tptp.bit1 _let_49))) (let ((_let_73 (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_6)))) (let ((_let_74 (@ tptp.power_power_complex tptp.zero_zero_complex))) (let ((_let_75 (@ tptp.power_power_int tptp.zero_zero_int))) (let ((_let_76 (@ tptp.power_power_real tptp.zero_zero_real))) (let ((_let_77 (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_78 (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))) (let ((_let_79 (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_80 (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))) (let ((_let_81 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_82 (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))) (let ((_let_83 (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))) (let ((_let_84 (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_85 (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))) (let ((_let_86 (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))) (let ((_let_87 (@ tptp.numeral_numeral_rat _let_49))) (let ((_let_88 (@ tptp.numera6690914467698888265omplex _let_49))) (let ((_let_89 (@ tptp.numeral_numeral_int _let_49))) (let ((_let_90 (@ tptp.numeral_numeral_int tptp.one))) (let ((_let_91 (@ tptp.ord_less_rat _let_4))) (let ((_let_92 (@ tptp.ord_le6747313008572928689nteger _let_81))) (let ((_let_93 (@ tptp.ord_less_real _let_11))) (let ((_let_94 (@ tptp.ord_less_int _let_5))) (let ((_let_95 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_96 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_97 (@ tptp.ord_less_eq_int _let_5))) (let ((_let_98 (@ tptp.ord_less_eq_rat _let_4))) (let ((_let_99 (@ tptp.ord_le3102999989581377725nteger _let_81))) (let ((_let_100 (@ tptp.ord_less_eq_real _let_11))) (let ((_let_101 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_102 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_103 (@ tptp.ord_less_rat tptp.one_one_rat))) (let ((_let_104 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_105 (@ tptp.ord_less_int tptp.one_one_int))) (let ((_let_106 (@ tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_107 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (let ((_let_108 (@ tptp.ord_less_eq_real tptp.one_one_real))) (let ((_let_109 (@ tptp.uminus_uminus_rat _let_66))) (let ((_let_110 (@ tptp.uminus1351360451143612070nteger _let_30))) (let ((_let_111 (@ tptp.uminus1482373934393186551omplex _let_42))) (let ((_let_112 (@ tptp.uminus_uminus_real _let_13))) (let ((_let_113 (@ tptp.uminus_uminus_int _let_36))) (let ((_let_114 (= (@ (@ tptp.modulo364778990260209775nteger _let_81) _let_30) tptp.one_one_Code_integer))) (let ((_let_115 (= (@ (@ tptp.modulo_modulo_int _let_5) _let_36) tptp.one_one_int))) (let ((_let_116 (@ tptp.minus_minus_rat _let_4))) (let ((_let_117 (@ tptp.minus_8373710615458151222nteger _let_81))) (let ((_let_118 (@ tptp.minus_minus_complex _let_45))) (let ((_let_119 (@ tptp.minus_minus_real _let_11))) (let ((_let_120 (@ tptp.minus_minus_int _let_5))) (let ((_let_121 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_122 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_123 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_124 (@ tptp.minus_minus_int tptp.one_one_int))) (let ((_let_125 (@ tptp.plus_plus_rat _let_4))) (let ((_let_126 (@ tptp.plus_p5714425477246183910nteger _let_81))) (let ((_let_127 (@ tptp.plus_plus_complex _let_45))) (let ((_let_128 (@ tptp.plus_plus_real _let_11))) (let ((_let_129 (@ tptp.plus_plus_int _let_5))) (let ((_let_130 (@ tptp.plus_plus_rat tptp.one_one_rat))) (let ((_let_131 (@ tptp.plus_plus_real tptp.one_one_real))) (let ((_let_132 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_133 (@ tptp.dvd_dvd_int _let_36))) (let ((_let_134 (@ tptp.dvd_dvd_nat _let_26))) (let ((_let_135 (@ tptp.dvd_dvd_Code_integer _let_30))) (let ((_let_136 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_137 (@ _let_101 tptp.zero_zero_int))) (let ((_let_138 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_139 (@ tptp.numeral_numeral_nat tptp.one))) (let ((_let_140 (@ _let_132 tptp.one_one_int))) (let ((_let_141 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_142 (@ _let_141 tptp.one_one_nat))) (let ((_let_143 (@ _let_130 tptp.one_one_rat))) (let ((_let_144 (@ _let_131 tptp.one_one_real))) (let ((_let_145 (@ _let_96 tptp.one_one_int))) (let ((_let_146 (@ _let_138 tptp.one_one_nat))) (let ((_let_147 (@ _let_95 tptp.one_one_rat))) (let ((_let_148 (@ _let_71 tptp.one_one_real))) (let ((_let_149 (@ tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_150 (@ _let_101 tptp.one_one_int))) (let ((_let_151 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_152 (@ _let_151 tptp.one_one_nat))) (let ((_let_153 (@ _let_102 tptp.one_one_rat))) (let ((_let_154 (@ _let_70 tptp.one_one_real))) (let ((_let_155 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (let ((_let_156 (= (@ (@ tptp.divide_divide_int tptp.one_one_int) _let_36) tptp.zero_zero_int))) (let ((_let_157 (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) _let_26) tptp.zero_zero_nat))) (let ((_let_158 (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) _let_30) tptp.one_one_Code_integer))) (let ((_let_159 (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) _let_36) tptp.one_one_int))) (let ((_let_160 (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) _let_26) tptp.one_one_nat))) (let ((_let_161 (= _let_142 _let_26))) (let ((_let_162 (= _let_139 tptp.one_one_nat))) (let ((_let_163 (= tptp.mi tptp.ma))) (let ((_let_164 (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList))) (let ((_let_165 (@ _let_33 tptp.deg))) (let ((_let_166 (not (or _let_2 _let_1)))) (let ((_let_167 (EQ_RESOLVE (ASSUME :args (_let_166)) (MACRO_SR_EQ_INTRO :args (_let_166 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (CONTRA (AND_INTRO (NOT_OR_ELIM _let_167 :args (0)) (NOT_OR_ELIM _let_167 :args (1))) (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)))) :args (_let_166 (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma) (=> _let_163 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1)))))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na)) _let_164) (@ (@ tptp.ord_less_nat tptp.xa) _let_165) (@ (@ tptp.ord_less_nat tptp.ma) _let_165) (@ (@ tptp.ord_less_nat tptp.mi) _let_165) (= _let_164 (@ _let_33 tptp.m)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X) tptp.na) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.ord_less_nat Xa) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert X) Xa)) Xa)))))) (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) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) _let_1)) (@ (@ tptp.power_power_nat N) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))) (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit0 N)))) (forall ((Ma tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N)) (@ _let_1 M))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num M) N))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num M) N))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num M) N))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num M) N))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_num M) N))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_num M) N))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_eq_num M) N))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_eq_num M) N))) (= tptp.vEBT_VEBT_high (lambda ((X2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_12)))) (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m) (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)) (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N)) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N)) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N)) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N)) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N)) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N)) (= M N))) (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)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))) (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.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W))) Z))) (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) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_eq_num M) N))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)) (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))) (= tptp.m (@ tptp.suc tptp.na)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert tptp.summary) X3)) X3))) (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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))) (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 ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) N) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))) (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B)) N) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))) (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) B)) N) (@ (@ tptp.divide_divide_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))) (forall ((X3 tptp.num)) (= (@ (@ tptp.ord_less_eq_num X3) tptp.one) (= X3 tptp.one))) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))) (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (forall ((Tree tptp.vEBT_VEBT) (X3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X3) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (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)))) (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 ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))) (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 ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A2))) A2)) (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 ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))) (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))) (=> (not _let_163) (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 ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low X) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X) (@ (@ tptp.ord_less_eq_nat X) tptp.ma)))))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X3))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X3))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X3) Y)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))) (forall ((X3 tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X3) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X3)) N) Y)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))) (forall ((X3 tptp.nat)) (=> (forall ((N3 tptp.nat)) (not (= X3 (@ (@ tptp.plus_plus_nat N3) N3)))) (not (forall ((N3 tptp.nat)) (not (= X3 (@ (@ tptp.plus_plus_nat N3) (@ tptp.suc N3)))))))) (forall ((T tptp.vEBT_VEBT) (X3 tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X3)))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X3) (@ (@ tptp.vEBT_vebt_member T) X3)))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X3) (@ (@ tptp.vEBT_vebt_member T) X3)))) (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ tptp.set_real2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) N))))) (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ tptp.set_complex2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) N))))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X5) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N))))) (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))) (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) N))))) (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) N))))) (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) N))))) (forall ((X3 tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X3) D)) (@ (@ tptp.vEBT_VEBT_low X3) D)) D) X3)) (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y2)) (= X22 Y2))) (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member T) X3) (@ (@ tptp.member_nat X3) (@ tptp.vEBT_set_vebt T))))) (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.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Z))) (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) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))) (forall ((X3 tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X3) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X3)) N) X3)))) (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 ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))) (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 ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N)))) (= 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))) (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.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))) (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.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.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))) (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 ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))) (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))) (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))) (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))) (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))) (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))) (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))) (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N))))) (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) _let_6) (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 ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))) (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 ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))) (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 ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))) (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 ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))) (forall ((B tptp.real) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X3) Y))))) (forall ((B tptp.rat) (X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X3) Y))))) (forall ((B tptp.nat) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X3) Y))))) (forall ((B tptp.int) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X3) Y))))) (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))) (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))) (forall ((A tptp.rat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))) (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))) (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))) (forall ((A tptp.complex) (M tptp.num) (N tptp.num) (B tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))) (forall ((A tptp.real) (M tptp.num) (N tptp.num) (B tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))) (forall ((A tptp.rat) (M tptp.num) (N tptp.num) (B tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))) (forall ((A tptp.nat) (M tptp.num) (N tptp.num) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))) (forall ((A tptp.int) (M tptp.num) (N tptp.num) (B tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))) (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))) (= (@ _let_40 tptp.one_one_complex) _let_42) (= _let_144 _let_13) (= _let_143 _let_66) _let_161 (= _let_140 _let_36) (forall ((B tptp.real) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X3) Y))))) (forall ((B tptp.rat) (X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X3) Y))))) (forall ((B tptp.nat) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X3) Y))))) (forall ((B tptp.int) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X3) Y))))) (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))) (= (@ tptp.suc tptp.one_one_nat) _let_26) (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))))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N) tptp.one))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N) tptp.one))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N) tptp.one))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N) tptp.one))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num tptp.one) N))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num tptp.one) N))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num tptp.one) N))) (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num tptp.one) N))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((P (-> tptp.extended_enat Bool)) (N tptp.extended_enat)) (=> (forall ((N3 tptp.extended_enat)) (=> (forall ((M2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N3) (@ P M2))) (@ P N3))) (@ P N))) (= tptp.suc _let_141) (= _let_141 tptp.suc) (= tptp.suc (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat M) N)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X3) (@ tptp.suc Y)) (= X3 Y))) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)) (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ _let_1 N)) A)))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) A)))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) A)))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) A)))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) A)))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ _let_1 N))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ _let_1 N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ _let_1 N))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ _let_1 N))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ _let_1 N))))) (forall ((X3 tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X3) Y) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.power_power_complex Y) N)) tptp.one_one_complex))) (forall ((X3 tptp.real) (Y tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X3) Y) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.power_power_real Y) N)) tptp.one_one_real))) (forall ((X3 tptp.rat) (Y tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X3) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X3) N)) (@ (@ tptp.power_power_rat Y) N)) tptp.one_one_rat))) (forall ((X3 tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X3) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X3) N)) (@ (@ tptp.power_power_nat Y) N)) tptp.one_one_nat))) (forall ((X3 tptp.int) (Y tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X3) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X3) N)) (@ (@ tptp.power_power_int Y) N)) tptp.one_one_int))) (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (=> (not (= K (@ tptp.suc I2))) (not (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (not (= K (@ tptp.suc J))))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))) (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K) (not (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (not (= K (@ tptp.suc J)))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (or (@ P N) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N) (@ P I3)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (and (@ P N) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ P I3)))))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M3 tptp.nat)) (and (= M (@ tptp.suc M3)) (@ (@ tptp.ord_less_nat N) M3))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (forall ((I4 tptp.nat)) (@ (@ P I4) (@ tptp.suc I4))) (=> (forall ((I4 tptp.nat) (J tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I4))) (=> (@ (@ tptp.ord_less_nat I4) J) (=> (@ (@ tptp.ord_less_nat J) K2) (=> (@ _let_1 J) (=> (@ (@ P J) K2) (@ _let_1 K2))))))) (@ (@ P I2) J2))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (forall ((I4 tptp.nat)) (=> (= J2 (@ tptp.suc I4)) (@ P I4))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ P (@ tptp.suc I4)) (@ P I4)))) (@ P I2))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))) (forall ((N tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M4) (exists ((M5 tptp.nat)) (= M4 (@ tptp.suc M5))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N3) (@ P M2))) (@ P N3))) (@ P N))) (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))) (forall ((M tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X5 tptp.nat)) (@ (@ R X5) X5)) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z2) (@ _let_1 Z2))))) (=> (forall ((N3 tptp.nat)) (@ (@ R N3) (@ tptp.suc N3))) (@ (@ R M) N)))))) (forall ((M tptp.nat)) (let ((_let_1 (@ 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tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) (@ tptp.suc N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc N)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real A) N)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat A) N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ 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tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))) (forall ((X3 tptp.complex) (Y tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X3) N))) (let ((_let_2 (@ tptp.times_times_complex Y))) (=> (= (@ (@ tptp.times_times_complex X3) Y) (@ _let_2 X3)) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ _let_2 _let_1)))))) (forall ((X3 tptp.real) (Y tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X3) N))) (let ((_let_2 (@ tptp.times_times_real Y))) (=> (= (@ (@ tptp.times_times_real X3) Y) (@ _let_2 X3)) (= (@ (@ tptp.times_times_real _let_1) Y) (@ _let_2 _let_1)))))) (forall ((X3 tptp.rat) (Y 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(let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_real (@ _let_1 M)) N)))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_int (@ _let_1 M)) N)))) (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_complex (@ _let_1 M)) N)))) (@ _let_108 tptp.one_one_real) (@ _let_107 tptp.one_one_rat) (@ _let_155 tptp.one_one_nat) (@ _let_106 tptp.one_one_int) (not (@ _let_104 tptp.one_one_real)) (not (@ _let_103 tptp.one_one_rat)) (not (@ _let_149 tptp.one_one_nat)) (not (@ _let_105 tptp.one_one_int)) (forall ((I2 tptp.nat) (U tptp.nat) (J2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) K)) (@ (@ 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tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_set_int (@ F N)) (@ F N4))))) (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N4))))) (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N4))))) (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N4))))) (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N4))))) (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_set_int (@ F N4)) (@ F N))))) (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_rat (@ F N4)) (@ F N))))) (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_num (@ F N4)) (@ F N))))) (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ F N))))) (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_int (@ F N4)) (@ F N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))) (forall ((I2 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ P I2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J2) (=> (@ P N3) (@ P (@ tptp.suc N3)))))) (@ P J2))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ P J2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J2) (=> (@ P (@ tptp.suc N3)) (@ P N3))))) (@ P I2))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))) (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) __flatten_var_0))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K2 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))) (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M6) K3)))))) (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I2)))) (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) M)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (forall ((Q3 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q3)))))))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N))) (forall ((M tptp.nat) (I2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I2) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) I2))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N))) M)) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N)) M)) (forall ((V tptp.num) (N tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N))) (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.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat 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 ((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.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat 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.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_1 N))))) (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_1 N))))) (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_1 N))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N))))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X3))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X3))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X3))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X3))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X3))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))) (= _let_61 tptp.one_one_complex) (= _let_62 tptp.one_one_real) (= _let_60 tptp.one_one_rat) _let_162 (= _let_90 tptp.one_one_int) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_complex A) N))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_real A) N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))) _let_162 (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))) (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N5)))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N5)))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N5)))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N5)))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N5)))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N5)))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N5)))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N5)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))) (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N3) (@ P M2))) (@ P N3))) (@ P N))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N3) (not (@ P M2)))))) (@ P N))) (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (not (= X3 Y)) (=> (not (@ (@ tptp.ord_less_nat X3) Y)) (@ (@ tptp.ord_less_nat Y) X3)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J2) (=> (@ (@ tptp.ord_less_eq_nat J2) K) (@ _let_1 K))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))) (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X5 tptp.nat)) (and (@ P X5) (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) X5)))))))) (forall ((X3 tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X3) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X3 Y)))) (forall ((X3 tptp.list_o) (Y tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X3) (@ tptp.size_size_list_o Y))) (not (= X3 Y)))) (forall ((X3 tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X3) (@ tptp.size_size_list_nat Y))) (not (= X3 Y)))) (forall ((X3 tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X3) (@ tptp.size_size_list_int Y))) (not (= X3 Y)))) (forall ((X3 tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X3) (@ tptp.size_size_num Y))) (not (= X3 Y)))) (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.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat 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))) (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.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat 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 ((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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) A)) B)))) (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 ((X3 tptp.complex)) (= (@ (@ tptp.power_power_complex X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X3) X3)) X3)) X3))) (forall ((X3 tptp.real)) (= (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X3) X3)) X3)) X3))) (forall ((X3 tptp.rat)) (= (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat X3) X3)) X3)) X3))) (forall ((X3 tptp.nat)) (= (@ (@ tptp.power_power_nat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X3) X3)) X3)) X3))) (forall ((X3 tptp.int)) (= (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X3) X3)) X3)) X3))) (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.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat 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) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1))))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1))))) (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) _let_26) tptp.one_one_rat) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) _let_26) tptp.one_one_nat) (= (@ (@ tptp.power_power_real tptp.one_one_real) _let_26) tptp.one_one_real) (= (@ (@ tptp.power_power_int tptp.one_one_int) _let_26) tptp.one_one_int) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) _let_26) tptp.one_one_complex) _let_161 (forall ((X3 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 X3) Y)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X3) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X3)) Y)))))) (forall ((X3 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 X3) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X3)) Y)))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X3) Y)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X3)) Y)))))) (forall ((X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X3) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X3) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X3)) Y))))) (forall ((X3 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 X3) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X3) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X3)) Y)))))) (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (not (= M6 N2))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))) (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N2) (= M6 N2)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat) (J2 tptp.nat)) (=> (forall ((I4 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J) (@ (@ tptp.ord_less_nat (@ F I4)) (@ F J)))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ F J2))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J2)) K) (@ (@ tptp.ord_less_nat I2) K))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat K) L2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2))))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J2)) I2))) (forall ((J2 tptp.nat) (I2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J2) I2)) I2))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) K)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) M))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J2))))) (forall ((K tptp.nat) (L2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L2) (=> (= (@ (@ tptp.plus_plus_nat M) L2) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))) (forall ((K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (exists ((N3 tptp.nat)) (= L2 (@ (@ tptp.plus_plus_nat K) N3))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) K)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) M))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J2))))) (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ (@ tptp.plus_plus_nat M6) K3))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N) K)))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)) (forall ((B tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))))))) (forall ((B tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B) (=> (@ _let_1 K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat)))))))))) (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N3) (@ (@ tptp.ord_less_nat (@ F M5)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))) (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))) (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))) (forall ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X3))) (forall ((X3 tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X3) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X3))) (= tptp.vEBT_V5917875025757280293ildren (lambda ((N2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X2) N2))) (@ (@ tptp.vEBT_VEBT_low X2) N2)))) (forall ((X3 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)) X3)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X3)) Y)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2)))))) (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X3) _let_3))) (@ (@ tptp.vEBT_VEBT_low X3) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X3)))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M) (@ tptp.suc (@ _let_1 N)))))) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)) (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 ((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 ((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.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat B) A)) C))) (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 ((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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))) (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)) (= (@ (@ 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.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) B))) (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)) (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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C)))) (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.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) 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)) (= (@ (@ 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.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) 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 ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) N) (= Deg N))) (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N))) TreeList3) S2))))) (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.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat 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.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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat 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.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))) (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.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))) (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 ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N))))) (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)) (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))) (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))) (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.power_power_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))) (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.power_power_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))) (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))) (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.power_power_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))) (forall ((X3 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 X3) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X3)) _let_2))))) (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 ((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 ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (not (= X3 Y)) (=> (not (@ (@ tptp.ord_less_real X3) Y)) (@ (@ tptp.ord_less_real Y) X3)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (not (= X3 Y)) (=> (not (@ (@ tptp.ord_less_rat X3) Y)) (@ (@ tptp.ord_less_rat Y) X3)))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (not (= X3 Y)) (=> (not (@ (@ tptp.ord_less_int X3) Y)) (@ (@ tptp.ord_less_int Y) X3)))) (forall ((X tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X) X_12))) (forall ((X tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_12))) (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X))) (forall ((X tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X))) (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.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (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_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real B2) A3))) (= tptp.times_times_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat B2) A3))) (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.times_times_nat B2) A3))) (= tptp.times_times_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.times_times_int B2) A3))) (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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))) (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 ((X3 tptp.complex)) (= (= tptp.one_one_complex X3) (= X3 tptp.one_one_complex))) (forall ((X3 tptp.real)) (= (= tptp.one_one_real X3) (= X3 tptp.one_one_real))) (forall ((X3 tptp.rat)) (= (= tptp.one_one_rat X3) (= X3 tptp.one_one_rat))) (forall ((X3 tptp.nat)) (= (= tptp.one_one_nat X3) (= X3 tptp.one_one_nat))) (forall ((X3 tptp.int)) (= (= tptp.one_one_int X3) (= X3 tptp.one_one_int))) (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.rat) (A tptp.rat) (C tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat 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.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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat 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.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.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B))) (let ((_let_2 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (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_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real B2) A3))) (= tptp.plus_plus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat B2) A3))) (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.plus_plus_nat B2) A3))) (= tptp.plus_plus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int B2) A3))) (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.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat 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.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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat 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) (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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))) (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 ((B3 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))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))) (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))) (forall ((B3 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))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))) (forall ((B3 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))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 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.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))) (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) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J2) (= K L2)) (= (@ (@ tptp.plus_plus_real I2) K) (@ (@ tptp.plus_plus_real J2) L2)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I2 J2) (= K L2)) (= (@ (@ tptp.plus_plus_rat I2) K) (@ (@ tptp.plus_plus_rat J2) L2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J2) (= K L2)) (= (@ (@ tptp.plus_plus_nat I2) K) (@ (@ tptp.plus_plus_nat J2) L2)))) (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J2) (= K L2)) (= (@ (@ tptp.plus_plus_int I2) K) (@ (@ tptp.plus_plus_int J2) L2)))) (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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))) (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 ((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.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))) (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 ((A3 tptp.nat) (B2 tptp.nat)) (exists ((C2 tptp.nat)) (= B2 (@ (@ tptp.plus_plus_nat A3) 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.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))) (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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))) (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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))) (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) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J2) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))) (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))) (forall ((I2 tptp.real) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))) (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))) (forall ((I2 tptp.real) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J2) (= K L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (= K L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (= K L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))) (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (= K L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) 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.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))) (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.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))) (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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))) (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.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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))) (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) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J2) (= K L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (= K L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (= K L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))) (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (= K L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))) (forall ((I2 tptp.real) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))) (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))) (forall ((I2 tptp.real) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J2) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))) (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))) (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.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) 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)) (= (@ (@ 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.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) 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.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.rat) (E tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E)) C))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))) (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.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)) (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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat C) B))))) (forall ((X3 tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X3) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X3) W)) (@ (@ tptp.times_times_complex Y) Z)))) (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X3) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X3) W)) (@ (@ tptp.times_times_real Y) Z)))) (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X3) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X3) W)) (@ (@ tptp.times_times_rat Y) Z)))) (forall ((X3 tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X3) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X3) Z)) (@ (@ tptp.times_times_complex Y) W)))) (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X3) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X3) Z)) (@ (@ tptp.times_times_real Y) W)))) (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X3) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X3) Z)) (@ (@ tptp.times_times_rat Y) W)))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)))) (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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))) (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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))) (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) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J2) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))) (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))) (forall ((I2 tptp.real) (J2 tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J2) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J2) L2)))) (forall ((I2 tptp.rat) (J2 tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J2) L2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J2) L2)))) (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J2) L2)))) (forall ((M tptp.real) (N tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_real M) N)))))) (forall ((M tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_rat M) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))) (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_int M) N)))))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (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.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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B) tptp.one_one_rat)))) (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) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B))) (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 ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))))) (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I3)))))) (forall ((Xs tptp.list_o) (P (-> Bool Bool))) (= (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I3)))))) (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I3)))))) (forall ((Xs tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I3)))))) (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (X3 tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) I4)))) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs)) (@ P X3)))) (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (X3 tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) I4)))) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs)) (@ P X3)))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (X3 tptp.product_prod_nat_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I4)))) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X3)))) (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X3 tptp.vEBT_VEBT)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I4)))) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X3)))) (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (X3 Bool)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I4)))) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs)) (@ P X3)))) (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (X3 tptp.nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I4)))) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (@ P X3)))) (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (X3 tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I4)))) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs)) (@ P X3)))) (forall ((X3 tptp.real) (Xs tptp.list_real)) (= (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_real Xs) I3) X3))))) (forall ((X3 tptp.complex) (Xs tptp.list_complex)) (= (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs)) (= (@ (@ tptp.nth_complex Xs) I3) X3))))) (forall ((X3 tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s5460976970255530739at_nat Xs)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I3) X3))))) (forall ((X3 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I3) X3))))) (forall ((X3 Bool) (Xs tptp.list_o)) (= (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I3) X3))))) (forall ((X3 tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I3) X3))))) (forall ((X3 tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I3) X3))))) (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_o Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_nat Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_int Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs) N)) (@ tptp.set_real2 Xs)))) (forall ((N tptp.nat) (Xs tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs) N)) (@ tptp.set_complex2 Xs)))) (forall ((N tptp.nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N)) (@ tptp.set_Pr5648618587558075414at_nat Xs)))) (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) N)) (@ tptp.set_VEBT_VEBT2 Xs)))) (forall ((N tptp.nat) (Xs tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs) N)) (@ tptp.set_o2 Xs)))) (forall ((N tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N)) (@ tptp.set_nat2 Xs)))) (forall ((N tptp.nat) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs) N)) (@ tptp.set_int2 Xs)))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) __flatten_var_0))) (= tptp.ord_less_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A3) tptp.one_one_int)) __flatten_var_0))) (= tptp.vEBT_VEBT_low (lambda ((X2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (= (lambda ((Y5 tptp.list_VEBT_VEBT) (Z3 tptp.list_VEBT_VEBT)) (= Y5 Z3)) (lambda ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I3) (@ (@ tptp.nth_VEBT_VEBT Ys) I3))))))) (= (lambda ((Y5 tptp.list_o) (Z3 tptp.list_o)) (= Y5 Z3)) (lambda ((Xs2 tptp.list_o) (Ys tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I3) (@ (@ tptp.nth_o Ys) I3))))))) (= (lambda ((Y5 tptp.list_nat) (Z3 tptp.list_nat)) (= Y5 Z3)) (lambda ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I3) (@ (@ tptp.nth_nat Ys) I3))))))) (= (lambda ((Y5 tptp.list_int) (Z3 tptp.list_int)) (= Y5 Z3)) (lambda ((Xs2 tptp.list_int) (Ys tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I3) (@ (@ tptp.nth_int Ys) I3))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X4 tptp.vEBT_VEBT)) (@ (@ P I3) X4)))) (exists ((Xs2 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_VEBT_VEBT Xs2) I3)))))))) (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X4 Bool)) (@ (@ P I3) X4)))) (exists ((Xs2 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs2) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_o Xs2) I3)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X4 tptp.nat)) (@ (@ P I3) X4)))) (exists ((Xs2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_nat Xs2) I3)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X4 tptp.int)) (@ (@ P I3) X4)))) (exists ((Xs2 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs2) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_int Xs2) I3)))))))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I4) (@ (@ tptp.nth_VEBT_VEBT Ys2) I4)))) (= Xs Ys2)))) (forall ((Xs tptp.list_o) (Ys2 tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I4) (@ (@ tptp.nth_o Ys2) I4)))) (= Xs Ys2)))) (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I4) (@ (@ tptp.nth_nat Ys2) I4)))) (= Xs Ys2)))) (forall ((Xs tptp.list_int) (Ys2 tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I4) (@ (@ tptp.nth_int Ys2) I4)))) (= Xs Ys2)))) (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 ((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.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) B))) (= (@ (@ tptp.modulo364778990260209775nteger _let_1) B) _let_1))) (forall ((R2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 R2)) (@ (@ tptp.divide_divide_real A) R2)))) (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 ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))) (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 ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))) (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 ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))) (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 ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))) (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.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))) (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 ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) K)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))) (forall ((K tptp.nat) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N) K)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))) _let_160 _let_159 _let_158 _let_160 _let_159 _let_158 (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) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) _let_1) tptp.one_one_nat)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.power_power_real X3) N3))))) (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y6) (= X2 Y6)))) (forall ((S3 tptp.set_real)) (=> (exists ((X tptp.real)) (@ (@ tptp.member_real X) S3)) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S3) (@ (@ tptp.ord_less_eq_real X5) Z4)))) (exists ((Y3 tptp.real)) (and (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) S3) (@ (@ tptp.ord_less_eq_real X) Y3))) (forall ((Z4 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S3) (@ (@ tptp.ord_less_eq_real X5) Z4))) (@ (@ tptp.ord_less_eq_real Y3) Z4)))))))) (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.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))) (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A4) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B4) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A4) B4)) C))))) (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A4) B4)) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A4) B4)) C))))) (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.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) C))) (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 ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 A)) (@ _let_1 B))))) (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 ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))) (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.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))) (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.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))) (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A4) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B4) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A4) B4)) C))))) (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A4) B4)) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A4) B4)) 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.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))) (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.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B)) N)) B) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N)) B))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B)) N)) B) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N)) B))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) N)) B) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) B))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) N))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat tptp.one))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int tptp.one))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger tptp.one))) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))) (forall ((X3 tptp.nat) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X3) N) (@ (@ tptp.modulo_modulo_nat Y) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (= (@ (@ tptp.plus_plus_nat X3) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))) (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 ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1))))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_1))))) (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) (C tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (not (forall ((D3 tptp.code_integer)) (not (= B (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) D3)))))))) (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 ((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 ((P (-> tptp.nat Bool)) (N tptp.nat) (P2 tptp.nat) (M tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P2) (=> (@ (@ tptp.ord_less_nat M) P2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) P2) (=> (@ P N3) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N3)) P2))))) (@ P M)))))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)) (forall ((X3 tptp.nat) (N tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X3) N) (@ (@ tptp.modulo_modulo_nat Y) N)) (=> (@ (@ tptp.ord_less_eq_nat Y) X3) (exists ((Q3 tptp.nat)) (= X3 (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N) Q3))))))) (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (forall ((S2 tptp.nat)) (not (= N (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q2) S2))))))))) (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (forall ((S2 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat Q2) S2))))))))) (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) (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 ((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 ((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 ((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 ((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)) (= 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)) (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)))) (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)) (= (@ (@ 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.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.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 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 B) (@ (@ tptp.divide6298287555418463151nteger 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 ((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 ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N))) (= (@ _let_1 (@ _let_2 Q2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N)) Q2))) (@ _let_1 N)))))) (forall ((P (-> tptp.nat Bool)) (X3 tptp.nat) (M7 tptp.nat)) (=> (@ P X3) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M7))) (not (forall ((M5 tptp.nat)) (=> (@ P M5) (not (forall ((X tptp.nat)) (=> (@ P X) (@ (@ tptp.ord_less_eq_nat X) M5)))))))))) (forall ((Xs tptp.list_real) (B3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) B3) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 (@ tptp.set_real2 Xs)) (@ _let_1 B3)))))) (forall ((Xs tptp.list_complex) (B3 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) B3) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 (@ tptp.set_complex2 Xs)) (@ _let_1 B3)))))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) B3) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ _let_1 B3)))))) (forall ((Xs tptp.list_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) B3) (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs)) (@ _let_1 B3)))))) (forall ((Xs tptp.list_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) B3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 (@ tptp.set_nat2 Xs)) (@ _let_1 B3)))))) (forall ((Xs tptp.list_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) B3) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B3)))))) (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N))) (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N))) (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))) (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_int)) (= (@ tptp.size_size_list_int Xs3) N))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys2))) (not (= Xs Ys2)))) (forall ((Xs tptp.list_o) (Ys2 tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys2))) (not (= Xs Ys2)))) (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys2))) (not (= Xs Ys2)))) (forall ((Xs tptp.list_int) (Ys2 tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys2))) (not (= Xs Ys2)))) (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))) (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))) (forall ((A tptp.code_integer) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))) (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (=> (forall ((Xs3 tptp.list_VEBT_VEBT)) (=> (forall ((Ys3 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))) (forall ((P (-> tptp.list_o Bool)) (Xs tptp.list_o)) (=> (forall ((Xs3 tptp.list_o)) (=> (forall ((Ys3 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys3)) (@ tptp.size_size_list_o Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))) (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys3 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys3)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))) (forall ((P (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (forall ((Xs3 tptp.list_int)) (=> (forall ((Ys3 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys3)) (@ tptp.size_size_list_int Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))) (forall ((A2 tptp.nat) (N tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) N)) N)) (@ (@ tptp.modulo_modulo_nat A2) N)))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))) (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) _let_42) (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) _let_13) (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) _let_66) (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) _let_36) (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 ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))) (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_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_rat (@ (@ 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 ((U tptp.real) (X3 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 X3) Y)) (=> (@ _let_2 X3) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) Y)) (@ tptp.numeral_numeral_real _let_1))))))))) (forall ((U tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_rat X3) Y)) (=> (@ _let_2 X3) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X3) Y)) (@ tptp.numeral_numeral_rat _let_1))))))))) (forall ((X3 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X3) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low X3) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X3))))))) (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) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((X22 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y2)) (= X22 Y2))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N) K)) (or (= M N) (= K tptp.zero_zero_nat)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))) (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (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 ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg) (=> (= Mi Ma) (and (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1))))) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N 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.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))) (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.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.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (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.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.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (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.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.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)) (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.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X3) Y)) (and (= X3 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X3) Y) tptp.zero_zero_nat) (and (= X3 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.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))) (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.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))) (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 tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))) (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))) (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))) (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))) (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))) (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))) (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.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) 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 ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (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 ((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.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))) (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 ((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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (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.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex 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.divide_divide_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)) (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.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.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.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 ((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.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)) (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.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.zero_z3403309356797280102nteger) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) A) tptp.zero_z3403309356797280102nteger)) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (@ _let_1 M) (@ _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N)) (and (= M _let_1) (= N _let_1))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N) _let_1) (and (= M _let_1) (= N _let_1))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N)))) (forall ((X3 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (or (= X3 Mi) (= X3 Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X3) _let_1))))) (forall ((X3 tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X3) X3))) (= X3 tptp.zero_zero_real))) (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))) (forall ((X3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X3) M) _let_1) (or (= M tptp.zero_zero_nat) (= X3 _let_1))))) (forall ((X3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X3) N)) (or (@ _let_1 X3) (= N tptp.zero_zero_nat))))) (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (= K tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat M) N)))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)) (= (@ 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_rat tptp.zero_zero_rat) tptp.zero_zero_rat) (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (and (@ (@ tptp.ord_less_eq_nat Mi) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))) (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))) (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (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) (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))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (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))) (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))) (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))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))) (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))) (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))) (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.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))) (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)) (= (@ (@ 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.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (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)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))) (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)))) (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))) (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))) (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))) (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))) (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))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))) (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))) (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))) (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))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))) (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))) (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))) (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))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))) (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))) (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))) (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.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))) (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)) (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.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat 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.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.rat) (C tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))) (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.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))) (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.rat) (A tptp.rat)) (= (= (@ (@ tptp.times_times_rat C) A) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))) (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.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))) (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 ((X3 tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) X3)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X3 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X3) X3)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X3 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))) (forall ((X3 tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X3) X3)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X3 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (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 ((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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat A) B)))))))) (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))) (=> (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_rat A) B))))) (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))) (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))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) A) B))) (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))) (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))) (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)) (=> (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.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C) A)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))) (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 A) C)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex 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.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) B) A))) (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.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) B) A))) (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 C) B)) (@ (@ tptp.divide_divide_real A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat C) B)) (@ (@ tptp.divide_divide_rat A) B)))) (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.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.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 ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (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.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (and (not (= B tptp.zero_zero_rat)) (= A B)))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) 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.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))) (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))) (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))) (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.one_one_real (@ (@ tptp.divide_divide_real A) B)) (and (not (= B tptp.zero_zero_real)) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat A) B)) (and (not (= B tptp.zero_zero_rat)) (= A B)))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) 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.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))) (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)) (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.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat A) A))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))) (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 ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat B) A) tptp.one_one_rat) (and (not (= A tptp.zero_zero_rat)) (= A B)))) (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.rat) (A tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat B) A)) (and (not (= A tptp.zero_zero_rat)) (= A B)))) (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (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.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)) (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)) (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.rat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (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.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)) (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 ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)) (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)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)) (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)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) 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 ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)) (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 ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N)) N) M))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) M)) N) M))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) 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 ((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_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ 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 ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X3) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X3) _let_1))) (@ (@ tptp.vEBT_VEBT_low X3) _let_1)) (= X3 Mi) (= X3 Ma)))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X3 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 X3) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X3) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X3 Mi) (= X3 Ma) (and (@ (@ tptp.ord_less_nat X3) Ma) (@ (@ tptp.ord_less_nat Mi) X3) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X3) _let_2)))))))))) (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.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (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.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))) (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 ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))) (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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ _let_1 B))))) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_rat B) A)))) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat B) A)))) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat A) B)))) (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.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))) (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 ((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.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))) (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 ((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.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))) (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.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.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) B)))) (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 ((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.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat B) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))) (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.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.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.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 ((A tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (@ (@ tptp.ord_less_eq_real A) B))))))) (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (@ (@ tptp.ord_less_eq_rat A) B))))))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.ord_less_eq_nat A) B))))))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.ord_less_eq_int A) B))))))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (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))) (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 ((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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat A) B)))) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat B) A)))) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat B) A)))) (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 ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat A) B)))) (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))) (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))) (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))) (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))) (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (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 ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))) (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)) _let_157 _let_156 _let_157 _let_156 (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))) (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))) (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))) (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))) (forall ((X3 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 X3) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X3) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X3 Y))))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_2 X3) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_rat X3) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (= X3 Y))))))) (forall ((X3 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 X3) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X3) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X3 Y))))))) (forall ((X3 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 X3) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X3) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X3 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.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (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.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_rat)))) (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 ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) tptp.zero_zero_rat) (and (= X3 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X3 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X3 tptp.zero_zero_int) (= Y 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.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.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_integer)) (= _let_1 tptp.zero_z3403309356797280102nteger)))) (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 ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_1 tptp.one_one_Code_integer)))) (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 ((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.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 ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I3 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ P I3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I3 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ P I3))))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.divide_divide_int A) B) Q2))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.divide_divide_int A) B) Q2))))) (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I3 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ (@ P I3) J3)))))) (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I3 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ (@ P I3) J3)))))) (forall ((X3 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X3) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X3) K)) X3)))) (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B3) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B3) N))))) (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 ((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 ((A2 tptp.int) (N tptp.int)) (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) N)) N)) (@ (@ tptp.modulo_modulo_int A2) N)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 B)))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (@ _let_1 A))))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((K tptp.int) (I2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K) (= (@ _let_1 (@ (@ tptp.divide_divide_int I2) K)) (@ (@ tptp.ord_less_eq_int K) I2))))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))) (forall ((L2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L2) K) (=> (@ _let_1 L2) (@ _let_1 (@ (@ tptp.divide_divide_int K) L2)))))) (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) L2)) (or (= K tptp.zero_zero_int) (= L2 tptp.zero_zero_int) (and (@ _let_1 K) (@ _let_1 L2)) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))) (forall ((A tptp.int) (B4 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B4)) (@ _let_1 B))))))) (forall ((A tptp.int) (A4 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A4) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A4) B)) (@ (@ tptp.divide_divide_int A) B))))) (forall ((I2 tptp.int) (K tptp.int)) (= (= (@ (@ tptp.divide_divide_int I2) K) tptp.zero_zero_int) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I2))))) (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (=> (= (@ (@ tptp.modulo_modulo_int A2) N) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B3) N) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ tptp.divide_divide_int B3) N))))))) (forall ((A tptp.int) (B4 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B4))))))) (forall ((A tptp.int) (A4 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A4) B))))) (forall ((X3 tptp.complex)) (= (= tptp.zero_zero_complex X3) (= X3 tptp.zero_zero_complex))) (forall ((X3 tptp.real)) (= (= tptp.zero_zero_real X3) (= X3 tptp.zero_zero_real))) (forall ((X3 tptp.rat)) (= (= tptp.zero_zero_rat X3) (= X3 tptp.zero_zero_rat))) (forall ((X3 tptp.nat)) (= (= tptp.zero_zero_nat X3) (= X3 tptp.zero_zero_nat))) (forall ((X3 tptp.int)) (= (= tptp.zero_zero_int X3) (= X3 tptp.zero_zero_int))) (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.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) 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 ((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 ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) N) tptp.zero_zero_real))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) N) tptp.zero_zero_int))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N) tptp.zero_zero_complex))) (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) N) A)))))) (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (= (@ (@ tptp.power_power_real X5) N) A) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.power_power_real Y4) N) A)) (= Y4 X5)))))))) (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X3)) (@ _let_70 tptp.zero_zero_real) (@ _let_102 tptp.zero_zero_rat) (@ _let_151 tptp.zero_zero_nat) _let_137 (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (not (@ _let_71 tptp.zero_zero_real)) (not (@ _let_95 tptp.zero_zero_rat)) (not (@ _let_138 tptp.zero_zero_nat)) (not (@ _let_96 tptp.zero_zero_int)) (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)))))))) (forall ((D1 tptp.rat) (D22 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat E2))) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ _let_1 D1) (@ _let_1 D22)))))))) (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))) (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)))) (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)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (= A B)))) (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)))) (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)))) (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))))) (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))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))) (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))))) (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))))) (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.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat))))) (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.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.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (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.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))))) (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))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B tptp.zero_zero_rat))))) (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))))) (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))))) (not (= tptp.zero_zero_complex tptp.one_one_complex)) (not (= tptp.zero_zero_real tptp.one_one_real)) (not (= tptp.zero_zero_rat tptp.one_one_rat)) (not (= tptp.zero_zero_nat tptp.one_one_nat)) (not (= tptp.zero_zero_int tptp.one_one_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)) (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.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) 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 ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((A tptp.rat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat)))) (forall ((A tptp.real) (N tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real)))) (forall ((A tptp.int) (N tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int)))) (forall ((A tptp.complex) (N tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex)))) (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))) (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 ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P tptp.zero_zero_nat)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X5 tptp.nat)) (@ (@ P X5) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X5) Y3) (@ (@ P (@ tptp.suc X5)) (@ tptp.suc Y3)))) (@ (@ P M) N))))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc N3)))) (@ P N)))) (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))) (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))) (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))) (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))) (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (not (@ P N3)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N3) (not (@ P M2))))))) (@ P N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (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 ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))) (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M) N)) (and (@ _let_1 M) (@ _let_1 N))))) (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))) (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))) (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)) (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))) (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))) (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))) (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))) (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (= A B))))))) (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (= A B))))))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (= A B))))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (= A B))))))) (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))) (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))) (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))) (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))) (= tptp.neg_numeral_dbl_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) X2))) (= tptp.neg_numeral_dbl_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat X2) X2))) (= tptp.neg_numeral_dbl_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) X2))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))) (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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))) (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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))) (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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))) (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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))) (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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))) (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.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))) (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.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))) (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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A) B))))) (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.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) 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_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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))) (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.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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))) (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 ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))) (not (@ _let_108 tptp.zero_zero_real)) (not (@ _let_107 tptp.zero_zero_rat)) (not (@ _let_155 tptp.zero_zero_nat)) (not (@ _let_106 tptp.zero_zero_int)) _let_154 _let_153 _let_152 _let_150 _let_154 _let_153 _let_152 _let_150 (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.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))) (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)))) (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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))) (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 ((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.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))) (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 ((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.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))) (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 ((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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))) (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 ((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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))) (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 ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X3) Y) tptp.zero_zero_real) (and (= X3 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X3) Y) tptp.zero_zero_rat) (and (= X3 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))) (forall ((X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X3) Y) tptp.zero_zero_nat) (and (= X3 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))) (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X3) Y) tptp.zero_zero_int) (and (= X3 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X3) Y) tptp.zero_zero_real) (and (= X3 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X3) Y) tptp.zero_zero_rat) (and (= X3 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))) (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X3) Y) tptp.zero_zero_nat) (and (= X3 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X3) Y) tptp.zero_zero_int) (and (= X3 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))) (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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))) (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.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))) (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.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))) (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.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))) (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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))) (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.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B))))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat B) A))))) (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.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))) (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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))) (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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))) (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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))) (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) (=> (@ (@ 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tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))) (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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))) (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.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))) (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))))) (not (@ _let_104 tptp.zero_zero_real)) (not (@ _let_103 tptp.zero_zero_rat)) (not (@ _let_149 tptp.zero_zero_nat)) (not (@ _let_105 tptp.zero_zero_int)) _let_148 _let_147 _let_146 _let_145 _let_148 _let_147 _let_146 _let_145 (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X3) Y)) tptp.zero_zero_real) (or (@ (@ 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(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 ((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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))) (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 (@ 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(@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) 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)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))) (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)) (@ (@ 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Y) (@ _let_1 (@ (@ tptp.divide_divide_real X3) Y)))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X3) Y)))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X3) Y)) tptp.zero_zero_real)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X3) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X3) Y)) tptp.zero_zero_rat)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X3) Y)) tptp.zero_zero_real)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X3) Y)) tptp.zero_zero_rat)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) 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 X3) Y))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X3) Y))))) (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 ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat A) C))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) 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 X3) Y))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X3) Y))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X3) Y)) tptp.zero_zero_real)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X3) Y)) tptp.zero_zero_rat)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X3) Y)) tptp.zero_zero_real)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X3) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X3) Y)) tptp.zero_zero_rat)))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X3) Y)))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X3) Y)))))) (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 ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))) (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.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)) (not (= C tptp.zero_zero_rat))))) (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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))) (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.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))) (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 ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))) (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))) (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))) (forall ((Y tptp.complex) (Z tptp.complex) (X3 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X3) Y) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X3) Z) (@ (@ tptp.times_times_complex W) Y)))))) (forall ((Y tptp.real) (Z tptp.real) (X3 tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X3) Y) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X3) Z) (@ (@ tptp.times_times_real W) Y)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X3) Y) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X3) Z) (@ (@ tptp.times_times_rat W) Y)))))) (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 ((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.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (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 ((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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))) (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 ((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.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B (@ (@ tptp.times_times_rat A) C)) (= (@ (@ tptp.divide_divide_rat B) C) A)))) (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) (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.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A) C) B) (= A (@ (@ tptp.divide_divide_rat B) C))))) (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) (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.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (= B (@ (@ tptp.times_times_rat A) C))))) (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) (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.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (= (@ (@ tptp.times_times_rat A) C) B)))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))) (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.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (= A B)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_int))) (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))))) (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.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) A))) (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 ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B))) (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)) (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 ((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 ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (and (@ P tptp.zero_zero_nat) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ P (@ tptp.suc I3))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M6 tptp.nat)) (= N (@ tptp.suc M6))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (or (@ P tptp.zero_zero_nat) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N) (@ P (@ tptp.suc I3))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (not (@ P I)))) (@ P K2)))))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I2) K2) J2))))) (forall ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B3) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ tptp.divide_divide_nat B3) N))))))) (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) (@ tptp.suc N)) A))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J2)))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J2) K))))) (= tptp.one_one_nat _let_34) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N) (= N tptp.zero_zero_nat)))) (forall ((Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X3) N3)) Y))))) (forall ((I2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))) (let ((_let_3 (= _let_1 N))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))) (forall ((X3 tptp.num)) (= (@ (@ tptp.pow X3) tptp.one) X3)) (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))))) (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X3) _let_1))) (forall ((A tptp.rat) (B tptp.rat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat B) A)))) (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_int)) (@ (@ tptp.ord_less_eq_set_int A) A)) (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat 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.real)) (not (@ (@ tptp.ord_less_real A) A))) (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat 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.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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))) (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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))) (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.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B))))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B))))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat B) A))))) (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.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))) (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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))) (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.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))) (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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B))))) (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.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))) (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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))) (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.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.plus_plus_rat A) C))))) (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.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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))) (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.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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))) (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.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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))) (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.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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))) (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 ((X3 tptp.real) (Y tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.plus_plus_real Y) E2)))) (@ (@ tptp.ord_less_eq_real X3) Y))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat X3) (@ (@ tptp.plus_plus_rat Y) E2)))) (@ (@ tptp.ord_less_eq_rat X3) Y))) (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.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) A)))) (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) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.one_one_rat))))) (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 ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X3) Y)) X3)))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X3) Y)) X3)))))) (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X3) Y)) X3)))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X3)) X3)))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X3)) X3)))))) (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X3)) X3)))))) (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) X3)) (@ (@ tptp.times_times_real Y) Y)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X3) X3)) (@ (@ tptp.times_times_rat Y) Y)))) (forall ((X3 tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X3) X3)) (@ (@ tptp.times_times_int Y) Y)))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) X3)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X3 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X3) X3)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X3 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))) (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X3) X3)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X3 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X3) Y)) tptp.zero_zero_real)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X3) Y)) tptp.zero_zero_rat)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) 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 X3) Y))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X3) Y))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X3) Y)))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X3) Y)))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X3) Y)) tptp.zero_zero_real)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X3) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X3) Y)) tptp.zero_zero_rat)))) (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 ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))) (forall ((X3 tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X3) Z)) (@ (@ tptp.divide_divide_real Y) W)))))))) (forall ((X3 tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X3) Z)) (@ (@ tptp.divide_divide_rat Y) W)))))))) (forall ((X3 tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) 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 X3) Z)) (@ (@ tptp.divide_divide_real Y) W))))))) (forall ((X3 tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X3) (=> (@ (@ tptp.ord_less_rat X3) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X3) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))) (forall ((Y tptp.real) (X3 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X3) 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 X3) Z)) (@ (@ tptp.divide_divide_real Y) W))))))) (forall ((Y tptp.rat) (X3 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X3) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))) (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.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 ((X3 tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) X3)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))) (forall ((X3 tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X3) X3)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))) (forall ((X3 tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X3) X3)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) X3)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X3 tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X3) X3)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X3 tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))) (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X3) X3)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X3 tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))) (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))) (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))) (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))) (@ _let_71 _let_144) (@ _let_95 _let_143) (@ _let_138 _let_142) (@ _let_96 _let_140) (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))))) (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 ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))) (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 ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))) (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 ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))) (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.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))) (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.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))) (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.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))) (forall ((Y tptp.real) (X3 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X3) Y)) Z)))) (forall ((Y tptp.rat) (X3 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X3) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X3) Y)) Z)))) (forall ((Y tptp.real) (Z tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y)) X3) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X3) Y))))) (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y)) X3) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X3) Y))))) (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 ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))) (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 ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))) (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 ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)) (and (@ _let_1 tptp.zero_zero_rat) (@ _let_1 B)) (= A tptp.zero_zero_rat))))) (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.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))) (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.one_one_real)))) (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.one_one_rat)))) (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat)))) (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int)))) (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) (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.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (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 ((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.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((Z tptp.complex) (X3 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X3) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X3) (@ (@ tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X3) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X3) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X3) (@ (@ tptp.times_times_rat Y) Z))) Z)))) (forall ((Z tptp.complex) (X3 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X3) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X3) Z)) Y)) Z)))) (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) Z)) Y)) Z)))) (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X3) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X3) Z)) Y)) Z)))) (forall ((Y tptp.complex) (Z tptp.complex) (X3 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X3) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X3) (@ (@ tptp.times_times_complex Z) Y))) Y)))) (forall ((Y tptp.real) (Z tptp.real) (X3 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X3) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real Z) Y))) Y)))) (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X3) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X3) (@ (@ tptp.times_times_rat Z) Y))) Y)))) (forall ((Y tptp.complex) (X3 tptp.complex) (Z tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X3) Y)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X3) (@ (@ tptp.times_times_complex Z) Y))) Y)))) (forall ((Y tptp.real) (X3 tptp.real) (Z tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X3) Y)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real Z) Y))) Y)))) (forall ((Y tptp.rat) (X3 tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X3) Y)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X3) (@ (@ tptp.times_times_rat Z) Y))) Y)))) (forall ((Y tptp.complex) (Z tptp.complex) (X3 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X3) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X3) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))) (forall ((Y tptp.real) (Z tptp.real) (X3 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 X3) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X3) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X3) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) 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 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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))) (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 ((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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))) (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real A) B))))) (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) (@ (@ tptp.power_power_rat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))) (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))) (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))) (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_rat A) _let_2) (@ (@ tptp.power_power_rat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))) (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))) (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))) (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.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)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.modulo364778990260209775nteger A) B)))) (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 ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.modulo364778990260209775nteger A) B) A)))) (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 ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat))) (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int))) (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)) (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)) (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)) (= _let_139 _let_34) (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)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K2) (not (@ P I)))) (@ P (@ tptp.suc K2))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M) N))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))) (forall ((X3 tptp.real) (Xs tptp.list_real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs)))) (forall ((X3 tptp.complex) (Xs tptp.list_complex)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs)))) (forall ((X3 tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s5460976970255530739at_nat Xs)))) (forall ((X3 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs)))) (forall ((X3 Bool) (Xs tptp.list_o)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs)))) (forall ((X3 tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)))) (forall ((X3 tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N) K)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N)) (and (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M)))))) (forall ((I2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I2) (@ _let_1 (@ (@ tptp.power_power_nat I2) N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.divide_divide_nat M) N))))) (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q2)) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N) Q2))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) M)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N) M) (= N tptp.one_one_nat)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))) (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X3) _let_1))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (=> (@ (@ tptp.ord_less_real Z2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z2) X3)) Y)))) (@ (@ tptp.ord_less_eq_real X3) Y))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (forall ((Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (=> (@ (@ tptp.ord_less_rat Z2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z2) X3)) Y)))) (@ (@ tptp.ord_less_eq_rat X3) Y))) (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.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))) (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.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))) (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.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))) (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.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))) (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.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))) (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.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))) (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.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))) (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.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))) (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 ((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 ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))) (forall ((Y tptp.real) (Z tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y)) X3) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X3) Y))))) (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y)) X3) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X3) Y))))) (forall ((Y tptp.real) (X3 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X3) Y)) Z)))) (forall ((Y tptp.rat) (X3 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X3) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X3) 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.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))) (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.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))) (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.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))) (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 ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))) (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 ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))) (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 ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))) (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.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A) C))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))) (forall ((X3 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 X3) 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) X3)) (@ (@ tptp.times_times_real V) Y))) A)))))))) (forall ((X3 tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X3) A) (=> (@ (@ tptp.ord_less_eq_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X3)) (@ (@ tptp.times_times_rat V) Y))) A)))))))) (forall ((X3 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 X3) 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) X3)) (@ (@ tptp.times_times_int V) Y))) 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.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))) (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 ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)) (= A tptp.zero_zero_rat)))) (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 ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))) (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 ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) _let_1))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) _let_1))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))) (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) A)))) (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) A)))) (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) A)))) (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) A)))) (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) tptp.one_one_real)))) (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) tptp.one_one_rat)))) (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) tptp.one_one_nat)))) (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) tptp.one_one_int)))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N5)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N5)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N5)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N5)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N5)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N5)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N5)) (@ _let_1 N))))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N5)) (@ _let_1 N))))))) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) _let_26) tptp.zero_zero_rat) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) _let_26) tptp.zero_zero_nat) (= (@ _let_76 _let_26) tptp.zero_zero_real) (= (@ _let_75 _let_26) tptp.zero_zero_int) (= (@ _let_74 _let_26) tptp.zero_zero_complex) (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N))))) (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N))))) (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N))))) (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_real A) N)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_nat A) N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_int A) N)))))) (= _let_26 _let_35) (@ _let_138 _let_26) (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N) Q2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q2)) N)))) (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I3)) J3)) (@ P I3))))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N)))))) (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I3)) J3)) (@ P J3))))))))) (forall ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B3) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B3) N))))) (forall ((X3 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 X3) 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) X3)) (@ (@ tptp.times_times_real V) Y))) A)))))))) (forall ((X3 tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X3) A) (=> (@ (@ tptp.ord_less_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X3)) (@ (@ tptp.times_times_rat V) Y))) A)))))))) (forall ((X3 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 X3) 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) X3)) (@ (@ 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_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 ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))) (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 ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))) (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.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))) (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 ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))) (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X3) Y))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat X3) Y))))) (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X3) Y))))) (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X3) Y))))) (forall ((X3 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 X3) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= X3 Y))))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_rat X3) _let_2) (@ (@ tptp.power_power_rat Y) _let_2)) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= X3 Y))))))) (forall ((X3 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 X3) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= X3 Y))))))) (forall ((X3 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 X3) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= X3 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.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat 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.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat))) (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 ((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) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 N) tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (@ _let_1 N) tptp.zero_zero_int))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 M) tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (@ _let_1 M) tptp.zero_zero_int))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ (@ tptp.plus_plus_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N))))) (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (or (and (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q4)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q4))) (@ P Q4))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N))) M) tptp.one_one_nat))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X3) Y))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat X3) Y))))) (forall ((X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X3) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X3) Y))))) (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X3) Y))))) (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X3 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat) (and (= X3 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))) (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X3 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))) (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))) (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X3 tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) (or (not (= X3 tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat)))))) (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X3 tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))) (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat)))) (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))) (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 ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) B) (= _let_2 (@ _let_1 B))))))) (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)) (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.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (forall ((B4 tptp.real) (A4 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B4) A4)) (@ (@ tptp.ord_less_real A4) B4))) (forall ((B4 tptp.rat) (A4 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B4) A4)) (@ (@ tptp.ord_less_rat A4) B4))) (forall ((B4 tptp.num) (A4 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B4) A4)) (@ (@ tptp.ord_less_num A4) B4))) (forall ((B4 tptp.nat) (A4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B4) A4)) (@ (@ tptp.ord_less_nat A4) B4))) (forall ((B4 tptp.int) (A4 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B4) A4)) (@ (@ tptp.ord_less_int A4) B4))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ P N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))) (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 ((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 ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))) (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_real))) (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_rat))) (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_int))) (forall ((M tptp.code_integer) (X3 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X3))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X3) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M))))))))) (forall ((M tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X3))) (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) X3) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))) (forall ((M tptp.int) (X3 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X3))) (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) X3) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))) (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((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 TreeList) I4)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N))) (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) TreeList) Summary)) Deg)))))))))))))) (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((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 TreeList) I4)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N))) (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) TreeList) Summary)) Deg)))))))))))))) (forall ((X3 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X3) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X3) N)) (@ _let_1 N)))))))) (forall ((X3 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X3) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X3) N)) (@ _let_1 M)))))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))) (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X3 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X3))) (forall ((Z tptp.real) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X3) Y))))) (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X3) Y))))) (forall ((Z tptp.int) (X3 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 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X3) Y))))) (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X3) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_eq_real X3) Y)))) (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X3) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X3) Y)))) (forall ((Z tptp.int) (X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X3) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X3) Y)))) (forall ((Q2 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R2)) (= R2 tptp.zero_zero_nat))) (forall ((Q2 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R2)) (= R2 tptp.zero_zero_int))) (forall ((N tptp.nat) (Xs tptp.list_num) (Ys2 tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_num Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6456567536196504476um_num (@ (@ tptp.product_num_num Xs) Ys2)) N) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_num Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_Code_integer) (Ys2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s3445333598471063425nteger Xs)) _let_1)) (= (@ (@ tptp.nth_Pr8522763379788166057eger_o (@ (@ tptp.produc3607205314601156340eger_o Xs) Ys2)) N) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.nth_Code_integer Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys2)) N) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys2)) N) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys2)) N) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys2)) N) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys2)) N) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs) Ys2)) N) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs) Ys2)) N) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs) Ys2)) N) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))) (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 ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N) K)) (@ _let_1 K)))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N) K)) (@ _let_1 K)))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N) K)) (@ _let_1 K)))) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys2)))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_o Ys2)))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_nat Ys2)))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_int Ys2)))) (forall ((Xs tptp.list_o) (Ys2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys2)))) (forall ((Xs tptp.list_o) (Ys2 tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_o Ys2)))) (forall ((Xs tptp.list_o) (Ys2 tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_nat Ys2)))) (forall ((Xs tptp.list_o) (Ys2 tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_int Ys2)))) (forall ((Xs tptp.list_nat) (Ys2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys2)))) (forall ((Xs tptp.list_nat) (Ys2 tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_o Ys2)))) (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))) (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 ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))) (forall ((K tptp.int) (I2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K) I2) (=> (@ P K) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I4) (=> (@ P I4) (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))))) (@ P I2))))) (forall ((K tptp.int) (I2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I2) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I4) (=> (@ P I4) (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))))) (@ P I2))))) (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))) (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W Z))))) (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I3 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I3 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ P J3))))))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))) (forall ((B4 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q5)) R4)) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (@ _let_1 Q5)))))) (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I2) J2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J2)))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))) (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (and (= M tptp.one_one_int) (= N tptp.one_one_int))))) (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))) (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B4 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))) (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B4 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R2) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))) (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_1 Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int R4) B) (=> (@ (@ tptp.ord_less_int R2) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))) (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_2 Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ _let_1 R2) (=> (@ _let_1 R4) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))) (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))) (forall ((L2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L2) tptp.zero_zero_int)) (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)) (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)) (forall ((M tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q3 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q3))))) (forall ((M tptp.int) (D tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q4 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q4))))) (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M) N) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))) (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))) (forall ((L2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L2) L2)) (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)) (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))) (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))) (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 ((K tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N) K))) (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 ((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 ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) K)) (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 ((M tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M) K)) M))) (forall ((I2 tptp.int) (K tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I2) K) I2) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I2))))) (forall ((A tptp.int) (X3 tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X3) (= A X3) (@ (@ tptp.ord_less_eq_int X3) A))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) B))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ tptp.ord_less_int B))) (=> (@ _let_2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (@ _let_2 _let_1)))))) _let_137 (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))) (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))) (forall ((X3 tptp.produc3368934014287244435at_num)) (not (forall ((F2 (-> tptp.nat tptp.num tptp.num)) (A5 tptp.nat) (B5 tptp.nat) (Acc tptp.num)) (not (= X3 (@ (@ tptp.produc851828971589881931at_num F2) (@ (@ tptp.produc1195630363706982562at_num A5) (@ (@ tptp.product_Pair_nat_num B5) Acc)))))))) (forall ((X3 tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B5 tptp.nat) (Acc tptp.nat)) (not (= X3 (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A5) (@ (@ tptp.product_Pair_nat_nat B5) Acc)))))))) (forall ((X3 tptp.nat)) (=> (not (= X3 tptp.zero_zero_nat)) (=> (not (= X3 (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X3 (@ tptp.suc (@ tptp.suc Va))))))))) (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X3) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_real X3) Y)))) (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X3) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X3) Y)))) (forall ((Z tptp.int) (X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X3) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X3) Y)))) (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X3 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X3))) (forall ((Uz tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va2) Vb) Vc)))) (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X tptp.int)) (=> (@ P X) (@ P (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int K) D))))))))) (forall ((N tptp.nat) (X3 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X3))) (forall ((TreeList tptp.list_VEBT_VEBT) (N 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 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))) (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))) (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X3 tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat X3) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X3 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X3) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X3) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))) (forall ((X3 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X3) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat Mi) X3) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X3 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList) Summary)) X3) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X3) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X3) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))) (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B5)))))) (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B5))))) (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A3 Bool) (B2 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B2))))) (forall ((Xs tptp.list_VEBT_VEBT) (I2 tptp.nat) (X3 tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2))) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 X3)) I2) Y) (@ _let_1 Y)))) (forall ((Xs tptp.list_VEBT_VEBT) (I2 tptp.nat) (X3 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3)) (@ tptp.size_s6755466524823107622T_VEBT Xs))) (forall ((Xs tptp.list_o) (I2 tptp.nat) (X3 Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs) I2) X3)) (@ tptp.size_size_list_o Xs))) (forall ((Xs tptp.list_nat) (I2 tptp.nat) (X3 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs) I2) X3)) (@ tptp.size_size_list_nat Xs))) (forall ((Xs tptp.list_int) (I2 tptp.nat) (X3 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs) I2) X3)) (@ tptp.size_size_list_int Xs))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)) (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)))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)) (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)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (Xs tptp.list_nat) (X3 tptp.nat)) (=> (not (= I2 J2)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I2) X3)) J2) (@ (@ tptp.nth_nat Xs) J2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (Xs tptp.list_int) (X3 tptp.int)) (=> (not (= I2 J2)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I2) X3)) J2) (@ (@ tptp.nth_int Xs) J2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X3 tptp.vEBT_VEBT)) (=> (not (= I2 J2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3)) J2) (@ (@ tptp.nth_VEBT_VEBT Xs) J2)))) (forall ((Xs tptp.list_nat) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs) I2) (@ (@ tptp.nth_nat Xs) I2)) Xs)) (forall ((Xs tptp.list_int) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs) I2) (@ (@ tptp.nth_int Xs) I2)) Xs)) (forall ((Xs tptp.list_VEBT_VEBT) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) (@ (@ tptp.nth_VEBT_VEBT Xs) I2)) Xs)) (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_rat U))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (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 ((X3 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X3))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X3))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X3))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X3))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X3))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X3))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X3))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X3))) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X3))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X3))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat) (= (@ (@ 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_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat) (= (@ (@ 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) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X3))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X3))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X3))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X3))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X3))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X3))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X3))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X3))) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X3))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X3))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))) (forall ((Xs tptp.list_VEBT_VEBT) (I2 tptp.nat) (X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) I2) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3) Xs))) (forall ((Xs tptp.list_o) (I2 tptp.nat) (X3 Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) I2) (= (@ (@ (@ tptp.list_update_o Xs) I2) X3) Xs))) (forall ((Xs tptp.list_nat) (I2 tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) I2) (= (@ (@ (@ tptp.list_update_nat Xs) I2) X3) Xs))) (forall ((Xs tptp.list_int) (I2 tptp.nat) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) I2) (= (@ (@ (@ tptp.list_update_int Xs) I2) X3) Xs))) (forall ((I2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3)) I2) X3))) (forall ((I2 tptp.nat) (Xs tptp.list_o) (X3 Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs) I2) X3)) I2) X3))) (forall ((I2 tptp.nat) (Xs tptp.list_nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I2) X3)) I2) X3))) (forall ((I2 tptp.nat) (Xs tptp.list_int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I2) X3)) I2) X3))) (forall ((I2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_VEBT_VEBT2 Xs))))))) (forall ((I2 tptp.nat) (Xs tptp.list_o) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (let ((_let_2 (@ tptp.size_size_list_o Xs))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_o2 Xs))))))) (forall ((I2 tptp.nat) (Xs tptp.list_nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_nat2 Xs))))))) (forall ((I2 tptp.nat) (Xs tptp.list_int) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs) I2) (@ _let_1 J2))) J2) (@ _let_1 I2))) (@ tptp.set_int2 Xs))))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= Q2 Q5))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= R2 R4))))) (forall ((I2 tptp.nat) (I5 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X3 tptp.vEBT_VEBT) (X6 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.list_u1324408373059187874T_VEBT Xs))) (=> (not (= I2 I5)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I2) X3)) I5) X6) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I5) X6)) I2) X3))))) (forall ((X3 tptp.vEBT_VEBT)) (=> (not (= X3 (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv Bool)) (not (= X3 (@ (@ tptp.vEBT_Leaf true) Uv)))) (=> (forall ((Uu Bool)) (not (= X3 (@ (@ tptp.vEBT_Leaf Uu) true)))) (=> (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2)))))))))) (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X3))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X3))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X3))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X3))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X3) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X3) Z)) (@ (@ tptp.plus_plus_real Y) Z)))) (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X3) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X3) Z)) (@ (@ tptp.plus_plus_rat Y) Z)))) (forall ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X3) Y)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X3) Z)) (@ (@ tptp.plus_plus_nat Y) Z)))) (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X3) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X3) Z)) (@ (@ tptp.plus_plus_int Y) Z)))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X3) (=> (not (= X3 (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy2)))))))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q2)) (@ (@ tptp.plus_plus_nat N) Q2)))) (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 ((X21 Bool) (X222 Bool)) (not (= Y (@ (@ tptp.vEBT_Leaf X21) X222))))))) (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X212 Bool) (X223 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X212) X223)))) (forall ((X3 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu Bool) (Uv Bool) (D3 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu) Uv)) D3)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) Deg3))))))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N) Q2)))) (forall ((A Bool) (B Bool) (X3 tptp.nat)) (let ((_let_1 (= X3 tptp.one_one_nat))) (let ((_let_2 (= X3 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X3) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))) (@ tptp.vEBT_VEBT_minNull _let_136) (forall ((Uv2 Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv2)))) (forall ((Uu2 Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu2) true)))) (forall ((X3 tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ tptp.vEBT_VEBT_minNull X3) Y) (=> (=> (= X3 (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv Bool)) (= X3 (@ (@ tptp.vEBT_Leaf true) Uv))) Y) (=> (=> (exists ((Uu Bool)) (= X3 (@ (@ tptp.vEBT_Leaf Uu) true))) Y) (=> (=> (exists ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) Y))))))))) (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))) (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R2)) (= (@ (@ tptp.divide_divide_int K) L2) Q2))) (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R2)) (= (@ (@ tptp.modulo_modulo_int K) L2) R2))) (forall ((Xs tptp.list_real) (A2 tptp.set_real) (X3 tptp.real) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) A2) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) I2) X3))) A2)))) (forall ((Xs tptp.list_complex) (A2 tptp.set_complex) (X3 tptp.complex) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs) I2) X3))) A2)))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (X3 tptp.product_prod_nat_nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) A2) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) I2) X3))) A2)))) (forall ((Xs tptp.list_nat) (A2 tptp.set_nat) (X3 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I2) X3))) A2)))) (forall ((Xs tptp.list_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (X3 tptp.vEBT_VEBT) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (=> (@ (@ tptp.member_VEBT_VEBT X3) A2) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3))) A2)))) (forall ((Xs tptp.list_int) (A2 tptp.set_int) (X3 tptp.int) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I2) X3))) A2)))) (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X3))) (forall ((X3 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2)) X5)))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ 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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2)) X5)))))))))) (forall ((X3 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw)))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ 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 (= X3 (@ (@ 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) (Vd tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd)) X5)))))))))) (forall ((X3 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X5)))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ 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 (= X3 (@ (@ 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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2)) X5)))))))))) (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy))) (forall ((X3 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X5 tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X5)))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (= X3 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)) Ux)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X3 (@ (@ 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))) (= (@ tptp.vEBT_vebt_buildup _let_34) _let_136) (forall ((L2 tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (=> (= K (@ (@ tptp.times_times_int Q2) L2)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) tptp.zero_zero_int))))) (forall ((A Bool) (B Bool) (X3 tptp.nat)) (let ((_let_1 (= X3 tptp.one_one_nat))) (let ((_let_2 (= X3 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X3) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))) (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2))) (forall ((X3 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) X3))) (let ((_let_4 (= X3 tptp.one_one_nat))) (let ((_let_5 (= X3 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 ((N tptp.nat) (Xs tptp.list_real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real X3) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) N) X3))))) (forall ((N tptp.nat) (Xs tptp.list_complex) (X3 tptp.complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs)) (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs) N) X3))))) (forall ((N tptp.nat) (Xs tptp.list_P6011104703257516679at_nat) (X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) N) X3))))) (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) N) X3))))) (forall ((N tptp.nat) (Xs tptp.list_o) (X3 Bool)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o X3) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) N) X3))))) (forall ((N tptp.nat) (Xs tptp.list_nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) N) X3))))) (forall ((N tptp.nat) (Xs tptp.list_int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int X3) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) N) X3))))) (forall ((I2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3) Xs) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I2) X3)))) (forall ((I2 tptp.nat) (Xs tptp.list_o) (X3 Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (= (= (@ (@ (@ tptp.list_update_o Xs) I2) X3) Xs) (= (@ (@ tptp.nth_o Xs) I2) X3)))) (forall ((I2 tptp.nat) (Xs tptp.list_nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (= (= (@ (@ (@ tptp.list_update_nat Xs) I2) X3) Xs) (= (@ (@ tptp.nth_nat Xs) I2) X3)))) (forall ((I2 tptp.nat) (Xs tptp.list_int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (= (= (@ (@ (@ tptp.list_update_int Xs) I2) X3) Xs) (= (@ (@ tptp.nth_int Xs) I2) X3)))) (forall ((I2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (J2 tptp.nat) (X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3)) J2))) (let ((_let_2 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (and (=> _let_2 (= _let_1 X3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs) J2)))))))) (forall ((I2 tptp.nat) (Xs tptp.list_o) (X3 Bool) (J2 tptp.nat)) (let ((_let_1 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs) I2) X3)) J2) (and (=> _let_1 X3) (=> (not _let_1) (@ (@ tptp.nth_o Xs) J2))))))) (forall ((I2 tptp.nat) (Xs tptp.list_nat) (J2 tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I2) X3)) J2))) (let ((_let_2 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (and (=> _let_2 (= _let_1 X3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs) J2)))))))) (forall ((I2 tptp.nat) (Xs tptp.list_int) (J2 tptp.nat) (X3 tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I2) X3)) J2))) (let ((_let_2 (= I2 J2))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (and (=> _let_2 (= _let_1 X3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs) J2)))))))) (forall ((P (-> tptp.real Bool)) (P3 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.rat Bool)) (P3 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.real Bool)) (P3 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.rat Bool)) (P3 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (not (= X T)))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (not (= X T)))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (not (= X T)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (not (= X T)))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (not (= X T)))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (not (= X T)))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (not (= X T)))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (not (= X T)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (not (= X T)))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (not (= X T)))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (not (@ (@ tptp.ord_less_real X) T)))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (not (@ (@ tptp.ord_less_rat X) T)))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (not (@ (@ tptp.ord_less_num X) T)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (not (@ (@ tptp.ord_less_nat X) T)))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (not (@ (@ tptp.ord_less_int X) T)))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (@ (@ tptp.ord_less_real T) X))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (@ (@ tptp.ord_less_rat T) X))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (@ (@ tptp.ord_less_num T) X))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (@ (@ tptp.ord_less_nat T) X))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (@ (@ tptp.ord_less_int T) X))))) (forall ((P (-> tptp.real Bool)) (P3 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z2) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.rat Bool)) (P3 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z2) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z2) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z2) (= (and (@ P X) (@ Q X)) (and (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.real Bool)) (P3 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z2) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.rat Bool)) (P3 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z2) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z2) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))) (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z2) (= (or (@ P X) (@ Q X)) (or (@ P3 X) (@ Q6 X))))))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z2) (not (= X T)))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z2) (not (= X T)))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z2) (not (= X T)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (= X T)))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z2) (not (= X T)))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z2) (not (= X T)))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z2) (not (= X T)))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z2) (not (= X T)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (= X T)))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z2) (not (= X T)))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Z2) (@ _let_1 T)))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Z2) (@ _let_1 T)))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Z2) (@ _let_1 T)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Z2) (@ _let_1 T)))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Z2) (@ _let_1 T)))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z2) (not (@ (@ tptp.ord_less_real T) X)))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z2) (not (@ (@ tptp.ord_less_rat T) X)))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z2) (not (@ (@ tptp.ord_less_num T) X)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (@ (@ tptp.ord_less_nat T) X)))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z2) (not (@ (@ tptp.ord_less_int T) X)))))) (forall ((X3 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X3)) (=> (forall ((Uv Bool)) (not (= X3 (@ (@ tptp.vEBT_Leaf true) Uv)))) (=> (forall ((Uu Bool)) (not (= X3 (@ (@ tptp.vEBT_Leaf Uu) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))))))))) (forall ((K tptp.int) (L2 tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K) L2)) (@ (@ tptp.modulo_modulo_int K) L2)))) (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary)) X3) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X3) X3))) _let_1) TreeList) Summary)))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (not (@ (@ tptp.ord_less_eq_real X) T)))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (not (@ (@ tptp.ord_less_eq_rat X) T)))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (not (@ (@ tptp.ord_less_eq_num X) T)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (not (@ (@ tptp.ord_less_eq_nat X) T)))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (not (@ (@ tptp.ord_less_eq_int X) T)))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (@ (@ tptp.ord_less_eq_real T) X))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (@ (@ tptp.ord_less_eq_rat T) X))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X) (@ (@ tptp.ord_less_eq_num T) X))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (@ (@ tptp.ord_less_eq_nat T) X))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X) (@ (@ tptp.ord_less_eq_int T) X))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z2) (@ (@ tptp.ord_less_eq_real X) T))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z2) (@ (@ tptp.ord_less_eq_rat X) T))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z2) (@ (@ tptp.ord_less_eq_num X) T))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (@ (@ tptp.ord_less_eq_nat X) T))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z2) (@ (@ tptp.ord_less_eq_int X) T))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z2) (not (@ (@ tptp.ord_less_eq_real T) X)))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z2) (not (@ (@ tptp.ord_less_eq_rat T) X)))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z2) (not (@ (@ tptp.ord_less_eq_num T) X)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (@ (@ tptp.ord_less_eq_nat T) X)))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z2) (not (@ (@ tptp.ord_less_eq_int T) X)))))) (forall ((X3 tptp.int) (X6 tptp.int) (P Bool) (P3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X3 X6) (=> (=> _let_2 (= P P3)) (= (=> (@ _let_1 X3) P) (=> _let_2 P3))))))) (forall ((X3 tptp.int) (X6 tptp.int) (P Bool) (P3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X3 X6) (=> (=> _let_2 (= P P3)) (= (and (@ _let_1 X3) P) (and _let_2 P3))))))) (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L2))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2))) (= (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R2)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L2) Q2)) R2)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (@ (@ tptp.ord_less_int R2) L2))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R2) (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))) (= tptp.vEBT_invar_vebt (lambda ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (or (and (exists ((A3 Bool) (B2 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A3) B2))) (= A22 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= A22 (@ (@ tptp.plus_plus_nat N2) N2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) 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))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N2))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A22 (@ (@ tptp.plus_plus_nat N2) _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 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 N2)) (= A22 (@ (@ tptp.plus_plus_nat N2) N2)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3)))) (=> _let_1 (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.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X2) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.suc N2))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 _let_3)) (= A22 (@ (@ tptp.plus_plus_nat N2) _let_3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3)))) (=> _let_1 (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.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X2) N2))) (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 ((A5 Bool) (B5 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A5) B5))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (=> (= M5 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_1))) (not (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (=> (= M5 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_1))) (not (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M5)) (=> (= M5 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2))))))))))))))))))))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M5)) (=> (= M5 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))))))))))))))))))) (forall ((TreeList tptp.list_VEBT_VEBT) (N 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 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))) (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (=> (@ (@ tptp.vEBT_vebt_member Tree) X3) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X3) (@ (@ tptp.vEBT_VEBT_membermima Tree) X3))))) (forall ((X3 tptp.extended_enat) (Y tptp.extended_enat) (Z tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X3) Y)) Z) (and (@ (@ tptp.ord_le72135733267957522d_enat X3) Z) (@ (@ tptp.ord_le72135733267957522d_enat Y) Z)))) (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X3) Y)) Z) (and (@ (@ tptp.ord_less_real X3) Z) (@ (@ tptp.ord_less_real Y) Z)))) (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X3) Y)) Z) (and (@ (@ tptp.ord_less_rat X3) Z) (@ (@ tptp.ord_less_rat Y) Z)))) (forall ((X3 tptp.num) (Y tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X3) Y)) Z) (and (@ (@ tptp.ord_less_num X3) Z) (@ (@ tptp.ord_less_num Y) Z)))) (forall ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X3) Y)) Z) (and (@ (@ tptp.ord_less_nat X3) Z) (@ (@ tptp.ord_less_nat Y) Z)))) (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X3) Y)) Z) (and (@ (@ tptp.ord_less_int X3) Z) (@ (@ tptp.ord_less_int Y) Z)))) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat 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 ((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.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat 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 ((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.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C) A)))) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat 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.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat 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))) (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X2 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X2) (@ (@ tptp.vEBT_VEBT_membermima T2) X2)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((M5 tptp.nat)) (@ (@ P M5) tptp.zero_zero_nat)) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P N3) (@ (@ tptp.modulo_modulo_nat M5) N3)) (@ (@ P M5) N3)))) (@ (@ P M) N)))) (forall ((N tptp.nat) (X3 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X3))) (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 ((Ux2 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) Ux2) Uy)) Uz))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X3 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va2) Vb)) X3) (or (= X3 Mi) (= X3 Ma)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (= (@ (@ P A5) B5) (@ (@ P B5) A5))) (=> (forall ((A5 tptp.nat)) (@ (@ P A5) tptp.zero_zero_nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.plus_plus_nat A5) B5))))) (@ (@ P A) B))))) (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.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))) (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 ((A3 tptp.extended_enat) (B2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2) B2))) (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_max_rat A3) B2) B2))) (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B2 tptp.num)) (= (@ (@ tptp.ord_max_num A3) B2) B2))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B2) B2))) (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B2) B2))) (= tptp.ord_le2932123472753598470d_enat (lambda ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2) A3))) (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (= (@ (@ tptp.ord_max_rat A3) B2) A3))) (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (= (@ (@ tptp.ord_max_num A3) B2) A3))) (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B2) A3))) (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B2) A3))) (forall ((Z tptp.extended_enat) (X3 tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))) (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))) (forall ((Z tptp.num) (X3 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))) (forall ((Z tptp.nat) (X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))) (forall ((Z tptp.int) (X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X3) Y)) (or (@ _let_1 X3) (@ _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.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat 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.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat 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 ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2)))) (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (= A3 (@ (@ tptp.ord_max_rat A3) B2)))) (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (= A3 (@ (@ tptp.ord_max_num A3) B2)))) (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (= A3 (@ (@ tptp.ord_max_nat A3) B2)))) (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (= A3 (@ (@ tptp.ord_max_int A3) B2)))) (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.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A)))) (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.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C) A)))))) (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.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat 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.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat 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.rat) (A tptp.rat) (D tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A) (=> (@ (@ tptp.ord_less_eq_rat D) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C) D)) (@ (@ tptp.ord_max_rat A) B))))) (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 ((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.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))) (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 ((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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))) (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))))) (= tptp.ord_le72135733267957522d_enat (lambda ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (and (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2)) (not (= A3 B2))))) (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (= A3 (@ (@ tptp.ord_max_real A3) B2)) (not (= A3 B2))))) (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (= A3 (@ (@ tptp.ord_max_rat A3) B2)) (not (= A3 B2))))) (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (= A3 (@ (@ tptp.ord_max_num A3) B2)) (not (= A3 B2))))) (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (= A3 (@ (@ tptp.ord_max_nat A3) B2)) (not (= A3 B2))))) (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (= A3 (@ (@ tptp.ord_max_int A3) B2)) (not (= A3 B2))))) (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.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat C) A)))))) (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)))))) (forall ((Z tptp.extended_enat) (X3 tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))) (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))) (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))) (forall ((Z tptp.num) (X3 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))) (forall ((Z tptp.nat) (X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))) (forall ((Z tptp.int) (X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X3) Y)) (or (@ _let_1 X3) (@ _let_1 Y))))) (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N)) K) L2) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N) (@ (@ tptp.divide_divide_int K) _let_1)) L2)))))) (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) _let_34) (= (@ tptp.size_size_option_num tptp.none_num) _let_34) (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.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))) (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B) (@ _let_2 R2)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A))) (@ _let_1 B)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R2)) tptp.one_one_int)))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))) (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X3) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 _let_2) (not (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B5))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) (=> (= X3 _let_1) (not (= Y _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (=> (= X3 _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)))) (=> (= X3 (@ (@ (@ (@ 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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat 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))) (=> (= X3 _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 ((R2 tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R2))) (=> (not (= R2 tptp.zero_zero_complex)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C)) (@ (@ tptp.plus_plus_complex B) (@ _let_1 D)))))))) (forall ((R2 tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (=> (not (= R2 tptp.zero_zero_real)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D)))))))) (forall ((R2 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D)))))))) (forall ((R2 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D)))))))) (forall ((R2 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D)))))))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))) (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N)) (= M N))) (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))) (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)) (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat 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.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.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat A) B))) (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 ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat 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 ((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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_rat A) B)))) (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.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int 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.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat 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.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))) (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))) (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))) (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))) (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.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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat 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 ((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.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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat 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 ((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.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 ((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 ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N)))) (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N)))) (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit1 N)))) (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))) (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 ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N))))) (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L2) L2)) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))) (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))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))) (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))) (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.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_rat 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 ((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.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat 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.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat 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))) (= (@ _let_122 tptp.one_one_complex) tptp.zero_zero_complex) (= (@ _let_123 tptp.one_one_real) tptp.zero_zero_real) (= (@ _let_121 tptp.one_one_rat) tptp.zero_zero_rat) (= (@ _let_124 tptp.one_one_int) tptp.zero_zero_int) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)) (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.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) _let_1) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))) (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.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))) (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 ((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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B))))) (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.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B)))) (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) (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.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.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.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C) A)) B)) (@ _let_1 B)))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.times_times_rat C) A))) (@ _let_1 B)))) (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) 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 (@ (@ 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 A) (@ (@ tptp.divide6298287555418463151nteger B) 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) 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) (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)) (=> (@ (@ 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)) (=> (@ (@ 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)) (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 ((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 ((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 ((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.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger 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.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.modulo364778990260209775nteger B) A) tptp.zero_z3403309356797280102nteger))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M)))) (= (@ _let_1 (@ tptp.bit0 N)) (@ tptp.bit0 (@ _let_1 N))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M) _let_1))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))) (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N) K) L2)) (@ _let_1 L2)))) (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N) K) L2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))) (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 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 (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))) (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 ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N))) (@ _let_1 N)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N)) (not (@ _let_1 N))))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.dvd_dvd_nat A) B)))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.dvd_dvd_int A) B)))) (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 ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N)) (@ tptp.bit1 N))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N) tptp.one)))) (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))) (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) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) tptp.one)))) (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W) Z))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N)))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))) (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))))) (= (@ _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) (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.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 ((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 ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ (@ tptp.divide_divide_nat N) _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N) _let_1)))))) (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.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))) (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) (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.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))) (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.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))) (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 ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))) (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 ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))) (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 ((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.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_rat))) (and (not _let_3) (@ _let_1 A)))))))) (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.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.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)))) (=> (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)))) (=> (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)))) (=> (@ (@ 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)))) (=> (@ (@ 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) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))) (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.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.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.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_2 (= A tptp.zero_zero_rat)))))))) (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 ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer)) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat)) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int)) (= N tptp.zero_zero_nat)))) (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 ((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.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 ((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.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.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_set_complex (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) A)))) (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) B)))) (and (@ (@ tptp.dvd_dvd_complex A) B) (not (@ (@ tptp.dvd_dvd_complex B) A))))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) A)))) (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) B)))) (and (@ (@ tptp.dvd_dvd_real A) B) (not (@ (@ tptp.dvd_dvd_real B) A))))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) A)))) (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) B)))) (and (@ (@ tptp.dvd_dvd_nat A) B) (not (@ (@ tptp.dvd_dvd_nat B) A))))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) A)))) (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) B)))) (and (@ (@ tptp.dvd_dvd_int A) B) (not (@ (@ tptp.dvd_dvd_int B) A))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) A)))) (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) B)))) (and (@ (@ tptp.dvd_dvd_Code_integer A) B) (not (@ (@ tptp.dvd_dvd_Code_integer B) A))))) (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))) (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger 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.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.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 ((X3 tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X3))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y) Z)))))) (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X3))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_real Y) Z)))))) (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X3))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_rat Y) Z)))))) (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X3))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_int Y) Z)))))) (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)) (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)) (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) A)) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (= A B) (= C D)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (= A B) (= C D)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (= A B) (= C D)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_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) (=> (@ (@ tptp.dvd_dvd_int B) C) (@ _let_1 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) (=> (@ (@ tptp.dvd_dvd_Code_integer B) C) (@ _let_1 C))))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 C)) B) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (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.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat Z) _let_2)) _let_2))))) (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))))) (= (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.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)) (= (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)) (= (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.rat)) X2) (@ tptp.times_times_rat tptp.one_one_rat)) (= (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)) (= tptp.ord_ma741700101516333627d_enat (lambda ((A3 tptp.extended_enat) (B2 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A3) B2)) B2) A3))) (= tptp.ord_max_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A3) B2)) B2) A3))) (= tptp.ord_max_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A3) B2)) B2) A3))) (= tptp.ord_max_num (lambda ((A3 tptp.num) (B2 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A3) B2)) B2) A3))) (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B2)) B2) A3))) (= tptp.ord_max_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B2)) B2) A3))) (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X) T))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T)))))))) (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real K4) D4))) T)))))))) (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat K4) D4))) T)))))))) (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X) (@ (@ 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 ((X tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X) T)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T))))))) (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real K4) D4))) T))))))) (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat K4) D4))) T))))))) (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K4) D4))) T))))))) (= tptp.dvd_dvd_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (=> (= A3 tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))) (= tptp.dvd_dvd_real (lambda ((A3 tptp.real) (B2 tptp.real)) (=> (= A3 tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))) (= tptp.dvd_dvd_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (=> (= A3 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))) (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))) (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))) (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))) (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))) (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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C) D)))) (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_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))) (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 ((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.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))) (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) (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.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))) (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))))) (= (lambda ((Y5 tptp.complex) (Z3 tptp.complex)) (= Y5 Z3)) (lambda ((A3 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A3) B2) tptp.zero_zero_complex))) (= (lambda ((Y5 tptp.real) (Z3 tptp.real)) (= Y5 Z3)) (lambda ((A3 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real A3) B2) tptp.zero_zero_real))) (= (lambda ((Y5 tptp.rat) (Z3 tptp.rat)) (= Y5 Z3)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A3) B2) tptp.zero_zero_rat))) (= (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3)) (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B2) tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))) (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat 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)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer 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.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat 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) (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.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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A) B) (=> (@ (@ tptp.dvd_dvd_rat C) D) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))) (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)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))) (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat 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)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer 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.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat 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) (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.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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))) (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) (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.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.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))) (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))))) (= tptp.dvd_dvd_Code_integer (lambda ((B2 tptp.code_integer) (A3 tptp.code_integer)) (exists ((K3 tptp.code_integer)) (= A3 (@ (@ tptp.times_3573771949741848930nteger B2) K3))))) (= tptp.dvd_dvd_real (lambda ((B2 tptp.real) (A3 tptp.real)) (exists ((K3 tptp.real)) (= A3 (@ (@ tptp.times_times_real B2) K3))))) (= tptp.dvd_dvd_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (exists ((K3 tptp.rat)) (= A3 (@ (@ tptp.times_times_rat B2) K3))))) (= tptp.dvd_dvd_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (exists ((K3 tptp.nat)) (= A3 (@ (@ tptp.times_times_nat B2) K3))))) (= tptp.dvd_dvd_int (lambda ((B2 tptp.int) (A3 tptp.int)) (exists ((K3 tptp.int)) (= A3 (@ (@ tptp.times_times_int B2) K3))))) (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.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))) (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat 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))) (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.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.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (not (forall ((K2 tptp.rat)) (not (= A (@ (@ tptp.times_times_rat 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 ((P2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P2) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (@ (@ tptp.times_times_nat X5) Y3)) (=> (@ (@ tptp.dvd_dvd_nat X5) A) (not (@ (@ tptp.dvd_dvd_nat Y3) B)))))))) (forall ((P2 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P2) (@ (@ tptp.times_times_int A) B)) (not (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (= P2 (@ (@ tptp.times_times_int X5) Y3)) (=> (@ (@ tptp.dvd_dvd_int X5) A) (not (@ (@ tptp.dvd_dvd_int Y3) B)))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B6 tptp.nat) (C4 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B6) C4)) (@ (@ tptp.dvd_dvd_nat B6) B) (@ (@ tptp.dvd_dvd_nat C4) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B6 tptp.int) (C4 tptp.int)) (and (= A (@ (@ tptp.times_times_int B6) C4)) (@ (@ tptp.dvd_dvd_int B6) B) (@ (@ tptp.dvd_dvd_int C4) C))))) (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.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))) (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.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))) (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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C) D)))) (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.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))) (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.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.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.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) 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) (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.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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 C))))) (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) (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.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.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 B))))) (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 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger 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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)))))) (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 ((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 ((X tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real K4) D4)))) (= (or (@ P X) (@ Q X)) (or (@ P _let_1) (@ Q _let_1)))))))) (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X5 tptp.rat) (K2 tptp.rat)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K2) D4))))) (=> (forall ((X5 tptp.rat) (K2 tptp.rat)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K2) D4))))) (forall ((X tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat K4) D4)))) (= (or (@ P X) (@ Q X)) (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 ((X tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K4) D4)))) (= (or (@ P X) (@ Q X)) (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 ((X tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real K4) D4)))) (= (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1)))))))) (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X5 tptp.rat) (K2 tptp.rat)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K2) D4))))) (=> (forall ((X5 tptp.rat) (K2 tptp.rat)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K2) D4))))) (forall ((X tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat K4) D4)))) (= (and (@ P X) (@ Q X)) (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 ((X tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K4) D4)))) (= (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1)))))))) (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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))) (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.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.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) C)) A) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B) A)) (@ (@ tptp.times_times_rat C) A)))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))) (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 ((X22 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X32)))) (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 ((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 ((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 ((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.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.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))) (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.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 ((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 ((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.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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (= A B)))))) (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.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 ((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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))) (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.real) (B tptp.real) (A tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C) B) A) (= C (@ (@ tptp.minus_minus_real A) B)))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C) B) A) (= C (@ (@ tptp.minus_minus_rat 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.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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B)))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))) (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.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.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))) (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.real) (C tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.minus_minus_real C) B)) (= (@ (@ tptp.plus_plus_real A) B) C))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.minus_minus_rat C) B)) (= (@ (@ tptp.plus_plus_rat 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.real) (B tptp.real) (C tptp.real)) (= (= (@ (@ tptp.minus_minus_real A) B) C) (= A (@ (@ tptp.plus_plus_real C) B)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A) B) C) (= A (@ (@ tptp.plus_plus_rat 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.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.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A2) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B)))))) (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 ((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.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat C) D)))) (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 ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))) (forall ((X3 tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X3) Y) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X3) N)) (@ (@ tptp.power_8256067586552552935nteger Y) N)))) (forall ((X3 tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X3) Y) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X3) N)) (@ (@ tptp.power_power_nat Y) N)))) (forall ((X3 tptp.real) (Y tptp.real) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X3) Y) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.power_power_real Y) N)))) (forall ((X3 tptp.int) (Y tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X3) Y) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X3) N)) (@ (@ tptp.power_power_int Y) N)))) (forall ((X3 tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X3) Y) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.power_power_complex Y) N)))) (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 ((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.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo_modulo_nat M) N)))))) (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo_modulo_int M) N)))))) (forall ((K tptp.code_integer) (M tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger M) N)))))) (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 ((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.dvd_dvd_nat C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ _let_1 A))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ _let_1 A))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ _let_1 A))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (=> (@ _let_1 B) (@ _let_1 A))))) (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.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C))) (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A4) B4)) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A4) B4)) 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.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C))) (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.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))) (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z22))))) (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z22)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))) (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X3) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X3) Z)) (@ (@ tptp.minus_minus_real Y) Z)))) (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X3) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X3) Z)) (@ (@ tptp.minus_minus_rat Y) Z)))) (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X3) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X3) Z)) (@ (@ tptp.minus_minus_int Y) Z)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))) (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))) (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))) (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))) (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))))) (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (forall ((N tptp.nat) (K tptp.int) (M tptp.nat) (L2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L2) R2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 L2)) R2)))) (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.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_rat _let_2) _let_2))))) (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 ((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))))) (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A3) B2)) tptp.zero_zero_real))) (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A3) B2)) tptp.zero_zero_rat))) (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A3) B2)) tptp.zero_zero_int))) (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)) (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A3) B2)) tptp.zero_zero_real))) (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A3) B2)) tptp.zero_zero_rat))) (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A3) B2)) tptp.zero_zero_int))) (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X) S))))) (=> (@ (@ tptp.ord_less_real X) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X) S))))) (=> (@ (@ tptp.ord_less_rat X) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X) S))))) (=> (@ (@ tptp.ord_less_nat X) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X) S))))) (=> (@ (@ tptp.ord_less_int X) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X) S)))) (=> (@ (@ tptp.ord_less_real X) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X) S)))) (=> (@ (@ tptp.ord_less_rat X) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X) S)))) (=> (@ (@ tptp.ord_less_nat X) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X) S)))) (=> (@ (@ tptp.ord_less_int X) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X) S))))) (=> (@ (@ tptp.ord_less_real Z2) X) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X) S))))) (=> (@ (@ tptp.ord_less_rat Z2) X) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X) S))))) (=> (@ (@ tptp.ord_less_nat Z2) X) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X) S))))) (=> (@ (@ tptp.ord_less_int Z2) X) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X) S)))) (=> (@ (@ tptp.ord_less_real Z2) X) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X) S)))) (=> (@ (@ tptp.ord_less_rat Z2) X) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X) S)))) (=> (@ (@ tptp.ord_less_nat Z2) X) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X) S)))) (=> (@ (@ tptp.ord_less_int Z2) X) (= _let_1 _let_1)))))) (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 ((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.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.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))) (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.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 ((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 ((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.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 ((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 ((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 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 ((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 ((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.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat C) B)))) (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) (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.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) C))) (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 ((I2 tptp.real) (K tptp.real) (N tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N) (@ (@ tptp.ord_less_eq_real I2) (@ (@ tptp.minus_minus_real N) K)))) (forall ((I2 tptp.rat) (K tptp.rat) (N tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) N) (@ (@ tptp.ord_less_eq_rat I2) (@ (@ tptp.minus_minus_rat N) K)))) (forall ((I2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat N) K)))) (forall ((I2 tptp.int) (K tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N) (@ (@ tptp.ord_less_eq_int I2) (@ (@ tptp.minus_minus_int N) K)))) (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) (N tptp.real) (J2 tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N) (@ (@ tptp.plus_plus_real J2) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N) K)) J2)))))))) (forall ((I2 tptp.rat) (K tptp.rat) (N tptp.rat) (J2 tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N) (@ (@ tptp.plus_plus_rat J2) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N) K)) J2)))))))) (forall ((I2 tptp.nat) (K tptp.nat) (N tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat J2) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N) K)) J2)))))))) (forall ((I2 tptp.int) (K tptp.int) (N tptp.int) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N) (@ (@ tptp.plus_plus_int J2) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N) K)) J2)))))))) (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 ((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)) (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)) (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)) (=> (@ (@ 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)) (=> (@ (@ 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.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)) (=> (@ (@ 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)) (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.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.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat C) B)))) (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 ((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.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) C))) (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)) (=> (not (@ (@ tptp.ord_less_real A) B)) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat A) B)) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))) (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 ((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)) (=> (@ (@ 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)) (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.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.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 ((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 ((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 ((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 ((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 ((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 ((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 ((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 ((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 ((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 ((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)) (=> (@ (@ 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)) (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) (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 ((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 ((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) (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) (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 ((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.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C) D))) (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.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.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))) (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 ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X3) X3)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.minus_minus_real X3) Y)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X3) X3)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X3) Y)) (@ (@ tptp.minus_minus_rat X3) Y)))) (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X3) X3)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X3) Y)) (@ (@ tptp.minus_minus_int X3) Y)))) (forall ((X3 tptp.real) (Y tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X3))) (= (@ (@ 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 X3) A)) B))))) (forall ((X3 tptp.rat) (Y tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X3))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y)) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y) B))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X3) A)) B))))) (forall ((X3 tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X3))) (= (@ (@ 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 X3) A)) B))))) (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 ((X3 tptp.product_prod_num_num)) (=> (not (= X3 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N3 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N3))))) (=> (forall ((N3 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N3))))) (=> (forall ((M5 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit0 N3))))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit1 N3))))) (=> (forall ((M5 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit0 N3))))) (not (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X3 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit1 N3))))))))))))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) N) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))) (forall ((B tptp.nat) (A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B)) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))) (forall ((B tptp.int) (A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B)) N) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))) (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B2) A3) tptp.zero_zero_nat))) (= tptp.dvd_dvd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B2) A3) tptp.zero_zero_int))) (= tptp.dvd_dvd_Code_integer (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B2) A3) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) (@ _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) (@ _let_1 N))))) (forall ((A tptp.code_integer) (N tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))) (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))) (forall ((A tptp.real) (N tptp.nat) (B tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B))))) (forall ((A tptp.int) (N tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))) (forall ((A tptp.complex) (N tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B))))) (forall ((X3 tptp.code_integer) (Y tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X3) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X3) N)) (@ (@ tptp.power_8256067586552552935nteger Y) M))))) (forall ((X3 tptp.nat) (Y tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X3) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X3) N)) (@ (@ tptp.power_power_nat Y) M))))) (forall ((X3 tptp.real) (Y tptp.real) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X3) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.power_power_real Y) M))))) (forall ((X3 tptp.int) (Y tptp.int) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X3) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X3) N)) (@ (@ tptp.power_power_int Y) M))))) (forall ((X3 tptp.complex) (Y tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X3) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.power_power_complex Y) M))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (not (@ (@ tptp.dvd_dvd_nat N) M))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M) N) (@ _let_1 M))))) (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_int M) N) (=> (@ (@ tptp.dvd_dvd_int N) M) (= M N))))))) (forall ((K tptp.int) (M tptp.int) (T tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (not (= K tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M) T) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 T)))))) (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (=> (not (= K tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M) N))))) (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X5) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D3)) (= (@ _let_2 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D3))))))))) (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X3 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 X3) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D)) (= (@ _let_2 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y)) D))) (exists ((X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A) B))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X5) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D)) (= (@ _let_3 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D)))))))))))))))) (forall ((I2 tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I2) K) (=> (@ P K) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I4) K) (=> (@ P I4) (@ P (@ (@ tptp.minus_minus_int I4) tptp.one_one_int))))) (@ P I2))))) (forall ((I2 tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I2) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_int I4) K) (=> (@ P I4) (@ P (@ (@ tptp.minus_minus_int I4) tptp.one_one_int))))) (@ P I2))))) (forall ((K tptp.int) (N tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N) (@ (@ tptp.times_times_int K) M))) (@ _let_1 N)))) (forall ((A tptp.int) (D tptp.int) (X3 tptp.int) (T tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X3))) (let ((_let_2 (@ tptp.dvd_dvd_int A))) (=> (@ _let_2 D) (= (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C) D))) T))))))) (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 ((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.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.rat Bool)) (L2 tptp.rat)) (= (exists ((X2 tptp.rat)) (@ P (@ (@ tptp.times_times_rat L2) X2))) (exists ((X2 tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L2) (@ (@ tptp.plus_plus_rat X2) tptp.zero_zero_rat)) (@ P X2))))) (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))))) (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 ((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 ((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 ((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 ((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 ((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 ((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 ((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 ((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)) (=> (@ (@ 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 ((N tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N)))) (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)))) (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (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.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))) (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_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.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))) (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 ((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) (= (= (@ (@ 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) (= (= A (@ (@ tptp.divide6298287555418463151nteger C) B)) (= (@ (@ tptp.times_3573771949741848930nteger A) B) C)))) (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 ((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 ((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 ((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 ((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 ((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 ((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 ((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 ((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 ((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.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))) (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 ((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.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))) (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 ((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 ((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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))) (forall ((Y tptp.complex) (Z tptp.complex) (X3 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X3) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X3) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))) (forall ((Y tptp.real) (Z tptp.real) (X3 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 X3) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X3) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X3) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X3) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))) (forall ((Z tptp.complex) (X3 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X3) Z)) Y)) Z)))) (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X3) Z)) Y)) Z)))) (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X3) Z)) Y)) Z)))) (forall ((Z tptp.complex) (X3 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X3) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X3) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X3) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat Y) Z))) Z)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (forall ((X3 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X3) X3)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X3) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X3) tptp.one_one_complex)))) (forall ((X3 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X3) X3)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X3) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X3) tptp.one_one_real)))) (forall ((X3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X3) X3)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X3) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X3) tptp.one_one_rat)))) (forall ((X3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X3) X3)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X3) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X3) tptp.one_one_int)))) (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 ((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 ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N tptp.zero_zero_nat)))) (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N tptp.zero_zero_nat)))) (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N tptp.zero_zero_nat)))) (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))) (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 ((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.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.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 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 B) (@ (@ tptp.divide6298287555418463151nteger 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.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat K) N)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M) N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D3))))))) (forall ((Z tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int Z) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N)) (not (@ (@ tptp.dvd_dvd_nat N) M)))) (forall ((D tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P1 X5) (@ P1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P1 X5))))) (=> (exists ((X_1 tptp.int)) (@ P1 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))) (forall ((D tptp.int) (P3 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P3 X5) (@ P3 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((X_1 tptp.int)) (@ P3 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))) (forall ((P (-> tptp.int Bool)) (K tptp.int) (I2 tptp.int)) (=> (@ P K) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I4) (=> (@ P I4) (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I4) K) (=> (@ P I4) (@ P (@ (@ tptp.minus_minus_int I4) tptp.one_one_int))))) (@ P I2))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M) N))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M) N))))))) (@ _let_135 tptp.zero_z3403309356797280102nteger) (@ _let_134 tptp.zero_zero_nat) (@ _let_133 tptp.zero_zero_int) (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B5 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B5 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B5) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B5) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B5)))))))))))))) (forall ((A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B5 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B5 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B5) tptp.one_one_nat) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_times_nat A) B5) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B5)))))))))))))) (forall ((A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B5 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B5 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B5) tptp.one_one_int) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_times_int A) B5) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B5)))))))))))))) (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 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 B) A)) (@ (@ 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)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B5))))))) (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B5))))))) (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B5))))))) (not (@ _let_135 tptp.one_one_Code_integer)) (not (@ _let_134 tptp.one_one_nat)) (not (@ _let_133 tptp.one_one_int)) (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)))))) (forall ((Y tptp.real) (Z tptp.real) (X3 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 X3) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X3) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))) (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X3) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X3) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))) (= (lambda ((Y5 tptp.code_integer) (Z3 tptp.code_integer)) (= Y5 Z3)) (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide6298287555418463151nteger A3) _let_1) (@ (@ tptp.divide6298287555418463151nteger B2) _let_1))))))) (= (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide_divide_nat A3) _let_1) (@ (@ tptp.divide_divide_nat B2) _let_1))))))) (= (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3)) (lambda ((A3 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide_divide_int A3) _let_1) (@ (@ tptp.divide_divide_int B2) _let_1))))))) (forall ((Y tptp.real) (Z tptp.real) (X3 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 X3) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X3) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))) (forall ((Y tptp.rat) (Z tptp.rat) (X3 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X3) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X3) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))) (forall ((X3 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X3))) (=> (not (= X3 tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X3) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N)))))) (forall ((X3 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X3))) (=> (not (= X3 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X3) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N)))))) (forall ((X3 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X3))) (=> (not (= X3 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X3) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N)))))) (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))) (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))) (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat))) (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int))) (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.nat) (X3 tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X3 tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X3) (@ (@ tptp.power_8256067586552552935nteger X3) N)))) (forall ((N tptp.nat) (X3 tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X3 tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X3) (@ (@ tptp.power_power_rat X3) N)))) (forall ((N tptp.nat) (X3 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X3 tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X3) (@ (@ tptp.power_power_nat X3) N)))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X3 tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X3) (@ (@ tptp.power_power_real X3) N)))) (forall ((N tptp.nat) (X3 tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X3 tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X3) (@ (@ tptp.power_power_int X3) N)))) (forall ((N tptp.nat) (X3 tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X3 tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X3) (@ (@ tptp.power_power_complex X3) N)))) (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.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat A) A)) A))) (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))) (forall ((X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X3) Y)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y) X3)) _let_1)))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X3) Y)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y) X3)) _let_1)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X3) Y)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y) X3)) _let_1)))) (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X3) Y)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y) X3)) _let_1)))) (= (@ tptp.numeral_numeral_nat _let_49) (@ tptp.suc _let_35)) (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))) (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 ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M)) M) (= N tptp.one_one_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N)) M) (= N tptp.one_one_nat)))) (forall ((I2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I2) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X tptp.int)) (=> (@ P X) (@ P (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K) D))))))))) (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L2)) (or (@ (@ tptp.dvd_dvd_int L2) K) (and (= L2 tptp.zero_zero_int) (@ _let_1 K)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2))))) (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (=> (@ (@ tptp.ord_less_eq_int L2) K) (= (@ (@ tptp.modulo_modulo_int K) L2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) L2)) L2))))) (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 ((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.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 ((U tptp.real) (V tptp.real) (R2 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_eq_real R2) S) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.minus_minus_real V) U))) S))) V))))) (forall ((U tptp.rat) (V tptp.rat) (R2 tptp.rat) (S tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (=> (@ (@ tptp.ord_less_eq_rat R2) S) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R2) (@ (@ tptp.minus_minus_rat V) U))) S))) V))))) (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)))) (= (@ (@ 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)))) (= (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 ((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 ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))) (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 ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))) (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))) (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))) (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))) (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 ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 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 X3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S)) X3) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X3) _let_2))) _let_4))))))) (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_Code_integer))))))) (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_nat))))))) (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_int))))))) (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.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))) (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))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_integer))))))) (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N)))) (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) N)))) (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N)))) (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (@ _let_1 A))))) (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (@ _let_1 A))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (@ _let_1 A))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))) (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X3 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 X3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd2)) X3) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X3) _let_2))) _let_4))))))) (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (=> (@ (@ tptp.ord_less_eq_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K) L2)) L2)) tptp.one_one_int))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X3 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 X3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Vc)) X3) (or (= X3 Mi) (= X3 Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X3) _let_2))) _let_4)))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X3)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X3) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X3) (=> (not (= X3 Mi)) (=> (not (= X3 Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X3) _let_2))) _let_4))))))))))))))) (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.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))) (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 ((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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_rat (@ _let_2 D)) (@ _let_1 C)))))))) (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 ((W tptp.real) (Y tptp.real) (X3 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X3))) (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 X3) (= Y Z)))))) (forall ((W tptp.rat) (Y tptp.rat) (X3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X3))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X3) (= Y Z)))))) (forall ((W tptp.nat) (Y tptp.nat) (X3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X3))) (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 X3) (= Y Z)))))) (forall ((W tptp.int) (Y tptp.int) (X3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X3))) (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 X3) (= Y Z)))))) (forall ((X3 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 X3) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X3) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X3)) Y)))))) (forall ((X3 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 X3) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X3)) Y)))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X3) Y)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X3) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X3)) Y)))))) (forall ((X3 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 X3) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X3) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X3)) Y)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))) (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)))) (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)) (= X3 (@ (@ (@ (@ 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))))))))))) (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X3) Xa2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (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)) (= X3 (@ (@ (@ (@ 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 ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X3) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) 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)) (= X3 (@ (@ (@ (@ 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 ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N))))))) (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X3) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ 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)) (= X3 (@ (@ (@ (@ 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 ((Vd tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (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 ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) _let_2) (= (@ (@ tptp.minus_8373710615458151222nteger _let_2) B) (@ _let_1 B)))))))) (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 ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_1 (= A tptp.zero_zero_rat))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))) (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X3) Xa2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high 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)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) 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 ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X3) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (not (= X3 (@ (@ tptp.vEBT_Leaf Uu) Uv)))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ 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)) (= X3 (@ (@ (@ (@ 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 ((Vd tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))) (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X3) Xa2) Y) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X3 (@ (@ tptp.vEBT_Leaf Uu) Uv))) Y) (=> (=> (exists ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2))) Y) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ 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)) (= X3 (@ (@ (@ (@ 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 ((Vd tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (= 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 ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X3) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X3))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X3) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X3 Mi) (= X3 Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X3) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))) (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X3) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X3 (@ (@ (@ (@ 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)) (= X3 (@ (@ (@ (@ 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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high 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)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) 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 ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X3 (@ (@ (@ (@ 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 (= X3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high 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)) (= X3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) 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.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))))) (forall ((L2 tptp.num) (R2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L2) (@ (@ tptp.product_Pair_nat_nat Q2) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R2))))))))) (forall ((L2 tptp.num) (R2 tptp.int) (Q2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L2) (@ (@ tptp.product_Pair_int_int Q2) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_int L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R2))))))))) (forall ((L2 tptp.num) (R2 tptp.code_integer) (Q2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L2) (@ (@ tptp.produc1086072967326762835nteger Q2) R2)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R2))))))))) (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 ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X3) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 _let_2) (=> (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B5))) (=> (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) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) (=> (= X3 _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) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (=> (= X3 _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))) (=> (= X3 _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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat 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))) (=> (= X3 _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 ((X3 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 X3) _let_1) (@ (@ tptp.divide_divide_nat Y) _let_1)) (=> (= (@ _let_2 X3) (@ _let_2 Y)) (= X3 Y)))))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (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_nu8557863876264182079omplex tptp.one_one_complex) _let_88) (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) _let_50) (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) _let_87) (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) _let_89) (forall ((X3 tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X3) Y) (=> (=> (= X3 tptp.zero_zero_nat) _let_1) (=> (=> (= X3 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X3 _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 ((I2 tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool)) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (=> (@ P X3) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X3)) I2))))) (forall ((I2 tptp.nat) (N tptp.nat) (P (-> tptp.int Bool)) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N) (=> (@ P X3) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X3)) I2))))) (forall ((I2 tptp.nat) (N tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N) (=> (@ P X3) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X3)) I2))))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))) (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)) (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)) (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)) (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)) (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K))) (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((I2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ _let_1 (@ _let_1 I2)) I2)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) K))))) (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)) (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)) (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.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) B))) (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 ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))) (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))) (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))) (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))) (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))) (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))) (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real) (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat) (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.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.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))) (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) B))) (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= M N))) (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.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.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.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat 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.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.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.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) 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.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.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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B))))) (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.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real 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.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat 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.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real 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.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) 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.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.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.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))) (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))) (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 ((X3 tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X3)) Y) (@ (@ tptp.dvd_dvd_int X3) Y))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X3)) Y) (@ (@ tptp.dvd_dvd_real X3) Y))) (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X3)) Y) (@ (@ tptp.dvd_dvd_complex X3) Y))) (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.uminus1351360451143612070nteger X3)) Y) (@ (@ tptp.dvd_dvd_Code_integer X3) Y))) (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X3)) Y) (@ (@ tptp.dvd_dvd_rat X3) Y))) (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X3))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X3))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y)) (@ _let_1 Y)))) (forall ((X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X3))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y)) (@ _let_1 Y)))) (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X3))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger Y)) (@ _let_1 Y)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X3))) (= (@ _let_1 (@ tptp.uminus_uminus_rat Y)) (@ _let_1 Y)))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))) (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 ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat I2) (@ (@ tptp.minus_minus_nat J2) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) J2)))) (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J2) K)) I2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J2) I2)) K)))) (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J2) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K))))) (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)) (forall ((M tptp.nat) (X3 tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X3) (@ (@ tptp.replicate_VEBT_VEBT N) Y)) (and (= M N) (=> (not (= M tptp.zero_zero_nat)) (= X3 Y))))) (forall ((N tptp.nat) (X3 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X3)) N)) (forall ((N tptp.nat) (X3 Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N) X3)) N)) (forall ((N tptp.nat) (X3 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N) X3)) N)) (forall ((N tptp.nat) (X3 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N) X3)) N)) (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.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) 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)) (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.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))) (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)) 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.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))) (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)) (= (@ (@ 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.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (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.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.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.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))) (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.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.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))) (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.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))) (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.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.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)) (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.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)) (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.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)) (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))) (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))) (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))) (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int _let_2) _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (let ((_let_2 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real _let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (let ((_let_2 (@ tptp.numeral_numeral_rat M))) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat _let_2)) (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat _let_2) _let_1)))))) (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.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real 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 ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat 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.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real 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.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))) (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.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real 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.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))) (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.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real 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.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat 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 ((X3 tptp.real)) (= (@ (@ tptp.divide_divide_real X3) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X3))) (forall ((X3 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X3) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X3))) (forall ((X3 tptp.rat)) (= (@ (@ tptp.divide_divide_rat X3) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X3))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))) (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 ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J2) K))) I2) (@ (@ tptp.minus_minus_nat (@ tptp.suc J2)) (@ (@ tptp.plus_plus_nat K) I2))))) (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat I2) (@ tptp.suc (@ (@ tptp.minus_minus_nat J2) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ tptp.suc J2))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N) _let_1) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N) _let_1) _let_1))) (forall ((X3 tptp.real) (N tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X3) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) Y))) (and (= X3 Y) (not (= N tptp.zero_zero_nat))))) (forall ((X3 tptp.complex) (N tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N) Y))) (and (= X3 Y) (not (= N tptp.zero_zero_nat))))) (forall ((X3 tptp.product_prod_nat_nat) (N tptp.nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.replic4235873036481779905at_nat N) Y))) (and (= X3 Y) (not (= N tptp.zero_zero_nat))))) (forall ((X3 tptp.int) (N tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X3) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) Y))) (and (= X3 Y) (not (= N tptp.zero_zero_nat))))) (forall ((X3 tptp.nat) (N tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) Y))) (and (= X3 Y) (not (= N tptp.zero_zero_nat))))) (forall ((X3 tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) Y))) (and (= X3 Y) (not (= N tptp.zero_zero_nat))))) (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))) (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))) (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))) (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))) (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N) (@ tptp.pred_numeral K)))) (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N))) (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))) (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))) (forall ((I2 tptp.nat) (N tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X3)) I2) X3))) (forall ((I2 tptp.nat) (N tptp.nat) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X3)) I2) X3))) (forall ((I2 tptp.nat) (N tptp.nat) (X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X3)) I2) X3))) (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.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.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))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_numeral_dbl_rat _let_1))))) (= (@ 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_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat) (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int) (= (@ tptp.neg_nu5851722552734809277nc_int _let_5) _let_5) (= (@ tptp.neg_nu8295874005876285629c_real _let_11) _let_11) (= (@ tptp.neg_nu8557863876264182079omplex _let_45) _let_45) (= (@ tptp.neg_nu5831290666863070958nteger _let_81) _let_81) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_4) _let_4) (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_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))) (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (= (@ _let_132 _let_5) tptp.zero_zero_int) (= (@ _let_131 _let_11) tptp.zero_zero_real) (= (@ _let_40 _let_45) tptp.zero_zero_complex) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) _let_81) tptp.zero_z3403309356797280102nteger) (= (@ _let_130 _let_4) tptp.zero_zero_rat) (= (@ _let_129 tptp.one_one_int) tptp.zero_zero_int) (= (@ _let_128 tptp.one_one_real) tptp.zero_zero_real) (= (@ _let_127 tptp.one_one_complex) tptp.zero_zero_complex) (= (@ _let_126 tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) (= (@ _let_125 tptp.one_one_rat) tptp.zero_zero_rat) (= (@ _let_120 _let_5) tptp.zero_zero_int) (= (@ _let_119 _let_11) tptp.zero_zero_real) (= (@ _let_118 _let_45) tptp.zero_zero_complex) (= (@ _let_117 _let_81) tptp.zero_z3403309356797280102nteger) (= (@ _let_116 _let_4) tptp.zero_zero_rat) (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))) (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (= N tptp.one))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)))) (= (@ _let_1 (@ _let_1 A)) A))) (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_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (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_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (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_rat U))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (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 ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))) (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.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.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 ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W)))) Y))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))) (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.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.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 ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ 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.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.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.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ 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.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.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.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N) (@ tptp.pred_numeral K)))) (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N))) (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.pred_numeral K)))) (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_eq_num N) M))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_eq_num N) M))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_eq_num N) M))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_eq_num N) M))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_num N) M))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_num N) M))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_num N) M))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_num N) M))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) (@ tptp.pred_numeral K))))) (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N)))) (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_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat 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 ((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 ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))) (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 ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))) (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 ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))) (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 ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))) (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_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_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (not (= M tptp.one)))) (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 ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))) (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 ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))) (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.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.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 ((A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))) (= (@ _let_129 _let_5) _let_113) (= (@ _let_128 _let_11) _let_112) (= (@ _let_127 _let_45) _let_111) (= (@ _let_126 _let_81) _let_110) (= (@ _let_125 _let_4) _let_109) (= (@ _let_124 _let_5) _let_36) (= (@ _let_123 _let_11) _let_13) (= (@ _let_122 _let_45) _let_42) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) _let_81) _let_30) (= (@ _let_121 _let_4) _let_66) (= (@ _let_120 tptp.one_one_int) _let_113) (= (@ _let_119 tptp.one_one_real) _let_112) (= (@ _let_118 tptp.one_one_complex) _let_111) (= (@ _let_117 tptp.one_one_Code_integer) _let_110) (= (@ _let_116 tptp.one_one_rat) _let_109) (= (@ (@ tptp.divide_divide_int _let_5) _let_36) _let_5) (= (@ (@ tptp.divide6298287555418463151nteger _let_81) _let_30) _let_81) _let_115 _let_114 _let_115 _let_114 (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))) (forall ((N tptp.nat) (A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int A) N))))) (forall ((N tptp.nat) (A tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real A) N))))) (forall ((N tptp.nat) (A tptp.complex)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex A) N))))) (forall ((N tptp.nat) (A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger A) N))))) (forall ((N tptp.nat) (A tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat A) N))))) (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.power_power_int A) N)))) (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.power_power_real A) N)))) (forall ((N tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.power_power_complex A) N)))) (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.power_8256067586552552935nteger A) N)))) (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.power_power_rat A) N)))) (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (or (@ (@ tptp.ord_less_nat M) N) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)))))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))) (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_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_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 ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) tptp.one))))) (= (@ tptp.neg_numeral_dbl_int _let_5) _let_113) (= (@ tptp.neg_numeral_dbl_real _let_11) _let_112) (= (@ tptp.neg_nu7009210354673126013omplex _let_45) _let_111) (= (@ tptp.neg_nu8804712462038260780nteger _let_81) _let_110) (= (@ tptp.neg_numeral_dbl_rat _let_4) _let_109) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_real)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_complex)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_Code_integer)) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_rat)) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int _let_1) N) _let_1)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real _let_1) N) _let_1)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_complex _let_1) N) _let_1)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) N) _let_1)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat _let_1) N) _let_1)))) (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N) tptp.one_one_int))) (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N) tptp.one_one_real))) (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N) tptp.one_one_complex))) (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N) tptp.one_one_Code_integer))) (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N) tptp.one_one_rat))) (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 ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (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 ((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))) (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (= (= X3 (@ (@ tptp.minus_minus_real Y) Z)) (= Y (@ (@ tptp.plus_plus_real X3) Z)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))) (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))) (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))) (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.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_eq_rat B) (@ tptp.uminus_uminus_rat A)))) (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.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) A))) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))) (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 ((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.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.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_rat B) (@ tptp.uminus_uminus_rat A)))) (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.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.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) A))) (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.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.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))) (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)))) (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)))) (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)))) (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)))) (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)))) (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))) (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))) (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))) (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))) (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))) (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.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.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.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) A) (@ (@ tptp.times_times_rat B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_rat B))))) (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.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.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.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.times_times_rat A) (@ tptp.uminus_uminus_rat B)))) (not (= tptp.one_one_int _let_5)) (not (= tptp.one_one_real _let_11)) (not (= tptp.one_one_complex _let_45)) (not (= tptp.one_one_Code_integer _let_81)) (not (= tptp.one_one_rat _let_4)) (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.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.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 ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))) (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.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.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 ((A2 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A2 (@ (@ tptp.plus_plus_rat K) A)) (= (@ tptp.uminus_uminus_rat A2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ tptp.uminus_uminus_rat A))))) (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.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.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 ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))) (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B)) A) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) B))) (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real B)) A) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) B))) (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))) (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat B)) A) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) B))) (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.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.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.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)))) (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)) (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 ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B))))) (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.rat) (B tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat 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.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I2 tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P (@ (@ tptp.minus_minus_nat K) I2))))) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))) (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L2) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))) (forall ((J2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J2) N)) K))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) (or (@ (@ tptp.ord_less_nat N) M) (@ _let_1 N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))) (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L2)) (@ (@ tptp.minus_minus_nat N) L2)))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) 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) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 M)))))) (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) (A4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) (@ (@ tptp.modulo_modulo_int A4) B)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A4)) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (A4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) (@ (@ tptp.modulo364778990260209775nteger A4) B)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A4)) 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 ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M) N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M) N))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N))))) (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X5)) (@ _let_2 Y3)) D3) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X5)) (@ _let_1 Y3)) D3)))))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))) (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))) (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))) (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))) (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))) (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))) (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))) (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))) (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))) (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))) (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))) (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))) (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))) (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))) (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))) (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))) (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))) (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))) (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))) (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))) (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))) (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))) (@ _let_100 tptp.one_one_real) (@ _let_99 tptp.one_one_Code_integer) (@ _let_98 tptp.one_one_rat) (@ _let_97 tptp.one_one_int) (not (@ _let_108 _let_11)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) _let_81)) (not (@ _let_107 _let_4)) (not (@ _let_106 _let_5)) (not (= tptp.zero_zero_int _let_5)) (not (= tptp.zero_zero_real _let_11)) (not (= tptp.zero_zero_complex _let_45)) (not (= tptp.zero_z3403309356797280102nteger _let_81)) (not (= tptp.zero_zero_rat _let_4)) (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.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real 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)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)) (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.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)) (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.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real 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.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))) (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.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))) (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.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))) (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.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))) (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.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))) (@ _let_94 tptp.one_one_int) (@ _let_93 tptp.one_one_real) (@ _let_92 tptp.one_one_Code_integer) (@ _let_91 tptp.one_one_rat) (not (@ _let_105 _let_5)) (not (@ _let_104 _let_11)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) _let_81)) (not (@ _let_103 _let_4)) (forall ((W tptp.num) (X3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X3)) (@ (@ tptp.times_times_int X3) (@ tptp.uminus_uminus_int _let_1))))) (forall ((W tptp.num) (X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X3)) (@ (@ tptp.times_times_real X3) (@ tptp.uminus_uminus_real _let_1))))) (forall ((W tptp.num) (X3 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X3)) (@ (@ tptp.times_times_complex X3) (@ tptp.uminus1482373934393186551omplex _let_1))))) (forall ((W tptp.num) (X3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X3)) (@ (@ tptp.times_3573771949741848930nteger X3) (@ tptp.uminus1351360451143612070nteger _let_1))))) (forall ((W tptp.num) (X3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X3)) (@ (@ tptp.times_times_rat X3) (@ tptp.uminus_uminus_rat _let_1))))) (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 ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B)))))) (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.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B)))) (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))) (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))) (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))) (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))) (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))) (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((X3 tptp.int)) (= (= (@ (@ tptp.times_times_int X3) X3) tptp.one_one_int) (or (= X3 tptp.one_one_int) (= X3 (@ tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((X3 tptp.real)) (= (= (@ (@ tptp.times_times_real X3) X3) tptp.one_one_real) (or (= X3 tptp.one_one_real) (= X3 (@ tptp.uminus_uminus_real tptp.one_one_real))))) (forall ((X3 tptp.complex)) (= (= (@ (@ tptp.times_times_complex X3) X3) tptp.one_one_complex) (or (= X3 tptp.one_one_complex) (= X3 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))) (forall ((X3 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X3) X3) tptp.one_one_Code_integer) (or (= X3 tptp.one_one_Code_integer) (= X3 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((X3 tptp.rat)) (= (= (@ (@ tptp.times_times_rat X3) X3) tptp.one_one_rat) (or (= X3 tptp.one_one_rat) (= X3 (@ tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((B3 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B3 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))) (forall ((B3 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B3 (@ (@ tptp.plus_plus_real K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B)))))) (forall ((B3 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B3 (@ (@ tptp.plus_plus_complex K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B)))))) (forall ((B3 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B3 (@ (@ tptp.plus_p5714425477246183910nteger K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B)))))) (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B3 (@ (@ tptp.plus_plus_rat K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B)))))) (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))) (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))) (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))) (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))) (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))) (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))) (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))) (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))) (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))) (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))) (forall ((Xs tptp.list_real) (N tptp.nat) (X3 tptp.real)) (=> (= (@ tptp.size_size_list_real Xs) N) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs)) (= Y3 X3))) (= Xs (@ (@ tptp.replicate_real N) X3))))) (forall ((Xs tptp.list_complex) (N tptp.nat) (X3 tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs) N) (=> (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) (@ tptp.set_complex2 Xs)) (= Y3 X3))) (= Xs (@ (@ tptp.replicate_complex N) X3))))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (N tptp.nat) (X3 tptp.product_prod_nat_nat)) (=> (= (@ tptp.size_s5460976970255530739at_nat Xs) N) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y3) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (= Y3 X3))) (= Xs (@ (@ tptp.replic4235873036481779905at_nat N) X3))))) (forall ((Xs tptp.list_VEBT_VEBT) (N tptp.nat) (X3 tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N) (=> (forall ((Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y3) (@ tptp.set_VEBT_VEBT2 Xs)) (= Y3 X3))) (= Xs (@ (@ tptp.replicate_VEBT_VEBT N) X3))))) (forall ((Xs tptp.list_o) (N tptp.nat) (X3 Bool)) (=> (= (@ tptp.size_size_list_o Xs) N) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ tptp.set_o2 Xs)) (= Y3 X3))) (= Xs (@ (@ tptp.replicate_o N) X3))))) (forall ((Xs tptp.list_nat) (N tptp.nat) (X3 tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs) N) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs)) (= Y3 X3))) (= Xs (@ (@ tptp.replicate_nat N) X3))))) (forall ((Xs tptp.list_int) (N tptp.nat) (X3 tptp.int)) (=> (= (@ tptp.size_size_list_int Xs) N) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs)) (= Y3 X3))) (= Xs (@ (@ tptp.replicate_int N) X3))))) (forall ((Xs tptp.list_VEBT_VEBT) (X3 tptp.vEBT_VEBT)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (= X5 X3))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs)) X3) Xs))) (forall ((Xs tptp.list_o) (X3 Bool)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (= X5 X3))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs)) X3) Xs))) (forall ((Xs tptp.list_nat) (X3 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (= X5 X3))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs)) X3) Xs))) (forall ((Xs tptp.list_int) (X3 tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (= X5 X3))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs)) X3) Xs))) (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.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.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 ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))))) (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.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.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.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B)))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) M))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M) N)))))) (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 ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat J2) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) J2))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (= (@ (@ tptp.minus_minus_nat J2) I2) K) (= J2 (@ (@ tptp.plus_plus_nat K) I2))))) (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J2) I2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J2) K)) I2)))) (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J2) K)))))) (forall ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat J2) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) J2)))) (forall ((J2 tptp.nat) (K tptp.nat) (I2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J2) K)) I2) (@ (@ tptp.ord_less_eq_nat J2) (@ (@ tptp.plus_plus_nat I2) K)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))) (forall ((M tptp.int) (N tptp.int)) (=> (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (@ tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (and (= M tptp.one_one_int) (= N tptp.one_one_int)) (and (= M _let_1) (= N _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))) (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M6) N2)) M6) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M6) N2)) N2)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))) (forall ((N tptp.nat) (M tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (@ (@ tptp.dvd_dvd_nat Q2) (@ (@ tptp.minus_minus_nat M) N))))) (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))) (forall ((K tptp.int) (L2 tptp.int)) (=> (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L2) tptp.zero_zero_int)) (not (= (@ (@ tptp.modulo_modulo_int K) L2) tptp.zero_zero_int)))) (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int K))) (=> (not (= (@ _let_1 (@ tptp.uminus_uminus_int L2)) tptp.zero_zero_int)) (not (= (@ _let_1 L2) tptp.zero_zero_int))))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N) M)) M) (@ (@ tptp.ord_max_nat N) M))) (forall ((Z tptp.extended_enat) (Y tptp.extended_enat) (X3 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X3))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y)) Z))))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)) (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)) (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))) (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)) (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)) (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)) (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))) (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))) (not (@ _let_70 _let_11)) (not (@ _let_31 _let_81)) (not (@ _let_102 _let_4)) (not (@ _let_101 _let_5)) (@ _let_100 tptp.zero_zero_real) (@ _let_99 tptp.zero_z3403309356797280102nteger) (@ _let_98 tptp.zero_zero_rat) (@ _let_97 tptp.zero_zero_int) (not (@ _let_96 _let_5)) (not (@ _let_71 _let_11)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) _let_81)) (not (@ _let_95 _let_4)) (@ _let_94 tptp.zero_zero_int) (@ _let_93 tptp.zero_zero_real) (@ _let_92 tptp.zero_z3403309356797280102nteger) (@ _let_91 tptp.zero_zero_rat) (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_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)) (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_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat 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_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (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_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (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_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat 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)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)) (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_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)) (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)) (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_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real 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_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))) (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_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (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_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real 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_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat 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_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_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))) (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.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))) (= (@ (@ tptp.times_times_rat C) B) (@ tptp.uminus_uminus_rat A))))) (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.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) C) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.times_times_rat C) B))))) (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 ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B) (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (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 ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) (@ tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (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))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B tptp.zero_zero_rat)) (= A (@ tptp.uminus_uminus_rat B))))) (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.real)) (= (@ (@ tptp.times_times_real B) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) (@ tptp.uminus_uminus_real 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 ((B tptp.rat)) (= (@ (@ tptp.times_times_rat B) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) (@ tptp.uminus_uminus_rat 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.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) B) (@ tptp.uminus_uminus_real 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.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) B) (@ tptp.uminus_uminus_rat B))) (= (@ tptp.uminus_uminus_int _let_90) _let_5) (= (@ tptp.uminus_uminus_real _let_62) _let_11) (= (@ tptp.uminus1482373934393186551omplex _let_61) _let_45) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_81) (= (@ tptp.uminus_uminus_rat _let_60) _let_4) (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ (@ tptp.power_power_int A) N)))) (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.power_power_real A) N)))) (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ (@ tptp.power_power_complex A) N)))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ (@ tptp.power_8256067586552552935nteger A) N)))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ (@ tptp.power_power_rat A) N)))) (forall ((X3 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X3)) _let_1) (@ (@ tptp.power_power_int X3) _let_1)))) (forall ((X3 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X3)) _let_1) (@ (@ tptp.power_power_real X3) _let_1)))) (forall ((X3 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X3)) _let_1) (@ (@ tptp.power_power_complex X3) _let_1)))) (forall ((X3 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X3)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X3) _let_1)))) (forall ((X3 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X3)) _let_1) (@ (@ tptp.power_power_rat X3) _let_1)))) (forall ((X3 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X3)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X3) _let_1))))) (forall ((X3 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X3)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X3) _let_1))))) (forall ((X3 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X3)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X3) _let_1))))) (forall ((X3 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X3)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X3) _let_1))))) (forall ((X3 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X3)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X3) _let_1))))) (forall ((N tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I2))) N))) (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 ((K tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J2) K)) I2) (@ (@ tptp.ord_less_nat J2) (@ (@ tptp.plus_plus_nat I2) K))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))) (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M)) N)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))) (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) 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 J2) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M)) N)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))) (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M) N)))) (forall ((Q2 tptp.nat) (N tptp.nat) (R2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R2) M))) (let ((_let_2 (@ tptp.dvd_dvd_nat M))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q2))) (=> (@ _let_3 N) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N) Q2)) (@ _let_2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat _let_1) Q2)))))))))) (forall ((R2 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R2) N) (=> (@ (@ tptp.ord_less_eq_nat R2) M) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M) R2)) (= (@ (@ tptp.modulo_modulo_nat M) N) R2))))) (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N2)) N2)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= _let_1 tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int B) _let_1)))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= _let_2 tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) 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.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.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))) (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.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))) (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.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))) (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 ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))) (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 ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B))) (let ((_let_4 (@ (@ tptp.times_times_rat A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))) (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 ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))) (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 ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (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 ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))) (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X3) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X3)) (@ (@ tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.complex) (X3 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X3) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X3)) (@ (@ tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X3) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X3)) (@ (@ tptp.times_times_rat Y) Z))) Z)))) (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X3) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X3)) (@ (@ tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.complex) (X3 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X3) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X3)) (@ (@ tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X3) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X3)) (@ (@ tptp.times_times_rat 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.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))) (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 ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))) (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 ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X3) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (or (= X3 Y) (= X3 (@ tptp.uminus_uminus_int Y)))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X3) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (or (= X3 Y) (= X3 (@ tptp.uminus_uminus_real Y)))))) (forall ((X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X3) _let_1) (@ (@ tptp.power_power_complex Y) _let_1)) (or (= X3 Y) (= X3 (@ tptp.uminus1482373934393186551omplex Y)))))) (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X3) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (or (= X3 Y) (= X3 (@ tptp.uminus1351360451143612070nteger Y)))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X3) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (or (= X3 Y) (= X3 (@ tptp.uminus_uminus_rat Y)))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (let ((_let_2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))) (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))) (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1482373934393186551omplex _let_1)))))))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))) (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))) (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M)) (@ _let_1 N))))))) (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_real (@ _let_1 M)) (@ _let_1 N))))))) (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_rat (@ _let_1 M)) (@ _let_1 N))))))) (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N))))))) (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N))))))) (= 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_nu5219082963157363817nc_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))) (= tptp.neg_nu5851722552734809277nc_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))) (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M6) N2) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M6) N2)) N2))))) (= tptp.plus_plus_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N2))))) (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M)) N)))) (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N))))) (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N2))))) (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B3) N)) (@ (@ tptp.divide_divide_int A2) N))))) (forall ((B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.divide_divide_int _let_1) B) _let_1)))) (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.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))) (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.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))) (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.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))) (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 ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))) (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 ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))) (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 ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))) (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 ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))) (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)))))))))))) (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))) (= tptp.bit_ri6519982836138164636nteger (lambda ((N2 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A3) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N2 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger _let_2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))))))))) (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A3) _let_1))) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int _let_2)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) _let_1))))))))) (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.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.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 ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (or (= A tptp.one_one_rat) (= A (@ tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (@ (@ tptp.power_power_complex _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_2 (@ (@ tptp.power_power_rat _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_zero_nat)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_zero_nat))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_zero_int)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_zero_int))))) (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))) (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))) (= 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_rat (lambda ((P4 tptp.rat) (M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P4) (@ (@ tptp.power_power_rat 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 ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))) (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))) (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))) (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L2) (@ (@ tptp.minus_minus_int (@ (@ tptp.minus_minus_int L2) tptp.one_one_int)) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) L2))))) (forall ((B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) B) (@ (@ tptp.minus_minus_int B) tptp.one_one_int)))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B)))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ _let_1 B)))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R2 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q2))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (not (= B tptp.zero_zero_int)) (@ (@ (@ tptp.eucl_rel_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.product_Pair_int_int (@ (@ _let_1 _let_2) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int))) (@ (@ _let_1 tptp.zero_zero_int) (@ (@ tptp.minus_minus_int B) R2))))))))) (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 ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))) (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 ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X3) (=> (@ (@ tptp.ord_le3102999989581377725nteger X3) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X3) (=> (@ (@ tptp.ord_less_eq_rat X3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X3) (=> (@ (@ tptp.ord_less_eq_int X3) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) (@ (@ tptp.power_power_complex A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) _let_1))) (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 ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) K))) (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))) (forall ((X3 tptp.nat)) (=> (not (= X3 tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X3 (@ tptp.suc N3))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) _let_3)) _let_2))))))) (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 ((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 ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))) (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K) (@ tptp.uminus_uminus_int (@ _let_1 N))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))) (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))) (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))) (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)) (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 ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X3) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X3 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) (=> (= X3 _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))) (=> (= X3 _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))) (=> (= X3 _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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high 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))) (=> (= X3 _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 ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X3) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 _let_1) (=> (= Y (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B5) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) (=> (= X3 _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))) (=> (= X3 _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))) (=> (= X3 _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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high 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)))) (=> (= X3 _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 ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X3) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X3 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) (=> (= X3 _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))) (=> (= X3 _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 ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X3) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X3 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (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))) (=> (= X3 _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 ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X3) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X3 _let_1) (=> (= Y (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B5) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) (=> (= X3 _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)))) (=> (= X3 _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 ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X3) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X3 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high 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))) (=> (= X3 _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 ((X3 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X3) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X3 A))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J2)))) (= tptp.minus_minus_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real Y6)))) (forall ((U tptp.real) (X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X3) X3))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X3)) Y))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X3) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) (@ tptp.uminus_uminus_real X3)))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X3)) Y))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X3) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.uminus_uminus_real X3)))) (forall ((C tptp.real)) (= (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C)) (@ tptp.times_times_real C))) (forall ((C tptp.rat)) (= (lambda ((X2 tptp.rat)) (@ (@ tptp.times_times_rat X2) C)) (@ tptp.times_times_rat 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))) (forall ((U tptp.real) (X3 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 X3) _let_1)))) (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X3) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X3 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2))) (=> (= X3 _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))) (=> (= X3 _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)))) (=> (= X3 _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) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (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)))) (=> (= X3 _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 ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X3) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X3 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2))) (=> (= X3 _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))) (=> (= X3 _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))) (=> (= X3 _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) (Vd 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) Vd))) (=> (= X3 _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 ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X3) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) 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))) (=> (= X3 _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))) (=> (= X3 _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) (Vd 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) Vd))) (=> (= X3 _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 ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (not (= A2 B3)) (@ (@ tptp.ord_less_set_int A2) B3)))) (forall ((X3 tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X3)) (@ tptp.uminus1532241313380277803et_int Y)) (@ (@ tptp.ord_less_eq_set_int Y) X3))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X5))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_nat A2) B3))) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.member_real X5))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_real A2) B3))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (forall ((X5 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X5))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_le211207098394363844omplex A2) B3))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X5 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X5))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.member_int X5))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_int A2) B3))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= A2 B3)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int A2)) (@ tptp.uminus1532241313380277803et_int B3)) (@ (@ tptp.ord_less_eq_set_int B3) A2))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int B3)) (@ tptp.uminus1532241313380277803et_int A2)))) (forall ((L2 tptp.set_int) (H2 tptp.set_int) (L3 tptp.set_int) (H3 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int L2) H2) (@ (@ tptp.set_or370866239135849197et_int L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_int L2) H2)) (not (@ (@ tptp.ord_less_eq_set_int L3) H3)))))) (forall ((L2 tptp.rat) (H2 tptp.rat) (L3 tptp.rat) (H3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L2) H2) (@ (@ tptp.set_or633870826150836451st_rat L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_rat L2) H2)) (not (@ (@ tptp.ord_less_eq_rat L3) H3)))))) (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_int) (L2 tptp.set_int) (U tptp.set_int)) (= (@ (@ tptp.member_set_int I2) (@ (@ tptp.set_or370866239135849197et_int L2) U)) (and (@ (@ tptp.ord_less_eq_set_int L2) I2) (@ (@ tptp.ord_less_eq_set_int I2) U)))) (forall ((I2 tptp.rat) (L2 tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ (@ tptp.set_or633870826150836451st_rat L2) U)) (and (@ (@ tptp.ord_less_eq_rat L2) I2) (@ (@ tptp.ord_less_eq_rat I2) U)))) (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 ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ (@ tptp.ord_less_eq_set_int C) A) (@ (@ tptp.ord_less_eq_set_int B) D))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat B) D))))) (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 ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ P M6))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (@ P M6))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (= (@ (@ tptp.ord_less_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_int B) D) (or (@ (@ tptp.ord_less_set_int C) A) (@ (@ tptp.ord_less_set_int B) D)))) (@ _let_1 D))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) D) (or (@ (@ tptp.ord_less_rat C) A) (@ (@ tptp.ord_less_rat B) D)))) (@ _let_1 D))))) (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 ((A2 tptp.set_nat) (C5 tptp.set_nat) (D4 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C5) (=> (@ (@ tptp.ord_less_eq_set_nat D4) B3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_set_nat C5) D4))))) (forall ((A2 tptp.set_int) (C5 tptp.set_int) (D4 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int D4) B3) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_set_int C5) D4))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B3)) A2)) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B3)) A2)) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C5) (= (@ (@ tptp.minus_minus_set_nat B3) (@ (@ tptp.minus_minus_set_nat C5) A2)) A2)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C5) (= (@ (@ tptp.minus_minus_set_int B3) (@ (@ tptp.minus_minus_set_int C5) A2)) A2)))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_real) (B3 tptp.set_real) (X3 tptp.real)) (let ((_let_1 (@ tptp.member_real X3))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (X3 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X3))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (X3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X3))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_real) (B3 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (not (@ (@ tptp.ord_less_eq_set_int B3) A2)))))) (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))) (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))) (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))) (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B7 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))) (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (@ (@ tptp.ord_less_eq_set_int A2) B3))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (@ (@ tptp.ord_less_eq_set_int B3) A2))) (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))) (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (forall ((T2 tptp.real)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))) (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (forall ((T2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))) (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B7 tptp.set_Pr1261947904930325089at_nat)) (forall ((T2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))) (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))) (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)) (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.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.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.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 ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C5 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C5) (@ _let_1 C5))))) (= (lambda ((Y5 tptp.set_int) (Z3 tptp.set_int)) (= Y5 Z3)) (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B7) (@ (@ tptp.ord_less_eq_set_int B7) A6)))) (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.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.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.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))))) (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)) (forall ((X2 tptp.int)) (=> (@ P X2) (@ Q X2))))) (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_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_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_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 ((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)) (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A6))) (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) B7))))) (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A6))) (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) B7))))) (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (@ (@ tptp.ord_le4573692005234683329plex_o (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A6))) (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) B7))))) (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B7 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le704812498762024988_nat_o (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A6))) (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) B7))))) (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A6))) (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) B7))))) (forall ((Y tptp.set_int) (X3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) X3) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X3)) Y))) (forall ((Y tptp.set_int) (X3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) (@ tptp.uminus1532241313380277803et_int X3)) (@ (@ tptp.ord_less_eq_set_int X3) (@ tptp.uminus1532241313380277803et_int Y)))) (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X3) Y) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) (@ tptp.uminus1532241313380277803et_int X3)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ (@ tptp.ord_less_eq_set_int B3) A2))))) (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B7) (not (= A6 B7))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (@ (@ tptp.ord_less_eq_set_int A2) B3))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C5 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C5) (@ _let_1 C5))))) (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B7) (not (@ (@ tptp.ord_less_eq_set_int B7) A6))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_set_int B3) C5) (@ (@ tptp.ord_less_set_int A2) C5)))) (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A6) B7) (= A6 B7)))) (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A5 tptp.real) (B5 tptp.real) (C3 tptp.real)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B5) (=> (@ (@ P B5) C3) (=> (@ (@ tptp.ord_less_eq_real A5) B5) (=> (@ (@ tptp.ord_less_eq_real B5) C3) (@ _let_1 C3))))))) (=> (forall ((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 ((A5 tptp.real) (B5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A5) X5) (@ (@ tptp.ord_less_eq_real X5) B5) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B5) A5)) D5)) (@ (@ P A5) B5)))))))) (@ (@ P A) B))))) (= (@ tptp.neg_nu3811975205180677377ec_int _let_5) (@ tptp.uminus_uminus_int _let_89)) (= (@ tptp.neg_nu6075765906172075777c_real _let_11) (@ tptp.uminus_uminus_real _let_50)) (= (@ tptp.neg_nu6511756317524482435omplex _let_45) (@ tptp.uminus1482373934393186551omplex _let_88)) (= (@ tptp.neg_nu7757733837767384882nteger _let_81) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger _let_49))) (= (@ tptp.neg_nu3179335615603231917ec_rat _let_4) (@ tptp.uminus_uminus_rat _let_87)) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (= tptp.nat_triangle (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((X3 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 X3) Y) (=> (@ _let_2 X3) (=> (=> (= X3 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X3 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X3 _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)))))))))))))))))))))) (= (@ 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_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat) (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N)) _let_1)))) (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) _let_5) (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) _let_11) (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) _let_45) (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) _let_81) (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) _let_4) (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.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.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_rat K))) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu3179335615603231917ec_rat _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.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.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)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu5219082963157363817nc_rat _let_1))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N) M)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N) M)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.unique5706413561485394159nteger (@ (@ tptp.unique3479559517661332726nteger N) M)))) (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 ((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.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))) (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))) (forall ((D4 tptp.int) (B3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D4))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.minus_minus_int X5) D4))))) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1))))))))) (forall ((D4 tptp.int) (B3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D4))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.minus_minus_int X5) D4))))) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (or (@ P X) (@ Q X)) (or (@ P _let_1) (@ Q _let_1))))))))) (forall ((D4 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D4))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.plus_plus_int X5) D4))))) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1))))))))) (forall ((D4 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D4))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.plus_plus_int X5) D4))))) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (or (@ P X) (@ Q X)) (or (@ P _let_1) (@ Q _let_1))))))))) (forall ((D tptp.int) (D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X) D4)) T)))))))) (forall ((D tptp.int) (D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X) D4)) T))))))))) (forall ((D tptp.int) (D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T))))))))) (forall ((D tptp.int) (D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T)))))))))) (forall ((D tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (= (exists ((X4 tptp.int)) (@ P X4)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X2))))))) (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B3) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (= X T) (= (@ (@ tptp.minus_minus_int X) D4) T))))))) (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B3) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (= X T)) (not (= (@ (@ tptp.minus_minus_int X) D4) T)))))))) (forall ((D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X) D4)) T)))))) (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B3) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.minus_minus_int X) D4))))))))) (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (= X T) (= (@ (@ tptp.plus_plus_int X) D4) T))))))) (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (= X T)) (not (= (@ (@ tptp.plus_plus_int X) D4) T)))))))) (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) D4)) T))))))) (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.plus_plus_int X) D4)))))))) (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))) (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))) (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))) (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))) (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))) (forall ((D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X) D4)) T)))))) (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B3) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.minus_minus_int X) D4))))))))) (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X) D4)) T))))))) (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.plus_plus_int X) D4)))))))) (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P3 X5) (@ P3 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X4 tptp.int)) (@ P X4)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P3 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) A2) (@ P (@ (@ tptp.minus_minus_int Y6) X2))))))))))))) (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P3 X5) (@ P3 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X4 tptp.int)) (@ P X4)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P3 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) B3) (@ P (@ (@ tptp.plus_plus_int Y6) X2))))))))))))) (= 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_nu3179335615603231917ec_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))) (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))) (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M6) N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.unique5026877609467782581ep_nat N2) (@ (@ tptp.unique5055182867167087721od_nat M6) (@ tptp.bit0 N2)))))) (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M6) N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.unique5024387138958732305ep_int N2) (@ (@ tptp.unique5052692396658037445od_int M6) (@ tptp.bit0 N2)))))) (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M6) N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.unique4921790084139445826nteger N2) (@ (@ tptp.unique3479559517661332726nteger M6) (@ tptp.bit0 N2)))))) (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))) (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))) (forall ((X3 (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X3) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X3 X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X3 (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X3) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X3 X22)) (@ tptp.suc tptp.zero_zero_nat)))) (= 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_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_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))))))))) (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_int)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_rat (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_rat _let_3) tptp.one_one_rat))))))))) (forall ((X3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X3) X3)) (forall ((X3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X3) X3)) (forall ((X3 tptp.num)) (@ (@ tptp.ord_less_eq_num X3) X3)) (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X3) X3)) (forall ((X3 tptp.int)) (@ (@ tptp.ord_less_eq_int X3) X3)) (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)) (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat 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 ((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_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat 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 ((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)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat 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) (N tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N)) (= Z (@ tptp.numeral_numeral_int N)))) (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z) (@ tptp.numeral_numeral_real N)) (= Z (@ tptp.numeral_numeral_int N)))) (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_rat Z) (@ tptp.numeral_numeral_rat N)) (= Z (@ tptp.numeral_numeral_int N)))) (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (= (@ tptp.ring_1_of_int_int Z) _let_1) (= Z _let_1)))) (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_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat 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) (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat) (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 ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))) (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_rat (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))) (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_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 ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))) (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat Z)) N))) (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z)) N))) (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z)) N))) (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z)) N))) (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W) (@ tptp.ring_1_of_int_rat X3)) (= (@ (@ tptp.power_power_int B) W) X3))) (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X3)) (= (@ (@ tptp.power_power_int B) W) X3))) (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X3)) (= (@ (@ tptp.power_power_int B) W) X3))) (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X3)) (= (@ (@ tptp.power_power_int B) W) X3))) (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X3) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (= X3 (@ (@ tptp.power_power_int B) W)))) (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X3) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X3 (@ (@ tptp.power_power_int B) W)))) (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X3) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X3 (@ (@ tptp.power_power_int B) W)))) (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X3) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X3 (@ (@ tptp.power_power_int B) W)))) (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)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (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_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_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ 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_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_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ 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 ((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)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat 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) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))) (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))) (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_eq_int Z) _let_1)))) (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))) (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))) (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))) (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))) (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))) (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_int Z) _let_1)))) (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))) (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))) (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))) (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)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))) (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_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ 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)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat 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_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ 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 ((B tptp.int) (W tptp.nat) (X3 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 X3)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X3))) (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X3)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X3))) (forall ((B tptp.int) (W tptp.nat) (X3 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 X3)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X3))) (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X3)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X3) (@ (@ tptp.power_power_int B) W)))) (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X3)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_eq_int X3) (@ (@ tptp.power_power_int B) W)))) (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X3)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X3) (@ (@ tptp.power_power_int B) W)))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X3)) N) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N) Y))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N) Y))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N) Y))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))) (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X3)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))) (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))) (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))) (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))) (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X3)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X3))) (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X3)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X3))) (forall ((B tptp.int) (W tptp.nat) (X3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X3)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X3))) (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X3)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X3) (@ (@ tptp.power_power_int B) W)))) (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X3)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_int X3) (@ (@ tptp.power_power_int B) W)))) (forall ((X3 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X3)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X3) (@ (@ tptp.power_power_int B) W)))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)) A))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)) A))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)) A))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)) A))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X3))) N) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N) Y))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X3))) N) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N) Y))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X3))) N) (@ tptp.ring_18347121197199848620nteger Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N) Y))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X3))) N) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N) Y))) (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))) (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X3))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))) (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X3))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))) (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X3))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))) (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X3))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X3))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)) A))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X3))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)) A))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X3))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)) A))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X3))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X3))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X3))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X3))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)) A))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X3))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)) A))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X3))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)) A))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X3))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X3))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X3))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X3))) N)))) (forall ((X3 tptp.int) (Y tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X3))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))) (forall ((X3 tptp.int) (Y tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X3))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))) (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X3))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))) (forall ((N tptp.int) (X3 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X3))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X3)))) (forall ((D tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) N) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) D)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real D))))) (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat B) A) (not (= B A))))) (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 ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X3))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X3))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X3))) (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 ((X3 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X3))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X3))) (let ((_let_5 (@ tptp.ord_less_eq_num Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X3))) (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 ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X3))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X3))) (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 ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X3))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X3))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X3))) (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)))))))))))))))))) (= (lambda ((Y5 tptp.set_int) (Z3 tptp.set_int)) (= Y5 Z3)) (lambda ((X2 tptp.set_int) (Y6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X2) Y6) (@ (@ tptp.ord_less_eq_set_int Y6) X2)))) (= (lambda ((Y5 tptp.rat) (Z3 tptp.rat)) (= Y5 Z3)) (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y6) (@ (@ tptp.ord_less_eq_rat Y6) X2)))) (= (lambda ((Y5 tptp.num) (Z3 tptp.num)) (= Y5 Z3)) (lambda ((X2 tptp.num) (Y6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y6) (@ (@ tptp.ord_less_eq_num Y6) X2)))) (= (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3)) (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y6) (@ (@ tptp.ord_less_eq_nat Y6) X2)))) (= (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3)) (lambda ((X2 tptp.int) (Y6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y6) (@ (@ tptp.ord_less_eq_int Y6) X2)))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ (@ tptp.ord_less_eq_set_int A) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_eq_rat A) C)))) (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)))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (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))))) (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))))) (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))))) (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X3) Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) X3) (= X3 Y)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (=> (@ (@ tptp.ord_less_eq_rat Y) X3) (= X3 Y)))) (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X3) (= X3 Y)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X3) (= X3 Y)))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X3) (= X3 Y)))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))) (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 ((X3 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))) (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))) (forall ((X3 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))) (forall ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))) (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))) (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))) (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))) (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))) (= (lambda ((Y5 tptp.set_int) (Z3 tptp.set_int)) (= Y5 Z3)) (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B2) A3) (@ (@ tptp.ord_less_eq_set_int A3) B2)))) (= (lambda ((Y5 tptp.rat) (Z3 tptp.rat)) (= Y5 Z3)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (@ (@ tptp.ord_less_eq_rat A3) B2)))) (= (lambda ((Y5 tptp.num) (Z3 tptp.num)) (= Y5 Z3)) (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (@ (@ tptp.ord_less_eq_num A3) B2)))) (= (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (@ (@ tptp.ord_less_eq_nat A3) B2)))) (= (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3)) (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (@ (@ tptp.ord_less_eq_int A3) B2)))) (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat 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)))) (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (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 ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat 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)))) (= (lambda ((Y5 tptp.set_int) (Z3 tptp.set_int)) (= Y5 Z3)) (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B2) (@ (@ tptp.ord_less_eq_set_int B2) A3)))) (= (lambda ((Y5 tptp.rat) (Z3 tptp.rat)) (= Y5 Z3)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (@ (@ tptp.ord_less_eq_rat B2) A3)))) (= (lambda ((Y5 tptp.num) (Z3 tptp.num)) (= Y5 Z3)) (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (@ (@ tptp.ord_less_eq_num B2) A3)))) (= (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (@ (@ tptp.ord_less_eq_nat B2) A3)))) (= (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3)) (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (@ (@ tptp.ord_less_eq_int B2) A3)))) (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _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_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _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) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _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) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))) (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) 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(@ tptp.ord_less_int A) (@ F C)))))) (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))) (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))) (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))) (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))) (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))) (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ 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A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))) (forall ((X3 tptp.real)) (not (@ (@ tptp.ord_less_real X3) X3))) (forall ((X3 tptp.rat)) (not (@ (@ tptp.ord_less_rat X3) X3))) (forall ((X3 tptp.num)) (not (@ (@ tptp.ord_less_num X3) X3))) (forall ((X3 tptp.nat)) (not (@ (@ tptp.ord_less_nat X3) X3))) (forall ((X3 tptp.int)) (not (@ (@ tptp.ord_less_int X3) X3))) (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _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) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _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) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F 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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ 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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ 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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ 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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (not (@ (@ tptp.ord_less_real Y) X3)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (not (@ (@ tptp.ord_less_rat Y) X3)))) (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y) (not (@ (@ tptp.ord_less_num Y) X3)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (not (@ (@ tptp.ord_less_nat Y) X3)))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y) (not (@ (@ tptp.ord_less_int Y) X3)))) (forall ((X3 tptp.real) (Y tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X3) Y) (=> (@ (@ tptp.ord_less_real Y) X3) P))) (forall ((X3 tptp.rat) (Y tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X3) Y) (=> (@ (@ tptp.ord_less_rat Y) X3) P))) (forall ((X3 tptp.num) (Y tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X3) Y) (=> (@ (@ tptp.ord_less_num Y) X3) P))) (forall ((X3 tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X3) Y) (=> (@ (@ tptp.ord_less_nat Y) X3) P))) (forall ((X3 tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X3) Y) (=> (@ (@ tptp.ord_less_int Y) X3) P))) (forall ((X3 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X3) Y) (= X3 Y) (@ (@ tptp.ord_less_real Y) X3))) (forall ((X3 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X3) Y) (= X3 Y) (@ (@ tptp.ord_less_rat Y) X3))) (forall ((X3 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X3) Y) (= X3 Y) (@ (@ tptp.ord_less_num Y) X3))) (forall ((X3 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y) (= X3 Y) (@ (@ tptp.ord_less_nat Y) X3))) (forall ((X3 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X3) Y) (= X3 Y) (@ (@ tptp.ord_less_int Y) X3))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (not (= X3 Y)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (not (= X3 Y)))) (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y) (not (= X3 Y)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (not (= X3 Y)))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y) (not (= X3 Y)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (not (= Y X3)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (not (= Y X3)))) (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y) (not (= Y X3)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (not (= Y X3)))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y) (not (= Y X3)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (not (@ (@ tptp.ord_less_real Y) X3)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (not (@ (@ tptp.ord_less_rat Y) X3)))) (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y) (not (@ (@ tptp.ord_less_num Y) X3)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (not (@ (@ tptp.ord_less_nat Y) X3)))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y) (not (@ (@ tptp.ord_less_int Y) X3)))) (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)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))) (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 ((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)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat 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 ((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_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)) (= (@ 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)))) (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K)))) (= tptp.ord_less_eq_int (lambda ((N2 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M6)) tptp.one_one_real)))) (= tptp.ord_less_int (lambda ((N2 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N2)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M6)))) (forall ((X3 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 X3)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X3) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X3) D))) _let_1))))) (forall ((N tptp.int) (X3 tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X3))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X3))))) (forall ((N tptp.int) (X3 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X3))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X3)))) 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 ((Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X3) (not (@ (@ tptp.ord_less_real X3) Y)))) (forall ((Y tptp.set_int) (X3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X3) (not (@ (@ tptp.ord_less_set_int X3) Y)))) (forall ((Y tptp.rat) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X3) (not (@ (@ tptp.ord_less_rat X3) Y)))) (forall ((Y tptp.num) (X3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X3) (not (@ (@ tptp.ord_less_num X3) Y)))) (forall ((Y tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X3) (not (@ (@ tptp.ord_less_nat X3) Y)))) (forall ((Y tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X3) (not (@ (@ tptp.ord_less_int X3) Y)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X3) Y)) (@ (@ tptp.ord_less_eq_real Y) X3))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X3) Y)) (@ (@ tptp.ord_less_eq_rat Y) X3))) (forall ((X3 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X3) Y)) (@ (@ tptp.ord_less_eq_num Y) X3))) (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X3) Y)) (@ (@ tptp.ord_less_eq_nat Y) X3))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X3) Y)) (@ (@ tptp.ord_less_eq_int Y) X3))) (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_int) (B tptp.set_int)) (= (not (@ (@ tptp.ord_less_set_int A) B)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_rat A) B)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (= A B)))) (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 ((X3 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X3) Y)) (= (@ (@ tptp.ord_less_eq_real X3) Y) (= X3 Y)))) (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (not (@ (@ tptp.ord_less_set_int X3) Y)) (= (@ (@ tptp.ord_less_eq_set_int X3) Y) (= X3 Y)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X3) Y)) (= (@ (@ tptp.ord_less_eq_rat X3) Y) (= X3 Y)))) (forall ((X3 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X3) Y)) (= (@ (@ tptp.ord_less_eq_num X3) Y) (= X3 Y)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X3) Y)) (= (@ (@ tptp.ord_less_eq_nat X3) Y) (= X3 Y)))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X3) Y)) (= (@ (@ tptp.ord_less_eq_int X3) Y) (= X3 Y)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (= (not (@ (@ tptp.ord_less_real X3) Y)) (= X3 Y)))) (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X3) Y) (= (not (@ (@ tptp.ord_less_set_int X3) Y)) (= X3 Y)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (= (not (@ (@ tptp.ord_less_rat X3) Y)) (= X3 Y)))) (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y) (= (not (@ (@ tptp.ord_less_num X3) Y)) (= X3 Y)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y) (= (not (@ (@ tptp.ord_less_nat X3) Y)) (= X3 Y)))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y) (= (not (@ (@ tptp.ord_less_int X3) Y)) (= X3 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 ((Z tptp.rat) (Y tptp.rat)) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (@ (@ tptp.ord_less_eq_rat Y) X5))) (@ (@ tptp.ord_less_eq_rat 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))) (forall ((Y tptp.rat) (Z tptp.rat)) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y) (@ (@ tptp.ord_less_eq_rat X5) Z))) (@ (@ tptp.ord_less_eq_rat Y) Z))) (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y6) (not (@ (@ tptp.ord_less_eq_real Y6) X2))))) (= tptp.ord_less_set_int (lambda ((X2 tptp.set_int) (Y6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X2) Y6) (not (@ (@ tptp.ord_less_eq_set_int Y6) X2))))) (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y6) (not (@ (@ tptp.ord_less_eq_rat Y6) X2))))) (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y6) (not (@ (@ tptp.ord_less_eq_num Y6) X2))))) (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y6) (not (@ (@ tptp.ord_less_eq_nat Y6) X2))))) (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y6) (not (@ (@ tptp.ord_less_eq_int Y6) X2))))) (forall ((Y tptp.real) (X3 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X3)) (@ (@ tptp.ord_less_real X3) Y))) (forall ((Y tptp.rat) (X3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X3)) (@ (@ tptp.ord_less_rat X3) Y))) (forall ((Y tptp.num) (X3 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X3)) (@ (@ tptp.ord_less_num X3) Y))) (forall ((Y tptp.nat) (X3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X3)) (@ (@ tptp.ord_less_nat X3) Y))) (forall ((Y tptp.int) (X3 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X3)) (@ (@ tptp.ord_less_int X3) Y))) (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B2 tptp.real)) (or (@ (@ tptp.ord_less_real A3) B2) (= A3 B2)))) (= tptp.ord_less_eq_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A3) B2) (= A3 B2)))) (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (or (@ (@ tptp.ord_less_rat A3) B2) (= A3 B2)))) (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B2 tptp.num)) (or (@ (@ tptp.ord_less_num A3) B2) (= A3 B2)))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B2) (= A3 B2)))) (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (or (@ (@ tptp.ord_less_int A3) B2) (= A3 B2)))) (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B2) (not (= A3 B2))))) (= tptp.ord_less_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B2) (not (= A3 B2))))) (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (not (= A3 B2))))) (= tptp.ord_less_num (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (not (= A3 B2))))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (not (= A3 B2))))) (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (not (= A3 B2))))) (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_int) (B tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_set_int B) C) (@ (@ tptp.ord_less_set_int A) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))) (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.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_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))) (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_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B2) (not (@ (@ tptp.ord_less_eq_real B2) A3))))) (= tptp.ord_less_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B2) (not (@ (@ tptp.ord_less_eq_set_int B2) A3))))) (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (not (@ (@ tptp.ord_less_eq_rat B2) A3))))) (= tptp.ord_less_num (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (not (@ (@ tptp.ord_less_eq_num B2) A3))))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (not (@ (@ tptp.ord_less_eq_nat B2) A3))))) (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (not (@ (@ tptp.ord_less_eq_int B2) A3))))) (forall ((Z tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X3) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W2) (=> (@ (@ tptp.ord_less_real W2) X3) (@ (@ tptp.ord_less_eq_real Y) W2)))) (@ (@ tptp.ord_less_eq_real Y) Z)))) (forall ((Z tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X3) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W2) (=> (@ (@ tptp.ord_less_rat W2) X3) (@ (@ tptp.ord_less_eq_rat Y) W2)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))) (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) W2) (=> (@ (@ tptp.ord_less_real W2) Y) (@ (@ tptp.ord_less_eq_real W2) Z)))) (@ (@ tptp.ord_less_eq_real Y) Z)))) (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) W2) (=> (@ (@ tptp.ord_less_rat W2) Y) (@ (@ tptp.ord_less_eq_rat W2) Z)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))) (= tptp.ord_less_eq_real (lambda ((B2 tptp.real) (A3 tptp.real)) (or (@ (@ tptp.ord_less_real B2) A3) (= A3 B2)))) (= tptp.ord_less_eq_set_int (lambda ((B2 tptp.set_int) (A3 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int B2) A3) (= A3 B2)))) (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (or (@ (@ tptp.ord_less_rat B2) A3) (= A3 B2)))) (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (or (@ (@ tptp.ord_less_num B2) A3) (= A3 B2)))) (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B2) A3) (= A3 B2)))) (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (or (@ (@ tptp.ord_less_int B2) A3) (= A3 B2)))) (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B2) A3) (not (= A3 B2))))) (= tptp.ord_less_set_int (lambda ((B2 tptp.set_int) (A3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B2) A3) (not (= A3 B2))))) (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (not (= A3 B2))))) (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (not (= A3 B2))))) (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (not (= A3 B2))))) (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (not (= A3 B2))))) (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_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (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.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_int) (A tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int C) B) (@ (@ tptp.ord_less_set_int C) A)))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_rat C) A)))) (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_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B2) A3) (not (@ (@ tptp.ord_less_eq_real A3) B2))))) (= tptp.ord_less_set_int (lambda ((B2 tptp.set_int) (A3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B2) A3) (not (@ (@ tptp.ord_less_eq_set_int A3) B2))))) (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (not (@ (@ tptp.ord_less_eq_rat A3) B2))))) (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (not (@ (@ tptp.ord_less_eq_num A3) B2))))) (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (not (@ (@ tptp.ord_less_eq_nat A3) B2))))) (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (not (@ (@ tptp.ord_less_eq_int A3) B2))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B) (@ (@ tptp.ord_less_eq_set_int A) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat 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.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))) (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (@ (@ tptp.ord_less_eq_set_int B) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat 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_less_eq_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y6) (= X2 Y6)))) (= tptp.ord_less_eq_set_int (lambda ((X2 tptp.set_int) (Y6 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X2) Y6) (= X2 Y6)))) (= tptp.ord_less_eq_rat (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y6) (= X2 Y6)))) (= tptp.ord_less_eq_num (lambda ((X2 tptp.num) (Y6 tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y6) (= X2 Y6)))) (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y6) (= X2 Y6)))) (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y6 tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y6) (= X2 Y6)))) (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y6) (not (= X2 Y6))))) (= tptp.ord_less_set_int (lambda ((X2 tptp.set_int) (Y6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X2) Y6) (not (= X2 Y6))))) (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y6) (not (= X2 Y6))))) (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y6) (not (= X2 Y6))))) (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y6) (not (= X2 Y6))))) (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y6) (not (= X2 Y6))))) (forall ((X3 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X3) Y)) (@ (@ tptp.ord_less_real Y) X3))) (forall ((X3 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X3) Y)) (@ (@ tptp.ord_less_rat Y) X3))) (forall ((X3 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X3) Y)) (@ (@ tptp.ord_less_num Y) X3))) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X3) Y)) (@ (@ tptp.ord_less_nat Y) X3))) (forall ((X3 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X3) Y)) (@ (@ tptp.ord_less_int Y) X3))) (forall ((X3 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X3) Y)) (@ (@ tptp.ord_less_eq_real Y) X3))) (forall ((X3 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X3) Y)) (@ (@ tptp.ord_less_eq_rat Y) X3))) (forall ((X3 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X3) Y)) (@ (@ tptp.ord_less_eq_num Y) X3))) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X3) Y)) (@ (@ tptp.ord_less_eq_nat Y) X3))) (forall ((X3 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X3) Y)) (@ (@ tptp.ord_less_eq_int Y) X3))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_eq_real X3) Y))) (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int X3) Y) (@ (@ tptp.ord_less_eq_set_int X3) Y))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (@ (@ tptp.ord_less_eq_rat X3) Y))) (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y) (@ (@ tptp.ord_less_eq_num X3) Y))) (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (@ (@ tptp.ord_less_eq_nat X3) Y))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y) (@ (@ tptp.ord_less_eq_int X3) Y))) (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_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_int A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat 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.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (@ (@ tptp.ord_less_set_int A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat 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 ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ (@ tptp.ord_less_real X3) Z)))) (forall ((X3 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X3) Y) (=> (@ (@ tptp.ord_less_set_int Y) Z) (@ (@ tptp.ord_less_set_int X3) Z)))) (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ (@ tptp.ord_less_rat X3) Z)))) (forall ((X3 tptp.num) (Y tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ (@ tptp.ord_less_num X3) Z)))) (forall ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X3) Z)))) (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X3) Z)))) (forall ((X3 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z) (@ _let_1 Z))))) (forall ((X3 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))) (forall ((X3 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))) (forall ((X3 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))) (forall ((X3 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))) (forall ((X3 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X3))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))) (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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))) (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real 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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real 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) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real 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) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))) (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))) (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))) (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))) (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))) (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ 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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ 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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ 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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ 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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))) (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F 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) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ 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) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ 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) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ 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) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))) (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))) (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))) (forall ((X3 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_real Y) X3))) (forall ((X3 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X3) Y) (@ (@ tptp.ord_less_rat Y) X3))) (forall ((X3 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X3) Y) (@ (@ tptp.ord_less_num Y) X3))) (forall ((X3 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X3) Y) (@ (@ tptp.ord_less_nat Y) X3))) (forall ((X3 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X3) Y) (@ (@ tptp.ord_less_int Y) X3))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (or (@ (@ tptp.ord_less_real X3) Y) (= X3 Y)))) (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X3) Y) (or (@ (@ tptp.ord_less_set_int X3) Y) (= X3 Y)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (or (@ (@ tptp.ord_less_rat X3) Y) (= X3 Y)))) (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y) (or (@ (@ tptp.ord_less_num X3) Y) (= X3 Y)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y) (or (@ (@ tptp.ord_less_nat X3) Y) (= X3 Y)))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y) (or (@ (@ tptp.ord_less_int X3) Y) (= X3 Y)))) (forall ((X3 tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X3) Y) (= (@ (@ tptp.ord_ma741700101516333627d_enat X3) Y) Y))) (forall ((X3 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X3) Y) (= (@ (@ tptp.ord_max_set_int X3) Y) Y))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (= (@ (@ tptp.ord_max_rat X3) Y) Y))) (forall ((X3 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y) (= (@ (@ tptp.ord_max_num X3) Y) Y))) (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y) (= (@ (@ tptp.ord_max_nat X3) Y) Y))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y) (= (@ (@ tptp.ord_max_int X3) Y) Y))) (forall ((Y tptp.extended_enat) (X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) X3) (= (@ (@ tptp.ord_ma741700101516333627d_enat X3) Y) X3))) (forall ((Y tptp.set_int) (X3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X3) (= (@ (@ tptp.ord_max_set_int X3) Y) X3))) (forall ((Y tptp.rat) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X3) (= (@ (@ tptp.ord_max_rat X3) Y) X3))) (forall ((Y tptp.num) (X3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X3) (= (@ (@ tptp.ord_max_num X3) Y) X3))) (forall ((Y tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X3) (= (@ (@ tptp.ord_max_nat X3) Y) X3))) (forall ((Y tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X3) (= (@ (@ tptp.ord_max_int X3) Y) X3))) (= tptp.ord_ma741700101516333627d_enat (lambda ((A3 tptp.extended_enat) (B2 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A3) B2)) B2) A3))) (= tptp.ord_max_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A3) B2)) B2) A3))) (= tptp.ord_max_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A3) B2)) B2) A3))) (= tptp.ord_max_num (lambda ((A3 tptp.num) (B2 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A3) B2)) B2) A3))) (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B2)) B2) A3))) (= tptp.ord_max_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B2)) B2) A3))) (forall ((X3 (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X3) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X3 (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X3) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X3 tptp.real)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X3) (@ (@ tptp.ord_less_real X3) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))) (forall ((X3 tptp.rat)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X3) (@ (@ tptp.ord_less_rat X3) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))) (forall ((X3 tptp.real)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X5)) X3) (@ (@ tptp.ord_less_real X3) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X5) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y4)) X3) (@ (@ tptp.ord_less_real X3) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X5)))))) (forall ((X3 tptp.rat)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X5)) X3) (@ (@ tptp.ord_less_rat X3) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X5) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y4)) X3) (@ (@ tptp.ord_less_rat X3) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X5)))))) (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))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_int)))) (@ (@ tptp.unique5052692396658037445od_int M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_nat)))) (@ (@ tptp.unique5055182867167087721od_nat M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q4) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_Code_integer)))) (@ (@ tptp.unique3479559517661332726nteger M) N)))) (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 ((X3 tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X3)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X3)))) (forall ((N tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N)) (@ tptp.nat_set_decode X3)) (@ (@ tptp.member_nat N) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))) (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))) (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex) (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real) (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat) (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat) (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int) (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger) (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not P))) (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))) (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not P))) (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))) (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))) (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not P))) (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_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat 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))) (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_n2052037380579107095ol_rat P) tptp.one_one_rat) 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)) (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex) (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real) (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat) (= (@ 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) (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_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat 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_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (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_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat 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 ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N) (@ tptp.zero_n2687167440665602831ol_nat (not (= N _let_1)))))) (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_nu3179335615603231917ec_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ 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 ((Q2 tptp.int) (R2 tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q2) R2)) (@ (@ tptp.plus_plus_int Q2) (@ tptp.zero_n2684676970156552555ol_int (not (= R2 tptp.zero_zero_int)))))) (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P2))) P2)) (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P2))) P2)) (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P2))) P2)) (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 ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5052692396658037445od_int M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5055182867167087721od_nat M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q4) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique3479559517661332726nteger M) N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P2) (@ tptp.zero_n2687167440665602831ol_nat Q2)) (= P2 Q2))) (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P2) (@ tptp.zero_n2684676970156552555ol_int Q2)) (= P2 Q2))) (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P2) (@ tptp.zero_n356916108424825756nteger Q2)) (= P2 Q2))) (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_n2052037380579107095ol_rat (and P Q)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat 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)))) (= (@ tptp.bitM tptp.one) tptp.one) (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))) (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat 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_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)) (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_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_n2052037380579107095ol_rat (lambda ((P4 Bool)) (@ (@ (@ tptp.if_rat P4) tptp.one_one_rat) tptp.zero_zero_rat))) (= 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.complex Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P2)) (and (=> P2 (@ P tptp.one_one_complex)) (=> (not P2) (@ P tptp.zero_zero_complex))))) (forall ((P (-> tptp.real Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P2)) (and (=> P2 (@ P tptp.one_one_real)) (=> (not P2) (@ P tptp.zero_zero_real))))) (forall ((P (-> tptp.rat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P2)) (and (=> P2 (@ P tptp.one_one_rat)) (=> (not P2) (@ P tptp.zero_zero_rat))))) (forall ((P (-> tptp.nat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P2)) (and (=> P2 (@ P tptp.one_one_nat)) (=> (not P2) (@ P tptp.zero_zero_nat))))) (forall ((P (-> tptp.int Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P2)) (and (=> P2 (@ P tptp.one_one_int)) (=> (not P2) (@ P tptp.zero_zero_int))))) (forall ((P (-> tptp.code_integer Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P2)) (and (=> P2 (@ P tptp.one_one_Code_integer)) (=> (not P2) (@ P tptp.zero_z3403309356797280102nteger))))) (forall ((P (-> tptp.complex Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P2)) (not (or (and P2 (not (@ P tptp.one_one_complex))) (and (not P2) (not (@ P tptp.zero_zero_complex))))))) (forall ((P (-> tptp.real Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P2)) (not (or (and P2 (not (@ P tptp.one_one_real))) (and (not P2) (not (@ P tptp.zero_zero_real))))))) (forall ((P (-> tptp.rat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P2)) (not (or (and P2 (not (@ P tptp.one_one_rat))) (and (not P2) (not (@ P tptp.zero_zero_rat))))))) (forall ((P (-> tptp.nat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P2)) (not (or (and P2 (not (@ P tptp.one_one_nat))) (and (not P2) (not (@ P tptp.zero_zero_nat))))))) (forall ((P (-> tptp.int Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P2)) (not (or (and P2 (not (@ P tptp.one_one_int))) (and (not P2) (not (@ P tptp.zero_zero_int))))))) (forall ((P (-> tptp.code_integer Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P2)) (not (or (and P2 (not (@ P tptp.one_one_Code_integer))) (and (not P2) (not (@ P tptp.zero_z3403309356797280102nteger))))))) (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N)) (@ tptp.bit1 (@ tptp.bitM N)))) (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 N)))) (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((N tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N))) tptp.one_one_complex))) (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.bitM N)) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 N))) tptp.one_one_real))) (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.bitM N)) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 N))) tptp.one_one_rat))) (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.bitM N)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) tptp.one_one_int))) (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 ((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)))) (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)))) (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)))) (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A5 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.nat) (B5 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B5)) (@ (@ tptp.times_times_nat _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))) (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A5 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A5) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.int) (B5 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B5)) (@ (@ tptp.times_times_int _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))) (forall ((P (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A5 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A5) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B5)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N))) _let_2))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N))) _let_2))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N))) _let_2))))) (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (exists ((N3 tptp.nat)) (and (not (@ P N3)) (@ P (@ tptp.suc N3))))))) (forall ((X3 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.ring_1_of_int_real Z2)))) (forall ((X3 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_rat X3) (@ tptp.ring_1_of_int_rat Z2)))) (forall ((X3 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) X3))) (forall ((X3 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) X3))) (forall ((X3 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real X3) (@ tptp.ring_1_of_int_real Z2)))) (forall ((X3 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat X3) (@ tptp.ring_1_of_int_rat Z2)))) (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide6298287555418463151nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))) (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))) (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))) (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))) (= tptp.unique4921790084139445826nteger (lambda ((L tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))) (= tptp.nat_set_decode (lambda ((X2 tptp.nat)) (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat _let_1) N2))))))))) (forall ((X3 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 X3) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X3) _let_1)) (= (@ tptp.archim8280529875227126926d_real X3) Y)))))) (forall ((X3 tptp.rat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_rat Y))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X3) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X3) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X3) Y)))))) (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M6) N2))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M6)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q4)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M6) N2)) N2))))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X3) (@ (@ 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 X3)))) (forall ((X3 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X3)))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X3) (@ (@ 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 X3)))) (forall ((X3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X3)))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X3))) (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (forall ((X3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X3))) (@ (@ tptp.plus_plus_rat X3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int M) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N) (@ (@ tptp.plus_plus_int N) tptp.one_one_int))) (@ (@ tptp.times_times_int M) (@ (@ tptp.minus_minus_int M) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))) (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_int N))) (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_int N))) (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int) (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int) (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) A))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) A))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X3)) (@ tptp.archim7778729529865785530nd_rat Y)))) (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N2)) (@ (@ tptp.modulo_modulo_nat M6) N2)))) (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_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A2)))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) A2)))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A2)))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) A2)))) (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)))) (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)))) (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)))) (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))) (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))) (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))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) tptp.zero_zero_rat))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) A2)) tptp.zero_zero_rat))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) tptp.zero_zero_rat))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) tptp.zero_zero_rat))) (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 ((N tptp.num)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.pred_numeral N)))))) (forall ((N tptp.num)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ tptp.pred_numeral N)))))) (forall ((X32 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))) (= tptp.bit_se1745604003318907178nteger (lambda ((N2 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_integer (= N2 tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A3) _let_1)))))) (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A3) _let_1)))))) (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A3) _let_1)))))) (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 ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N)) (@ _let_1 N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (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 ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) 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.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int) (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N) tptp.zero_zero_int) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) tptp.zero_zero_int) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (= (@ tptp.bit_se2002935070580805687sk_nat _let_34) tptp.one_one_nat) (= (@ tptp.bit_se2000444600071755411sk_int _let_34) tptp.one_one_int) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))) (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))) (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))) (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))) (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1745604003318907178nteger N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (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 ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se1745604003318907178nteger M) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N) M))) _let_1)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N) M))) _let_1)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N) M))) _let_1)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N))) _let_1)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2000444600071755411sk_int N))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q2)) (@ (@ tptp.bit_se2925701944663578781it_nat N) Q2)))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))) (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))) (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))) (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 ((N tptp.nat) (K tptp.int) (L2 tptp.int) (R2 tptp.int) (S tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ tptp.bit_concat_bit N))) (= (= (@ (@ _let_2 K) L2) (@ (@ _let_2 R2) S)) (and (= (@ _let_1 K) (@ _let_1 R2)) (= L2 S)))))) (forall ((N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) B)) (@ _let_1 B)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))) (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 ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc N)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X5)))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))) (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)))) (let ((_let_2 (@ tptp.bit_ri631733984087533419it_int N))) (= (= (@ _let_2 A) (@ _let_2 B)) (= (@ _let_1 A) (@ _let_1 B)))))) (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ _let_1 tptp.zero_zero_int)))) (forall ((N tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N) M)) _let_2) _let_1) A))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4203085406695923979it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4205575877204974255it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7879613467334960850it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7882103937844011126it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2159334234014336723it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2161824704523386999it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int))) (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ tptp.suc N)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) A)) (@ _let_1 A))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))) (forall ((X3 tptp.complex) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X3))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X3) (@ (@ tptp.plus_plus_nat M) I3)))) I6) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I6))))) (forall ((X3 tptp.rat) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_rat X3) (@ (@ tptp.plus_plus_nat M) I3)))) I6) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I6))))) (forall ((X3 tptp.int) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X3))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X3) (@ (@ tptp.plus_plus_nat M) I3)))) I6) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I6))))) (forall ((X3 tptp.real) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X3))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X3) (@ (@ tptp.plus_plus_nat M) I3)))) I6) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I6))))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I3)))) _let_1)))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I3)))) _let_1)))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat N) (@ tptp.bit_se2002935070580805687sk_nat N)))) (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) (@ tptp.bit_se2000444600071755411sk_int N)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))) (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.rat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_rat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))) (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.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G M)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))) (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))) (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= tptp.bit_se1745604003318907178nteger (lambda ((N2 tptp.nat) (A3 tptp.code_integer)) (@ (@ tptp.modulo364778990260209775nteger A3) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)))) (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (@ (@ tptp.modulo_modulo_int A3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))) (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M))) (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.modulo_modulo_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))) (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat) (forall ((N tptp.nat) (A tptp.code_integer)) (= (= (@ (@ tptp.bit_se1745604003318907178nteger N) A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) A))) (forall ((N tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) A) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) A))) (forall ((N tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) A) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) A))) (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 ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) M))) (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))) (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))) (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))) (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))) (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))) (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))) (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_rat (@ F N)) (@ F M))))) (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F M))))) (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F M))))) (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger N)) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N)) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N)) (= N tptp.zero_zero_nat))) (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K)))) (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))) (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))))) (= tptp.bit_se2002935070580805687sk_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))) (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_2)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) tptp.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))) (= tptp.bit_se2000444600071755411sk_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))) (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X3))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X3)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))) (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X3)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))) (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X3))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X3)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))) (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X3))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X3)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))) (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))) (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))) (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))) (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (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 ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))) (= tptp.bit_se2002935070580805687sk_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))) (= tptp.bit_se2000444600071755411sk_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))) (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))) (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer))))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int))))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2925701944663578781it_nat N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat))))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) K5)) (@ (@ tptp.groups2906978787729119204at_rat G) K5)))) (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) K5)) (@ (@ tptp.groups1300246762558778688al_rat G) K5)))) (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) K5)) (@ (@ tptp.groups3906332499630173760nt_rat G) K5)))) (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) K5)) (@ (@ tptp.groups5058264527183730370ex_rat G) K5)))) (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 ((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 ((R2 tptp.int) (F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.times_times_int R2) (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N2 tptp.int)) (@ (@ tptp.times_times_int R2) (@ F N2)))) A2))) (forall ((R2 tptp.nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R2) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_nat R2) (@ F N2)))) A2))) (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_real R2) (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real R2) (@ F N2)))) A2))) (forall ((R2 tptp.complex) (F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.times_times_complex R2) (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.times_times_complex R2) (@ F N2)))) A2))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (R2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) R2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N2 tptp.int)) (@ (@ tptp.times_times_int (@ F N2)) R2))) A2))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (R2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) R2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_nat (@ F N2)) R2))) A2))) (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) R2))) A2))) (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.times_times_complex (@ F N2)) R2))) A2))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (G (-> tptp.int tptp.int)) (B3 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) B3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I3)) (@ G J3)))) B3))) A2))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B3 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) B3)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I3)) (@ G J3)))) B3))) A2))) (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (B3 tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) B3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I3)) (@ G J3)))) B3))) A2))) (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (B3 tptp.set_complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) B3)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I3 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F I3)) (@ G J3)))) B3))) 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 ((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.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.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 ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) R2))) A2))) (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) R2))) A2))) (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))) (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I3) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N) D)))) _let_1)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (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 ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((N tptp.nat) (M tptp.nat) (X3 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X3))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X3 tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X3)))))))))))) (forall ((N tptp.nat) (M tptp.nat) (X3 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X3 tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X3)))))))))))) (forall ((N tptp.nat) (M tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X3))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X3 tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X3)))))))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (= 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))))))))))) (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N)) (= M N))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N)) (= M N))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) (@ tptp.semiri681578069525770553at_rat N)) (= M N))) (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 ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)) (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A2)) (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)) (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_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real) (= A2 tptp.bot_bot_set_real))) (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))) (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))) (forall ((X3 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X3) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((X3 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X3) 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 ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) (@ tptp.semiri1314217659103216013at_int M))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= 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.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= 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.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))) (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int) (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real) (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))) (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))) (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int A) B) tptp.bot_bot_set_set_int) (not (@ (@ tptp.ord_less_eq_set_int A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_eq_rat A) B)))) (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_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (not (@ (@ tptp.ord_less_eq_set_int A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat A) B)))) (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 ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat))) (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 ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real A2) B3) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A2) B3))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A2) B3) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A2) B3))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A2) B3) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A2) B3))) (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex) _let_86 (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real) (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat) (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat) (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))) (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 ((X3 tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X3) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X3)) (forall ((X3 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X3) (@ tptp.uminus_uminus_int tptp.one_one_int)) X3)) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat M)) N))) (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X3)) (= (@ (@ tptp.power_power_nat B) W) X3))) (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X3)) (= (@ (@ tptp.power_power_nat B) W) X3))) (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X3)) (= (@ (@ tptp.power_power_nat B) W) X3))) (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X3)) (= (@ (@ tptp.power_power_nat B) W) X3))) (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W) (@ tptp.semiri681578069525770553at_rat X3)) (= (@ (@ tptp.power_power_nat B) W) X3))) (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X3) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X3 (@ (@ tptp.power_power_nat B) W)))) (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X3) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X3 (@ (@ tptp.power_power_nat B) W)))) (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X3) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X3 (@ (@ tptp.power_power_nat B) W)))) (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X3) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X3 (@ (@ tptp.power_power_nat B) W)))) (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat X3) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (= X3 (@ (@ tptp.power_power_nat B) W)))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) (@ tptp.semiri1314217659103216013at_int M))) (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.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))) (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))) (forall ((P Bool)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2052037380579107095ol_rat 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_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= 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.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex 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.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real 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.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))) (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X3))) tptp.one_one_int) tptp.one_one_int)) (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3))) tptp.one_one_nat) tptp.one_one_nat)) (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 ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N))) (forall ((N tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat W)))) (forall ((N tptp.num) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.semiri5074537144036343181t_real M)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) M))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X3))) tptp.one_one_int) tptp.zero_zero_int)) (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X3))) tptp.one_one_nat) tptp.zero_zero_nat)) (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 ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_int Y))))) (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_nat Y))))) (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X3))) (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X3))) (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X3))) (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X3))) (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat B) W)))) (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat B) W)))) (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X3)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat B) W)))) (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat B) W)))) (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X3))) (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X3))) (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X3))) (forall ((B tptp.nat) (W tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X3))) (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ tptp.power_power_nat B) W)))) (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ tptp.power_power_nat B) W)))) (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X3)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ tptp.power_power_nat B) W)))) (forall ((X3 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ tptp.power_power_nat B) W)))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X3)) N) (@ tptp.semiri8010041392384452111omplex Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N) Y))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N) (@ tptp.semiri1314217659103216013at_int Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N) Y))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N) (@ tptp.semiri5074537144036343181t_real Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N) Y))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N) (@ tptp.semiri681578069525770553at_rat Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N) Y))) (forall ((Y tptp.nat) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X3)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)))) (forall ((Y tptp.nat) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)))) (forall ((Y tptp.nat) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X3)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)))) (forall ((Y tptp.nat) (X3 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N))) (= (= (@ tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))) (forall ((Y tptp.nat) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X3)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))) (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))) (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_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_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 ((M tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc M))))) (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_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_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 ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.inc M)))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))) (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))) (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int) tptp.one_one_int)) (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int)) (forall ((X3 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X3)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X3) (= N tptp.zero_zero_nat)))) (forall ((X3 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X3)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X3) (= N tptp.zero_zero_nat)))) (forall ((X3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X3)) N)) (or (@ _let_1 X3) (= N tptp.zero_zero_nat))))) (forall ((X3 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X3)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X3) (= N tptp.zero_zero_nat)))) (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_int Y))))) (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_nat Y))))) (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_int Y))))) (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_nat Y))))) (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.zero_zero_int)) (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) tptp.zero_zero_int)) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))) (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X3))) (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X3))) (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X3)) (@ _let_1 X3)))) (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X3))) (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X3)) _let_1) (@ (@ tptp.ord_less_nat X3) _let_1)))) (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X3))) (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X3))) (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X3)) (@ _let_1 X3)))) (forall ((I2 tptp.num) (N tptp.nat) (X3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X3))) (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X3)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X3)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X3)) _let_1) (@ (@ tptp.ord_less_eq_nat X3) _let_1)))) (forall ((X3 tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X3)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_int Y)))))) (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3))) (@ 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 X3)) (@ tptp.numeral_numeral_nat Y)))))) (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 ((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 ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))) (= tptp.bit_se725231765392027082nd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int B2) A3))) (= tptp.bit_se727722235901077358nd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat B2) A3))) (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.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))) (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_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))) (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))) (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.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))) (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_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))) (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)) (forall ((A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.bot_bo4199563552545308370d_enat) A)) (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)) (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) 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.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.bot_bo4199563552545308370d_enat))) (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.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.extended_enat)) (= (not (= A tptp.bot_bo4199563552545308370d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.bot_bo4199563552545308370d_enat) 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.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))) (forall ((X3 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.semiri5074537144036343181t_real N3)))) (forall ((X3 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X3) (@ tptp.semiri681578069525770553at_rat N3)))) (forall ((X3 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X3) (@ tptp.semiri5074537144036343181t_real N3)))) (forall ((X3 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X3) (@ tptp.semiri681578069525770553at_rat N3)))) (forall ((X3 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X3))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))) (forall ((X3 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X3))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X3))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))) (forall ((X3 tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X3))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se2925701944663578781it_nat N) M)))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N)) (@ tptp.bit_se2000444600071755411sk_int N))) (forall ((N tptp.nat) (X3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X3)) (@ _let_1 X3)))) (forall ((N tptp.nat) (X3 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ring_1_of_int_real X3)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X3))) (forall ((N tptp.nat) (X3 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.ring_1_of_int_rat X3)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X3))) (forall ((P (-> tptp.num Bool)) (X3 tptp.num)) (=> (@ P tptp.one) (=> (forall ((X5 tptp.num)) (=> (@ P X5) (@ P (@ tptp.inc X5)))) (@ P X3)))) (forall ((X3 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X3))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))) (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 ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))) (forall ((X3 tptp.set_real) (Y tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X3) Y) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X3) Y))) (forall ((X3 tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X3) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X3) Y))) (forall ((X3 tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X3) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X3) Y))) (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_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))) (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_3 (@ tptp.divide_divide_int A))) (= (@ _let_3 (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) _let_1)))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_3 (@ tptp.divide_divide_nat A))) (= (@ _let_3 (@ (@ tptp.times_times_nat _let_2) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_3 _let_2)) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((Y tptp.int) (Z tptp.int) (X3 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 X3) Y)) Z)))) (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) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X3) Y)) Y))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X3) Y)) X3))) (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X3) Y))))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I2)) (@ tptp.semiri5074537144036343181t_real J2)))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I2)) (@ tptp.semiri681578069525770553at_rat J2)))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I2)) (@ tptp.semiri1316708129612266289at_nat J2)))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J2)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.dvd_dvd_nat M) N))) (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ tptp.bit_se2000444600071755411sk_int N2)))) (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A3) (@ tptp.bit_se2002935070580805687sk_nat N2)))) (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))) (forall ((Z tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))) (forall ((P (-> tptp.int Bool)) (Z tptp.int)) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N3))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))) (@ P Z)))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N3))))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N3))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))) (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N))) Z))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)))) (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_86 (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z5 tptp.int)) (exists ((N2 tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N2)))))) (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)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.ord_max_nat X3) Y)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.semiri4216267220026989637d_enat X3)) (@ tptp.semiri4216267220026989637d_enat Y)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X3) Y)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X3)) (@ tptp.semiri1314217659103216013at_int Y)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X3) Y)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X3)) (@ tptp.semiri5074537144036343181t_real Y)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X3) Y)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X3)) (@ tptp.semiri1316708129612266289at_nat Y)))) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.ord_max_nat X3) Y)) (@ (@ tptp.ord_max_rat (@ tptp.semiri681578069525770553at_rat X3)) (@ tptp.semiri681578069525770553at_rat Y)))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat A2)) (= A2 tptp.bot_bot_set_nat))) (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_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int A2)) (= A2 tptp.bot_bot_set_int))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))) (= (@ tptp.inc tptp.one) _let_6) (forall ((X3 tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X3)) (@ tptp.bit0 (@ tptp.inc X3)))) (forall ((X3 tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X3)) (@ tptp.bit1 X3))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X3))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X3) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat Y) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N3)) X3))))) (forall ((X3 tptp.num)) (= (@ (@ tptp.plus_plus_num X3) tptp.one) (@ tptp.inc X3))) (forall ((Y tptp.int) (Z tptp.int) (X3 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 X3) Y)) Z)))) (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 ((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 ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N))))) (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (forall ((Y4 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X3)))))) (forall ((M tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))))))))) (forall ((N tptp.nat) (X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X3))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X3)))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))) (and (= N tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))) (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))) (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))) (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z5 tptp.int)) (exists ((N2 tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3)))))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_int)) (forall ((D tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) D)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real D))))) (forall ((X3 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X3))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X3)))) (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 ((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 ((X3 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X3)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X3)) tptp.one_one_complex))) (forall ((X3 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X3)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X3)) tptp.one_one_real))) (forall ((X3 tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X3)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X3)) tptp.one_one_rat))) (forall ((X3 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X3)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X3)) tptp.one_one_nat))) (forall ((X3 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X3)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X3)) tptp.one_one_int))) (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_3 (@ tptp.semiri4939895301339042750nteger N))) (let ((_let_4 (@ tptp.times_3573771949741848930nteger _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_4 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_4 (@ tptp.times_times_int _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_4 (@ tptp.times_times_nat _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri8010041392384452111omplex N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri5074537144036343181t_real N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri681578069525770553at_rat N)))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= K (@ tptp.semiri1314217659103216013at_int N3)))))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))) (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))))))) (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M6)))) (= tptp.ord_less_eq_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M6)) tptp.one_one_real)))) (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J2)))))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))))) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) tptp.zero_zero_int) (exists ((N3 tptp.nat)) (= X3 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)) (forall ((X3 tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X3)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X3) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X3) D))) _let_1))))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) tptp.one_one_Code_integer) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ 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))))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (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 ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) E)))))) (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) E)))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) N))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N))))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N))))))) (forall ((X3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _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)) X3)) C))) (= X3 tptp.zero_zero_real)))))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))) (forall ((P (-> tptp.int Bool)) (X3 tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X3) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X3) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X3)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X3) Y) (@ P tptp.zero_zero_int))))) (forall ((N tptp.nat) (X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X3))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X3))))) (forall ((N tptp.nat) (X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X3))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X3)))) tptp.one_one_real)) (forall ((X3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X3)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X3) tptp.one_one_real)) N)))) (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X3))) (@ (@ tptp.power_power_real (@ _let_1 X3)) N))))) (= 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 ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (forall ((A tptp.complex) (D tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (@ (@ tptp.plus_plus_complex (@ _let_2 A)) (@ (@ tptp.times_times_complex _let_1) D))))))) (forall ((A tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A)) (@ (@ tptp.times_times_int _let_1) D))))))) (forall ((A tptp.rat) (D tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (let ((_let_2 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat (@ _let_2 A)) (@ (@ tptp.times_times_rat _let_1) D))))))) (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A)) (@ (@ tptp.times_times_nat _let_1) D))))))) (forall ((A tptp.real) (D tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real (@ _let_2 A)) (@ (@ tptp.times_times_real _let_1) D))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((A tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A)) (@ (@ tptp.times_times_int _let_2) D)))) _let_1))))) (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat _let_2) D)))) _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X3))) (@ (@ tptp.power_power_real (@ _let_1 X3)) N))))) (forall ((X3 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X3))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X3 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X3)))))))))) (forall ((X3 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X3))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X3 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X3)))))))))) (forall ((X3 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X3))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X3 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X3)))))))))) (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_complex (= N2 tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M6)))) (@ (@ (@ tptp.if_complex (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M6)))) (@ (@ (@ tptp.if_int (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M6)))) (@ (@ (@ tptp.if_real (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M6)))) (@ (@ (@ tptp.if_nat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_rat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_rat) (@ (@ tptp.produc6207742614233964070at_rat (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ tptp.semiri681578069525770553at_rat M6)))) (@ (@ (@ tptp.if_rat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((H2 tptp.real) (Z tptp.real) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)))) (let ((_let_4 (@ tptp.power_power_real Z))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z) H2))) (=> (not (= H2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N)) (@ _let_4 N))) H2)) (@ _let_3 (@ _let_4 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H2)))))))))))) (forall ((H2 tptp.complex) (Z tptp.complex) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.power_power_complex Z))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z) H2))) (=> (not (= H2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N)) (@ _let_3 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H2))))))))))) (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.times_times_complex _let_2) Z)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z) N))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N)))))))) (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.times_times_real _let_2) Z)) _let_4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s7457072308508201937r_real Z) N))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N)))))))) (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.times_times_rat _let_2) Z)) _let_4) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s4028243227959126397er_rat Z) N))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N)))))))) (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I3 tptp.complex)) (@ (@ tptp.plus_plus_complex I3) tptp.one_one_complex))) N2) tptp.zero_zero_complex))) (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I3 tptp.int)) (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))) N2) tptp.zero_zero_int))) (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I3 tptp.real)) (@ (@ tptp.plus_plus_real I3) tptp.one_one_real))) N2) tptp.zero_zero_real))) (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat))) N2) tptp.zero_zero_nat))) (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I3 tptp.rat)) (@ (@ tptp.plus_plus_rat I3) tptp.one_one_rat))) N2) tptp.zero_zero_rat))) (forall ((H2 tptp.complex) (Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_complex Z))) (=> (not (= H2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((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 N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((H2 tptp.rat) (Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_rat Z))) (=> (not (= H2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_rat H2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) Q4)) (@ (@ tptp.power_power_rat Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((H2 tptp.real) (Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_real Z))) (=> (not (= H2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((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 N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))) (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K3)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N2))))))) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat X3) (@ tptp.set_ord_lessThan_nat Y)) (= X3 Y))) (forall ((X3 tptp.int) (Y tptp.int)) (= (= (@ tptp.set_ord_lessThan_int X3) (@ tptp.set_ord_lessThan_int Y)) (= X3 Y))) (forall ((X3 tptp.real) (Y tptp.real)) (= (= (@ tptp.set_or5984915006950818249n_real X3) (@ tptp.set_or5984915006950818249n_real Y)) (= X3 Y))) (forall ((I2 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat 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.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat 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.real) (K tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I2) K))) (= (@ 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 ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_lessThan_rat X3)) (@ tptp.set_ord_lessThan_rat Y)) (@ (@ tptp.ord_less_eq_rat X3) Y))) (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X3)) (@ tptp.set_ord_lessThan_num Y)) (@ (@ tptp.ord_less_eq_num X3) Y))) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X3)) (@ tptp.set_ord_lessThan_nat Y)) (@ (@ tptp.ord_less_eq_nat X3) Y))) (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X3)) (@ tptp.set_ord_lessThan_int Y)) (@ (@ tptp.ord_less_eq_int X3) Y))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X3)) (@ tptp.set_or5984915006950818249n_real Y)) (@ (@ tptp.ord_less_eq_real X3) Y))) (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.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)) (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)) (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat) (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N))) (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))) (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N))) (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))) (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N))) (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N)))) (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N)))) (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N))) (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N)))) (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N)))) (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N)))) (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 ((X3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X3))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (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 ((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 ((X3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)) (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N)))) (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.modulo_modulo_int A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.semiri1314217659103216013at_int M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.semiri1316708129612266289at_nat M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M) N))) (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))) (forall ((M tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))) (= _let_1 _let_1))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N3)) (not (@ (@ tptp.bit_se1146084159140164899it_int B) N3)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) B)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N) (@ (@ tptp.bit_se1146084159140164899it_int B) N))))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N3)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B) N3)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) B)) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (@ (@ tptp.bit_se1148574629649215175it_nat B) N))))) (= tptp.bot_bot_nat tptp.zero_zero_nat) (forall ((X3 tptp.int)) (not (= (@ tptp.set_ord_lessThan_int X3) tptp.bot_bot_set_int))) (forall ((X3 tptp.real)) (not (= (@ tptp.set_or5984915006950818249n_real X3) tptp.bot_bot_set_real))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int A) B)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N) (@ (@ tptp.bit_se1146084159140164899it_int B) N)))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) N) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (@ (@ tptp.bit_se1148574629649215175it_nat B) N)))) (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N)))) (forall ((M tptp.nat) (A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se4203085406695923979it_int M) A)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N) (not (= M N))))) (forall ((M tptp.nat) (A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) N) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (not (= M N))))) (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat) (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat 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_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat 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_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_real X2) U2))))) (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.suc N)))) (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.suc N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) N) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N) (= N tptp.zero_zero_nat))) (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.numeral_numeral_nat N)))) (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)))) (forall ((M tptp.nat) (A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se2923211474154528505it_int M) A)) N) (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1146084159140164899it_int A) N)))) (forall ((M tptp.nat) (A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) A)) N) (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))) (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.zero_n356916108424825756nteger B)) N) (and B (= N tptp.zero_zero_nat)))) (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.zero_n2684676970156552555ol_int B)) N) (and B (= N tptp.zero_zero_nat)))) (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.zero_n2687167440665602831ol_nat B)) N) (and B (= N tptp.zero_zero_nat)))) (forall ((N tptp.extended_enat)) (= (= (@ tptp.set_or8419480210114673929d_enat N) tptp.bot_bo7653980558646680370d_enat) (= N tptp.bot_bo4199563552545308370d_enat))) (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.bot_bot_nat))) (forall ((M tptp.rat) (N tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M)) (@ tptp.set_ord_lessThan_rat N)) (@ (@ tptp.ord_less_rat M) N))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N)) (@ (@ tptp.ord_less_num M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N)) (@ (@ tptp.ord_less_int M) N))) (forall ((M tptp.real) (N tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M)) (@ tptp.set_or5984915006950818249n_real N)) (@ (@ tptp.ord_less_real M) N))) (forall ((A tptp.int) (N tptp.nat)) (=> (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) A) (@ (@ tptp.bit_se2923211474154528505it_int N) A)))) (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X3) N))))) (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X3) N))))) (forall ((X3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X3) N))))) (forall ((X3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X3) N))))) (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_complex)))))) (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_real)))))) (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_rat)))))) (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_complex))))) (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_real))))) (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_rat))))) (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))) (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (R2 tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int F) _let_1)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) R2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I3)) R2))) _let_1)))) (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (R2 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat F) _let_1)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) R2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I3)) R2))) _let_1)))) (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (R2 tptp.real)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) _let_1)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) R2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I3)) R2))) _let_1)))) (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))) (forall ((X3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X3) N)))) (forall ((X3 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X3) N)))) (forall ((X3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X3) N)))) (forall ((X3 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X3) N)))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))) (= tptp.bit_se2159334234014336723it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (@ (@ (@ (@ (@ tptp.if_nat_int_int (@ (@ tptp.bit_se1146084159140164899it_int A3) N2)) tptp.bit_se4203085406695923979it_int) tptp.bit_se7879613467334960850it_int) N2) A3))) (= tptp.bit_se2161824704523386999it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (@ (@ (@ (@ (@ tptp.if_nat_nat_nat (@ (@ tptp.bit_se1148574629649215175it_nat A3) N2)) tptp.bit_se4205575877204974255it_nat) tptp.bit_se7882103937844011126it_nat) N2) A3))) (forall ((Q (-> tptp.int tptp.nat)) (P (-> tptp.int tptp.nat)) (N tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_int N))) (=> (forall ((X5 tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat P) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat Q) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))) (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N))) (=> (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)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (=> (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 ((N tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))) (forall ((M tptp.nat) (K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L2)) N) (or (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N)) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) (@ (@ tptp.minus_minus_nat N) M)))))) (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N)))) (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N)))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) N)))) (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N)))) (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N)))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N)))))) (forall ((Z tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N))) (@ _let_1 N))))) (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N))) (@ _let_1 N))))) (forall ((Z tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N))) (@ _let_1 N))))) (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N))) (@ _let_1 N))))) (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K3))))))) (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K3))))))) (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K3))))))) (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N) K))) (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N) K))) (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N) K))) (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N) K))) (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N) K))) (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex))) (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int))) (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real))) (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat)))) (forall ((Z tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N))) M))))) (forall ((Z tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N))) M))))) (forall ((Z tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N))) M))))) (forall ((Z tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N))) M))))) (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F M)))) (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))) (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M)))) (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F tptp.zero_zero_nat)))) (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))) (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F M)) (@ F tptp.zero_zero_nat)))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))) (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N2) K3) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N2)))))) (forall ((N tptp.nat) (A tptp.int)) (=> (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)))) (forall ((N tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))) (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.rat) (H2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_rat Z))) (@ (@ tptp.times_times_rat (@ _let_2 P4)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat 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 ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) N))) (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))) (forall ((A tptp.code_integer)) (=> (forall ((N3 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N3) (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 ((N3 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N3) (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 ((N3 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N3) (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 ((K tptp.int)) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N3) M2) (= (@ _let_1 M2) (@ _let_1 N3))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (not (@ _let_1 N3)))))))))) (forall ((N tptp.nat) (F (-> tptp.nat tptp.rat)) (K5 tptp.rat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_rat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) K5) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) K5))))) (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_int (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K5) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) K5))))) (forall ((N tptp.nat) (F (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_nat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) K5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) K5))))) (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_real (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) K5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) K5))))) (forall ((X3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X3))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_complex (@ _let_2 X3)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_rat (@ _let_2 X3)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((X3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X3))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_int (@ _let_2 X3)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X3))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_real (@ _let_2 X3)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((X3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X3))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X3) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N)))))) (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X3) tptp.one_one_rat)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)))))) (forall ((X3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X3))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X3) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N)))))) (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X3))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X3) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N)))))) (forall ((X3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X3))) (=> (not (= X3 tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X3) tptp.one_one_complex)))))) (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (=> (not (= X3 tptp.one_one_rat)) (= (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X3) tptp.one_one_rat)))))) (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X3))) (=> (not (= X3 tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X3) tptp.one_one_real)))))) (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N) M))))))) (forall ((M tptp.nat) (N tptp.nat) (Z tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real M))) (@ (@ tptp.minus_minus_nat N) M))))))) (forall ((M tptp.nat) (N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N) M))))))) (forall ((M tptp.nat) (N tptp.nat) (Z tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat M))) (@ (@ tptp.minus_minus_nat N) M))))))) (= tptp.bit_se9216721137139052372nteger (lambda ((A3 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger A3) (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))))))) (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int A3) (@ (@ tptp.power_power_int _let_1) N2))))))) (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat A3) (@ (@ tptp.power_power_nat _let_1) N2))))))) (forall ((A tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)))) (forall ((A tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.bit_se727722235901077358nd_nat A) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))) (= tptp.bit_se1146084159140164899it_int (lambda ((K3 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int _let_1) N2))))))) (forall ((X3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X3))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X3 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N))) (@ _let_1 X3)))))))))) (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X3))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X3 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 N))) (@ _let_1 X3)))))))))) (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X3))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X3 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N))) (@ _let_1 X3)))))))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ F I3)) (@ G I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) tptp.one_one_nat)))) _let_1))))) (forall ((X3 tptp.complex) (N tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.power_power_complex Y) N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X3) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3)))) (@ (@ tptp.power_power_complex X3) I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((X3 tptp.rat) (N tptp.nat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X3) N)) (@ (@ tptp.power_power_rat Y) N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X3) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3)))) (@ (@ tptp.power_power_rat X3) I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((X3 tptp.int) (N tptp.nat) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X3) N)) (@ (@ tptp.power_power_int Y) N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X3) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3)))) (@ (@ tptp.power_power_int X3) I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((X3 tptp.real) (N tptp.nat) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.power_power_real Y) N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X3) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3)))) (@ (@ tptp.power_power_real X3) I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((X3 tptp.complex) (N tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X3) _let_1)) (@ (@ tptp.power_power_complex Y) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X3) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X3) P4)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X3 tptp.rat) (N tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X3) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X3) P4)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X3 tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X3) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X3) P4)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X3 tptp.real) (N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X3) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X3) P4)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (forall ((R2 tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R2) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R2) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))) (forall ((R2 tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R2) (@ tptp.semiri4939895301339042750nteger K))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K)) (@ (@ tptp.times_3573771949741848930nteger R2) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K))))) (forall ((R2 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R2))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R2) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R2) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))) (forall ((R2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R2))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R2) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))) (forall ((R2 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R2))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R2) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K)) (@ (@ tptp.times_times_rat R2) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))) (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) N) (or (@ (@ tptp.bit_se9216721137139052372nteger A) N) (= N tptp.zero_zero_nat))))) (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N) (= N tptp.zero_zero_nat))))) (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (= N tptp.zero_zero_nat))))) (forall ((A tptp.code_integer) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N) (or (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.minus_8373710615458151222nteger A) tptp.one_one_Code_integer)) N) (= N tptp.zero_zero_nat))))) (forall ((A tptp.int) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N) (or (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int A) tptp.one_one_int)) N) (= N tptp.zero_zero_nat))))) (forall ((A tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.minus_minus_nat A) tptp.one_one_nat)) N) (= N tptp.zero_zero_nat))))) (forall ((X3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.times_times_complex (@ _let_1 X3)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N)))))) (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.power_power_rat X3) N)) (@ (@ tptp.times_times_rat (@ _let_1 X3)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_rat X3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N)))))) (forall ((X3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X3) N)) (@ (@ tptp.times_times_int (@ _let_1 X3)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N)))))) (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.times_times_real (@ _let_1 X3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N)))))) (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)))) (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)))) (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)))) (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)))) (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K)))) (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)))) (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)))) (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)))) (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)))) (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J tptp.nat)) (not (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc J)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N))))))))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N))))))))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1148574629649215175it_nat _let_2) N))))))))) (= tptp.bit_se9216721137139052372nteger (lambda ((A3 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A3) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))) (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_int _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A3) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))) (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_nat _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A3) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))) (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M6 tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))) (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M6)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))) (= tptp.bit_se7879613467334960850it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N2)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))) (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N2))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) K) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K) N)))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))) (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 ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X3)) tptp.zero_zero_real) (= X3 tptp.zero_zero_real))) (forall ((X3 tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X3)) tptp.zero_zero_real) (= X3 tptp.zero_zero_complex))) (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))) (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real) (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))) (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))) (= tptp.bit_se1148574629649215175it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat _let_1) N2))))))) (forall ((X3 tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X3))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X3) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.real_V7735802525324610683m_real Y)))) (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X3) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y)))) (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F) S3))) (@ (@ tptp.groups8097168146408367636l_real G) S3)))) (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S3))) (@ (@ tptp.groups8778361861064173332t_real G) S3)))) (forall ((S3 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) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups6381953495645901045omplex F) S3))) (@ (@ tptp.groups4567486121110086003t_real G) S3)))) (forall ((S3 tptp.set_nat) (F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S3))) (@ (@ tptp.groups6591440286371151544t_real G) S3)))) (forall ((S3 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S3) (@ (@ 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) S3))) (@ (@ tptp.groups6591440286371151544t_real G) S3)))) (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S3))) (@ (@ tptp.groups5808333547571424918x_real G) S3)))) (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 ((X3 tptp.real) (N tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X3)) N))) (forall ((X3 tptp.complex) (N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X3)) N))) (forall ((F (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F I3)))) A2))) (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F I3)))) A2))) (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) A2))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I3 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ F I3)))) A2))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X3)) Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X3) Y)))) (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X3)) Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X3) 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) (N tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N) (@ (@ tptp.power_power_real Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z))))) (forall ((W tptp.complex) (N tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N) (@ (@ tptp.power_power_complex Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z))))) (forall ((X3 tptp.real) (R2 tptp.real) (Y tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X3)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X3) Y))) (@ (@ tptp.times_times_real R2) S))))) (forall ((X3 tptp.complex) (R2 tptp.real) (Y tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X3)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X3) Y))) (@ (@ tptp.times_times_real R2) S))))) (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X3) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.real_V7735802525324610683m_real Y)))) (forall ((X3 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X3) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y)))) (forall ((X3 tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X3) Y))) E))) (forall ((X3 tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X3) Y))) E))) (forall ((X3 tptp.real) (R2 tptp.real) (Y tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X3)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X3) Y))) (@ (@ tptp.plus_plus_real R2) S))))) (forall ((X3 tptp.complex) (R2 tptp.real) (Y tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X3)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X3) Y))) (@ (@ tptp.plus_plus_real R2) S))))) (forall ((A tptp.real) (R2 tptp.real) (B tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real R2) S))))) (forall ((A tptp.complex) (R2 tptp.real) (B tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) (@ (@ tptp.plus_plus_real R2) S))))) (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X3) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.real_V7735802525324610683m_real Y)))) (forall ((X3 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X3) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y)))) (forall ((X3 tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X3) Y))) E))) (forall ((X3 tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X3) Y))) E))) (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 ((X3 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X3) N))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X3)) N))) (forall ((X3 tptp.complex) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X3) N))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X3)) N))) (forall ((X3 tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X3))) (=> (@ (@ 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 ((X3 tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X3))) (=> (@ (@ 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 ((X3 tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X3) Y))) E))) (forall ((X3 tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X3) Y))) E))) (forall ((X3 tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X3))) (=> (@ (@ 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 ((X3 tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X3))) (=> (@ (@ 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 ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X3)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X3) Y))))) (forall ((X3 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X3)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X3) 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) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N tptp.zero_zero_nat)))) (forall ((W tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N tptp.zero_zero_nat)))) (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 ((X3 tptp.real)) (=> (= (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X3) tptp.one_one_real))) (forall ((X3 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X3) 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))))))) (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real) (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 ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M6)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)) (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.comm_s2602460028002588243omplex Z) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K3)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))) (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_real (@ (@ tptp.comm_s7457072308508201937r_real Z) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))) (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.comm_s4028243227959126397er_rat Z) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat _let_1)))) _let_2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K3)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))) (= tptp.comm_s2602460028002588243omplex (lambda ((A3 tptp.complex) (N2 tptp.nat)) (@ (@ (@ tptp.if_complex (= N2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A3) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_complex)))) (= tptp.comm_s4660882817536571857er_int (lambda ((A3 tptp.int) (N2 tptp.nat)) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A3) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_int)))) (= tptp.comm_s7457072308508201937r_real (lambda ((A3 tptp.real) (N2 tptp.nat)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A3) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_real)))) (= tptp.comm_s4028243227959126397er_rat (lambda ((A3 tptp.rat) (N2 tptp.nat)) (@ (@ (@ tptp.if_rat (= N2 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A3) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_rat)))) (= tptp.comm_s4663373288045622133er_nat (lambda ((A3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A3) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_nat)))) (= 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 ((X3 tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X3) A2)) B3) (and (@ (@ tptp.member_nat X3) B3) (@ (@ tptp.ord_less_eq_set_nat A2) B3)))) (forall ((X3 tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X3) A2)) B3) (and (@ (@ tptp.member_real X3) B3) (@ (@ tptp.ord_less_eq_set_real A2) B3)))) (forall ((X3 tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ (@ tptp.insert_complex X3) A2)) B3) (and (@ (@ tptp.member_complex X3) B3) (@ (@ tptp.ord_le211207098394363844omplex A2) B3)))) (forall ((X3 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.insert8211810215607154385at_nat X3) A2)) B3) (and (@ (@ tptp.member8440522571783428010at_nat X3) B3) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3)))) (forall ((X3 tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X3) A2)) B3) (and (@ (@ tptp.member_int X3) B3) (@ (@ tptp.ord_less_eq_set_int A2) B3)))) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu3 tptp.nat)) tptp.one_one_int)) A2) tptp.one_one_int)) (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu3 tptp.int)) tptp.one_one_int)) A2) tptp.one_one_int)) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu3 tptp.nat)) tptp.one_one_nat)) A2) tptp.one_one_nat)) (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 ((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.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 ((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 ((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.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 ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups6464643781859351333omplex G) tptp.bot_bot_set_nat) tptp.one_one_complex)) (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups129246275422532515t_real G) tptp.bot_bot_set_nat) tptp.one_one_real)) (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups73079841787564623at_rat G) tptp.bot_bot_set_nat) tptp.one_one_rat)) (forall ((G (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups7440179247065528705omplex G) tptp.bot_bot_set_int) tptp.one_one_complex)) (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups2316167850115554303t_real G) tptp.bot_bot_set_int) tptp.one_one_real)) (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) tptp.bot_bot_set_int) tptp.one_one_rat)) (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) tptp.bot_bot_set_int) tptp.one_one_nat)) (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups713298508707869441omplex G) tptp.bot_bot_set_real) tptp.one_one_complex)) (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups1681761925125756287l_real G) tptp.bot_bot_set_real) tptp.one_one_real)) (forall ((G (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups4061424788464935467al_rat G) tptp.bot_bot_set_real) tptp.one_one_rat)) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) (@ (@ tptp.insert_nat C) tptp.bot_bot_set_nat)) (and (= A B) (= B C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) (@ (@ tptp.insert_int C) tptp.bot_bot_set_int)) (and (= A B) (= B C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) (@ (@ tptp.insert_real C) tptp.bot_bot_set_real)) (and (= A B) (= B C)))) (forall ((A tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat A) A) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (forall ((A tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int A) A) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (forall ((A tptp.real)) (= (@ (@ tptp.set_or1222579329274155063t_real A) A) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real) (forall ((K tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat))) (= (@ (@ tptp.minus_minus_set_nat _let_1) (@ tptp.set_ord_lessThan_nat K)) _let_1))) (forall ((K tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int K) tptp.bot_bot_set_int))) (= (@ (@ tptp.minus_minus_set_int _let_1) (@ tptp.set_ord_lessThan_int K)) _let_1))) (forall ((K tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real K) tptp.bot_bot_set_real))) (= (@ (@ tptp.minus_minus_set_real _let_1) (@ tptp.set_or5984915006950818249n_real K)) _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_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 ((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_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 ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))) (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))) (forall ((N tptp.nat) (X3 tptp.vEBT_VEBT)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X3)) (@ (@ tptp.insert_VEBT_VEBT X3) tptp.bot_bo8194388402131092736T_VEBT)))) (forall ((N tptp.nat) (X3 tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X3)) (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat)))) (forall ((N tptp.nat) (X3 tptp.int)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X3)) (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int)))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real N) X3)) (@ (@ tptp.insert_real X3) tptp.bot_bot_set_real)))) (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))) (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))) (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))) (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))) (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))) (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))) (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))) (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))) (forall ((G (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.one_one_complex)))))) (forall ((G (-> tptp.real tptp.complex)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups713298508707869441omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.one_one_complex)))))) (forall ((G (-> tptp.int tptp.complex)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups7440179247065528705omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G A5) tptp.one_one_complex)))))) (forall ((G (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups3708469109370488835omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (= (@ G A5) tptp.one_one_complex)))))) (forall ((G (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.one_one_real)))))) (forall ((G (-> tptp.real tptp.real)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1681761925125756287l_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.one_one_real)))))) (forall ((G (-> tptp.int tptp.real)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups2316167850115554303t_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G A5) tptp.one_one_real)))))) (forall ((G (-> tptp.complex tptp.real)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups766887009212190081x_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (= (@ G A5) tptp.one_one_real)))))) (forall ((G (-> tptp.nat tptp.rat)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups73079841787564623at_rat G) A2) tptp.one_one_rat)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.one_one_rat)))))) (forall ((G (-> tptp.real tptp.rat)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups4061424788464935467al_rat G) A2) tptp.one_one_rat)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.one_one_rat)))))) (forall ((C5 tptp.set_nat) (D4 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.ord_less_eq_set_nat C5) D4) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C5)) (@ _let_1 D4))))) (forall ((C5 tptp.set_real) (D4 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ tptp.insert_real A))) (=> (@ (@ tptp.ord_less_eq_set_real C5) D4) (@ (@ tptp.ord_less_eq_set_real (@ _let_1 C5)) (@ _let_1 D4))))) (forall ((C5 tptp.set_int) (D4 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.ord_less_eq_set_int C5) D4) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C5)) (@ _let_1 D4))))) (forall ((X3 tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (not (@ (@ tptp.member_nat X3) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X3) B3)) (@ _let_1 B3))))) (forall ((X3 tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (not (@ (@ tptp.member_real X3) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X3) B3)) (@ _let_1 B3))))) (forall ((X3 tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.ord_le211207098394363844omplex A2))) (=> (not (@ (@ tptp.member_complex X3) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X3) B3)) (@ _let_1 B3))))) (forall ((X3 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X3) A2)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X3) B3)) (@ _let_1 B3))))) (forall ((X3 tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (not (@ (@ tptp.member_int X3) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X3) B3)) (@ _let_1 B3))))) (forall ((B3 tptp.set_nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.insert_nat A) B3))) (forall ((B3 tptp.set_real) (A tptp.real)) (@ (@ tptp.ord_less_eq_set_real B3) (@ (@ tptp.insert_real A) B3))) (forall ((B3 tptp.set_int) (A tptp.int)) (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.insert_int A) B3))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.insert_nat B) B3))))) (forall ((A2 tptp.set_real) (B3 tptp.set_real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.insert_real B) B3))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.insert_int B) B3))))) (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)))) (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)))) (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)))) (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A2)) N) (@ (@ tptp.groups705719431365010083at_int (lambda ((X2 tptp.nat)) (@ (@ tptp.power_power_int (@ F X2)) N))) A2))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) N) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.power_power_int (@ F X2)) N))) A2))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) N) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.power_power_nat (@ F X2)) N))) A2))) (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.modulo_modulo_int (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int F) A2)) A))) (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) A))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) A))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) (@ (@ tptp.groups73079841787564623at_rat G) A2)))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) (@ (@ tptp.groups4061424788464935467al_rat G) A2)))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) (@ (@ tptp.groups1072433553688619179nt_rat G) A2)))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) (@ (@ tptp.groups225925009352817453ex_rat G) A2)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) A2)))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) A2)))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) A2)))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) A2)))) (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)))) (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)))) (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_complex))) (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_real))) (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_rat))) (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_int))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_nat))) (forall ((A2 tptp.set_nat) (X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X3) 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_real) (X3 tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real X3) 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_int) (X3 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X3) 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 ((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 ((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_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 ((A tptp.nat) (B tptp.nat)) (=> (= A B) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (= A B) (= (@ (@ tptp.set_or1266510415728281911st_int A) B) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)))) (forall ((A tptp.real) (B tptp.real)) (=> (= A B) (= (@ (@ tptp.set_or1222579329274155063t_real A) B) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)))) (forall ((A2 tptp.set_real) (B3 tptp.set_real) (X3 tptp.real) (C5 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real B3))) (let ((_let_2 (@ tptp.ord_less_eq_set_real A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_real X3) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_real X3) A2))))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (X3 tptp.complex) (C5 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex B3))) (let ((_let_2 (@ tptp.ord_le211207098394363844omplex A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_complex X3) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_complex X3) A2))))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (X3 tptp.product_prod_nat_nat) (C5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat B3))) (let ((_let_2 (@ tptp.ord_le3146513528884898305at_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X3) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member8440522571783428010at_nat X3) A2))))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (X3 tptp.nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B3))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X3) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_nat X3) A2))))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (X3 tptp.int) (C5 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B3))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X3) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_int X3) A2))))))) (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (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 ((A3 tptp.nat)) (@ (@ tptp.power_power_real C) (@ F A3)))) A2))) (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 ((A3 tptp.nat)) (@ (@ tptp.power_power_complex C) (@ F A3)))) A2))) (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 ((A3 tptp.nat)) (@ (@ tptp.power_power_int C) (@ F A3)))) A2))) (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 ((A3 tptp.int)) (@ (@ tptp.power_power_int C) (@ F A3)))) A2))) (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 ((A3 tptp.nat)) (@ (@ tptp.power_power_nat C) (@ F A3)))) A2))) (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (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))) (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))) (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))) (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))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_nat X5) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) tptp.one_one_rat))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_real X5) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) tptp.one_one_rat))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_int X5) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) tptp.one_one_rat))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X5 tptp.complex)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_complex X5) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) tptp.one_one_rat))) (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))) (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))) (forall ((A2 tptp.set_real) (X3 tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X3))) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) B3) (@ (@ tptp.ord_less_eq_set_real A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_nat) (X3 tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X3))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) B3) (@ (@ tptp.ord_less_eq_set_nat A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_int) (X3 tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X3))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) B3) (@ (@ tptp.ord_less_eq_set_int A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_complex) (X3 tptp.complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.ord_le211207098394363844omplex A2))) (let ((_let_2 (@ (@ tptp.member_complex X3) A2))) (let ((_let_3 (@ tptp.insert_complex X3))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_le211207098394363844omplex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X3 tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (let ((_let_2 (@ (@ tptp.member8440522571783428010at_nat X3) A2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X3))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))) (forall ((A2 tptp.set_real) (X3 tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (let ((_let_2 (@ (@ tptp.member_real X3) A2))) (let ((_let_3 (@ tptp.insert_real X3))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))) (forall ((A2 tptp.set_nat) (X3 tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (let ((_let_2 (@ (@ tptp.member_nat X3) A2))) (let ((_let_3 (@ tptp.insert_nat X3))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))) (forall ((A2 tptp.set_int) (X3 tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (let ((_let_2 (@ (@ tptp.member_int X3) A2))) (let ((_let_3 (@ tptp.insert_int X3))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))) (forall ((Xs tptp.list_real) (I2 tptp.nat) (X3 tptp.real)) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) I2) X3))) (@ (@ tptp.insert_real X3) (@ tptp.set_real2 Xs)))) (forall ((Xs tptp.list_nat) (I2 tptp.nat) (X3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I2) X3))) (@ (@ tptp.insert_nat X3) (@ tptp.set_nat2 Xs)))) (forall ((Xs tptp.list_VEBT_VEBT) (I2 tptp.nat) (X3 tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I2) X3))) (@ (@ tptp.insert_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)))) (forall ((Xs tptp.list_int) (I2 tptp.nat) (X3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I2) X3))) (@ (@ tptp.insert_int X3) (@ tptp.set_int2 Xs)))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups705719431365010083at_int G) _let_1)))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups708209901874060359at_nat G) _let_1)))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I3)))) _let_1)))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I3)))) _let_1)))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))) (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G M)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G M)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G M)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G M)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((A2 tptp.set_complex) (X3 tptp.complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex X3))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_complex X3))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_complex A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B3)) (=> (not _let_2) (@ (@ tptp.ord_le211207098394363844omplex A2) B3)))))))))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X3 tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X3))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X3))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_le7866589430770878221at_nat A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B3)) (=> (not _let_2) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3)))))))))))) (forall ((A2 tptp.set_real) (X3 tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real X3))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_real X3))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_real A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A2) B3)))))))))))) (forall ((A2 tptp.set_nat) (X3 tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X3))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_nat X3))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_nat A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A2) B3)))))))))))) (forall ((A2 tptp.set_int) (X3 tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X3))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_int X3))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_int A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A2) B3)))))))))))) (forall ((N tptp.nat) (X3 tptp.vEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N)) X3)) (@ (@ tptp.insert_VEBT_VEBT X3) tptp.bot_bo8194388402131092736T_VEBT))) (forall ((N tptp.nat) (X3 tptp.nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat (@ tptp.suc N)) X3)) (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))) (forall ((N tptp.nat) (X3 tptp.int)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int (@ tptp.suc N)) X3)) (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))) (forall ((N tptp.nat) (X3 tptp.real)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real (@ tptp.suc N)) X3)) (@ (@ tptp.insert_real X3) tptp.bot_bot_set_real))) (forall ((N tptp.nat) (X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X3)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bo8194388402131092736T_VEBT)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_VEBT_VEBT X3) tptp.bot_bo8194388402131092736T_VEBT))))))) (forall ((N tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X3)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))))))) (forall ((N tptp.nat) (X3 tptp.int)) (let ((_let_1 (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X3)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))))))) (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.set_real2 (@ (@ tptp.replicate_real N) X3)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_real X3) tptp.bot_bot_set_real))))))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N))) (=> (@ (@ tptp.ord_less_eq_int M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N))))))) (= tptp.set_or1266510415728281911st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I3)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I3) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups129246275422532515t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((X3 (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb3 tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X3))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb3) Xa2))) (=> (= (@ (@ (@ _let_1 Xa2) Xb3) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb3) (@ (@ X3 Xa2) Xc))))))))) (= tptp.set_fo2584398358068434914at_nat (lambda ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B2 tptp.nat) (Acc2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B2) A3)) Acc2) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F3) (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) B2) (@ (@ F3 A3) Acc2))))) (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 ((I3 tptp.real)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I6))))) (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 ((I3 tptp.int)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I6))))) (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 ((I3 tptp.complex)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I6))))) (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 ((I3 tptp.product_prod_nat_nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I6))))) (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 ((I3 tptp.real)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I6))))) (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 ((I3 tptp.int)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I6))))) (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 ((I3 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I6))))) (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 ((I3 tptp.product_prod_nat_nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I6))))) (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 ((I3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I6))))) (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 ((I3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I6))))) (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (= tptp.comm_s7457072308508201937r_real (lambda ((A3 tptp.real) (N2 tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A3) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))) (= tptp.comm_s4028243227959126397er_rat (lambda ((A3 tptp.rat) (N2 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))) (= tptp.comm_s4660882817536571857er_int (lambda ((A3 tptp.int) (N2 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))) (= tptp.comm_s4663373288045622133er_nat (lambda ((A3 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A3) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))) (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups129246275422532515t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))) (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))) (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))) (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))) (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 ((A3 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_complex))) (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_rat))) (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 ((A3 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_int))) (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 ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_nat))) (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 ((A3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_real))) (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))) (forall ((X3 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 X3)) (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 X3) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X3) 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 X3) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _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 ((X3 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 X3) 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 X3)) (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 X3) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X3) 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 X3) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))) (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((Z tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((R2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R2) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R2) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R2) _let_1))))) (forall ((R2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat R2) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat R2) _let_1))))) (forall ((R2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R2) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R2) _let_1))))) (forall ((X3 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) X3) (=> (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X3)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X3)))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) N)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) N)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))) (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)) (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real) (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_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)) (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 ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)) (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))) (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.rat)) (= (@ (@ tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)) (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)) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.binomial N))) (= (@ (@ tptp.binomial (@ tptp.suc N)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K)) (@ _let_2 _let_1)))))) (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)) (@ (@ tptp.ord_less_eq_nat K) N))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X3)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_eq_real X3) Y)))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X3) tptp.one_one_real)))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (= (@ _let_1 (@ tptp.ln_ln_real X3)) (@ (@ tptp.ord_less_real tptp.one_one_real) X3))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (= (@ tptp.ln_ln_real X3) tptp.zero_zero_real) (= X3 tptp.one_one_real)))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X3)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3)))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real)))) (forall ((A (-> tptp.nat tptp.complex)) (X3 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) X3) (= (@ A tptp.zero_zero_nat) X3))) (forall ((A (-> tptp.nat tptp.real)) (X3 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ A N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) X3) (= (@ A tptp.zero_zero_nat) X3))) (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)) (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) K)))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))) (forall ((M tptp.nat) (R2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (let ((_let_2 (@ _let_1 R2))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K)))) (let ((_let_4 (@ _let_1 K))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K)) (@ (@ tptp.times_times_nat (@ _let_3 K)) (@ (@ tptp.binomial _let_2) M)))))))) (forall ((R2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) R2)) (@ (@ tptp.power_power_nat N) R2)))) (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X3)) X3))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X3)) (=> (@ _let_1 X3) (@ (@ tptp.ord_less_real tptp.one_one_real) X3))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X3)) tptp.zero_zero_real)))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X3)))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X3)))) (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)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.minus_minus_nat M) K)))))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K))) _let_1))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))) (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 ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (= (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) _let_1) (@ (@ tptp.plus_plus_rat (@ _let_2 K)) (@ _let_2 _let_1)))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (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 ((I2 tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) J2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J2))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3)))) (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) (@ A tptp.zero_zero_nat))) (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ A N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) (@ A tptp.zero_zero_nat))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3))) X3))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X3) Y)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X3)) (@ tptp.ln_ln_real Y))))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) K))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (= (@ tptp.ln_ln_real X3) (@ (@ tptp.minus_minus_real X3) tptp.one_one_real)) (= X3 tptp.one_one_real)))) (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.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_rat A) _let_2) (@ (@ tptp.plus_plus_rat (@ _let_1 _let_2)) (@ _let_1 K)))))) (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 ((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.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ _let_1 tptp.one_one_rat)) K))))) (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 ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat K))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) _let_1)) K)) (@ (@ tptp.gbinomial_rat A) K))))) (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.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat _let_3) A) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))) (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.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat A) _let_3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) J2))) (= (@ (@ 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)))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real K))) K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri681578069525770553at_rat K))) K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K))))) (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K6)))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 N)))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K6)) (@ _let_1 K))))))) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real _let_13)) tptp.one_one_real) (forall ((N tptp.nat) (K tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X3)) (@ (@ tptp.minus_minus_real X3) tptp.one_one_real)))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X3)) (@ tptp.ln_ln_real Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X3) Y)) Y)))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3))) X3))) (forall ((X3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ln_ln_real X3))))) (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)))))) (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)))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_2)) (@ (@ tptp.gbinomial_rat _let_1) _let_2)) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.gbinomial_rat A) K)))))) (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))))) (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))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ (@ tptp.gbinomial_rat A) _let_1)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) K))))) (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))))))) (forall ((K tptp.nat) (M tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M)) K)) (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.minus_minus_nat M) K))))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 (@ tptp.suc K)))))) (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K6)))))) (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_nat (@ _let_1 K6)) (@ _let_1 K))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N) _let_1))) (let ((_let_3 (@ tptp.binomial N))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ _let_3 (@ tptp.suc _let_2)) (@ _let_3 _let_2))))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.binomial N) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X3))) (@ tptp.uminus_uminus_real X3))))) (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)))))) (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)))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))) (@ (@ tptp.gbinomial_rat A) K)))))) (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))))))) (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))))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))))))) (= tptp.gbinomial_complex (lambda ((A3 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)) A3)) tptp.one_one_complex)) K3)))) (= tptp.gbinomial_real (lambda ((A3 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)) A3)) tptp.one_one_real)) K3)))) (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat K3)) A3)) tptp.one_one_rat)) K3)))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (= (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) K)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) N))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (= (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) K)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) N))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) K)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N))))) (forall ((N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) Z)) (@ (@ tptp.insert_nat N) _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) _let_1)))) (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)))) (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)))) (forall ((A tptp.rat) (K tptp.nat)) (= (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))) (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)))))) (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)))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))) (forall ((G (-> tptp.nat tptp.real)) (X3 tptp.real)) (=> (@ (@ tptp.sums_real G) X3) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_1)))))) X3))) (forall ((G (-> tptp.nat tptp.real)) (X3 tptp.real) (F (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (@ (@ tptp.sums_real G) X3) (=> (@ (@ tptp.sums_real F) Y) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (@ F (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X3) Y))))) (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)))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3)))))) (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))) (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))) (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))) (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)))))) (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)))))) (forall ((K tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))) (= 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))))) (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 ((N2 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N2)))) tptp.one_one_real) (forall ((F (-> tptp.nat tptp.real)) (S tptp.real) (N tptp.nat)) (=> (@ (@ tptp.sums_real F) S) (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) (@ (@ tptp.minus_minus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))) (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) (@ (@ tptp.minus_minus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.sums_real F) S))) (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S tptp.real) (T tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_real F) S) (=> (@ (@ tptp.sums_real G) T) (@ (@ tptp.ord_less_eq_real S) T))))) (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S tptp.nat) (T tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_nat F) S) (=> (@ (@ tptp.sums_nat G) T) (@ (@ tptp.ord_less_eq_nat S) T))))) (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S tptp.int) (T tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_int F) S) (=> (@ (@ tptp.sums_int G) T) (@ (@ tptp.ord_less_eq_int S) T))))) (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) A)))) (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))) (@ (@ tptp.times_times_real A) C)))) (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (G (-> tptp.nat tptp.real)) (B tptp.real)) (=> (@ (@ tptp.sums_real F) A) (=> (@ (@ tptp.sums_real G) B) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_real A) B))))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (G (-> tptp.nat tptp.nat)) (B tptp.nat)) (=> (@ (@ tptp.sums_nat F) A) (=> (@ (@ tptp.sums_nat G) B) (@ (@ tptp.sums_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_nat A) B))))) (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (G (-> tptp.nat tptp.int)) (B tptp.int)) (=> (@ (@ tptp.sums_int F) A) (=> (@ (@ tptp.sums_int G) B) (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_int A) B))))) (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (@ (@ tptp.divide1717551699836669952omplex A) C)))) (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (@ (@ tptp.divide_divide_real A) C)))) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (@ (@ tptp.times_times_complex C) D)) (@ (@ tptp.sums_complex F) D)))) (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) D)) (@ (@ tptp.sums_real F) D)))) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) C))) (@ (@ tptp.times_times_complex D) C)) (@ (@ tptp.sums_complex F) D)))) (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))) (@ (@ tptp.times_times_real D) C)) (@ (@ tptp.sums_real F) D)))) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) A) (=> (not (= C tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A) C))))) (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) A) (=> (not (= C tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A) C))))) (forall ((F (-> tptp.nat tptp.complex)) (S tptp.complex)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S) (@ (@ tptp.sums_complex F) S)))) (forall ((F (-> tptp.nat tptp.real)) (S tptp.real)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S) (@ (@ tptp.sums_real F) S)))) (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L2) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.nat)) (L2 tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L2) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L2) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.int)) (L2 tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L2) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L2) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.real)) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ F tptp.zero_zero_nat))))) (forall ((N tptp.nat) (F (-> tptp.nat tptp.complex)) (S tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (= (@ F I4) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) S) (@ (@ tptp.sums_complex F) S)))) (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (S tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (= (@ F I4) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) S) (@ (@ tptp.sums_real F) S)))) (forall ((M tptp.nat) (Z tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N2 M)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.power_power_complex Z) M))) (forall ((M tptp.nat) (Z tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N2 M)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.power_power_real Z) M))) (forall ((M tptp.nat) (Z tptp.int)) (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N2 M)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z) N2)))) (@ (@ tptp.power_power_int Z) M))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X3) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X3) tptp.one_one_real)) (@ tptp.suc N2))))))))) (forall ((X3 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))) X3) (=> (@ (@ tptp.ord_less_eq_real X3) 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) X3))) X3))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1))))))))) (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) (J tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I4) J)) (=> (=> (@ (@ tptp.ord_less_eq_int I4) J) (@ (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J)) (@ (@ P I4) J)))) (@ (@ P A0) A12)))) (forall ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X3)) (@ (@ 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 ((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))))) (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))) (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))))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_atMost_nat X3) (@ tptp.set_ord_atMost_nat Y)) (= X3 Y))) (forall ((X3 tptp.int) (Y tptp.int)) (= (= (@ tptp.set_ord_atMost_int X3) (@ tptp.set_ord_atMost_int Y)) (= X3 Y))) _let_85 _let_84 _let_83 _let_82 (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))) _let_85 (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex) _let_84 _let_83 _let_82 (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.times_3573771949741848930nteger A) A)))) (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.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.times_times_rat 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)))) _let_80 (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex) _let_79 _let_78 _let_77 (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (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.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (= (@ tptp.abs_abs_rat _let_1) _let_1))) (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))) (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 ((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.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))) (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))) (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))) (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))) (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))) (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))) (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))) (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))) (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))) (forall ((M tptp.real) (K tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real M))) (= (@ _let_1 (@ tptp.abs_abs_real K)) (@ _let_1 K)))) (forall ((M tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int M))) (= (@ _let_1 (@ tptp.abs_abs_int K)) (@ _let_1 K)))) (forall ((M tptp.code_integer) (K tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer M))) (= (@ _let_1 (@ tptp.abs_abs_Code_integer K)) (@ _let_1 K)))) (forall ((M tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M)) K) (@ (@ tptp.dvd_dvd_real M) K))) (forall ((M tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M)) K) (@ (@ tptp.dvd_dvd_int M) K))) (forall ((M tptp.code_integer) (K tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.abs_abs_Code_integer M)) K) (@ (@ tptp.dvd_dvd_Code_integer M) K))) (forall ((I2 tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_ord_atMost_real K)) (@ (@ tptp.ord_less_eq_real I2) K))) (forall ((I2 tptp.set_int) (K tptp.set_int)) (= (@ (@ tptp.member_set_int I2) (@ tptp.set_or58775011639299419et_int K)) (@ (@ tptp.ord_less_eq_set_int I2) K))) (forall ((I2 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_atMost_rat K)) (@ (@ tptp.ord_less_eq_rat I2) K))) (forall ((I2 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_atMost_num K)) (@ (@ tptp.ord_less_eq_num I2) K))) (forall ((I2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_atMost_nat K)) (@ (@ tptp.ord_less_eq_nat I2) K))) (forall ((I2 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_atMost_int K)) (@ (@ tptp.ord_less_eq_int I2) K))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))) (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X3)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_eq_real X3) Y))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (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.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (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.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))) (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.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) 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.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))) (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat 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.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))) (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.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat _let_1)) _let_1))) (= (@ tptp.abs_abs_int _let_5) tptp.one_one_int) (= (@ tptp.abs_abs_real _let_11) tptp.one_one_real) (= (@ tptp.abs_abs_Code_integer _let_81) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_rat _let_4) tptp.one_one_rat) (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N)) (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)))) (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N)) (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N)) (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N)))) (forall ((X3 tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ tptp.set_or58775011639299419et_int X3)) (@ tptp.set_or58775011639299419et_int Y)) (@ (@ tptp.ord_less_eq_set_int X3) Y))) (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat X3)) (@ tptp.set_ord_atMost_rat Y)) (@ (@ tptp.ord_less_eq_rat X3) Y))) (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X3)) (@ tptp.set_ord_atMost_num Y)) (@ (@ tptp.ord_less_eq_num X3) Y))) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X3)) (@ tptp.set_ord_atMost_nat Y)) (@ (@ tptp.ord_less_eq_nat X3) Y))) (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X3)) (@ tptp.set_ord_atMost_int Y)) (@ (@ tptp.ord_less_eq_int X3) Y))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X3)) (@ _let_1 X3)))) (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A2))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ tptp.abs_abs_int (@ F I3)))) A2))) (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.abs_abs_real (@ F I3)))) A2))) (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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) (or (@ _let_1 A) (= B tptp.zero_zero_rat))))) (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.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (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.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat 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 ((L2 tptp.set_int) (H2 tptp.set_int) (H3 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int L2) H2)) (@ tptp.set_or58775011639299419et_int H3)) (or (not (@ (@ tptp.ord_less_eq_set_int L2) H2)) (@ (@ tptp.ord_less_eq_set_int H2) H3)))) (forall ((L2 tptp.rat) (H2 tptp.rat) (H3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat L2) H2)) (@ tptp.set_ord_atMost_rat H3)) (or (not (@ (@ tptp.ord_less_eq_rat L2) H2)) (@ (@ tptp.ord_less_eq_rat H2) H3)))) (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)))) (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)))) (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)))) (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)))) (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))) (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X3)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X3))))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ tptp.abs_abs_int (@ F I3)))) A2))) (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.abs_abs_real (@ F I3)))) A2))) (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ _let_27 tptp.bot_bot_set_nat)) (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N)) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) (or (not (= A tptp.zero_zero_real)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N)) (or (not (= A tptp.zero_zero_rat)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N)) (or (not (= A tptp.zero_zero_int)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (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.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))) (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 ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) (@ F tptp.zero_zero_nat))) (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) (@ F tptp.zero_zero_nat))) (forall ((W tptp.num) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1))))) (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 ((X3 tptp.int) (Y tptp.int)) (= (= (@ tptp.abs_abs_int X3) (@ tptp.abs_abs_int Y)) (or (= X3 Y) (= X3 (@ tptp.uminus_uminus_int Y))))) (forall ((X3 tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X3) (@ tptp.abs_abs_real Y)) (or (= X3 Y) (= X3 (@ tptp.uminus_uminus_real Y))))) (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer X3) (@ tptp.abs_abs_Code_integer Y)) (or (= X3 Y) (= X3 (@ tptp.uminus1351360451143612070nteger Y))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (= (= (@ tptp.abs_abs_rat X3) (@ tptp.abs_abs_rat Y)) (or (= X3 Y) (= X3 (@ tptp.uminus_uminus_rat Y))))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))) (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))) (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))) (forall ((L2 tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L2) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L2) K))) (forall ((L2 tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L2) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L2) K))) (forall ((L2 tptp.code_integer) (K tptp.code_integer)) (=> (= (@ tptp.abs_abs_Code_integer L2) (@ tptp.abs_abs_Code_integer K)) (@ (@ tptp.dvd_dvd_Code_integer L2) K))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))) (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))) (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat 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.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger A) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat A) B))) (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.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))) (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))) _let_80 _let_79 _let_78 _let_77 (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (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.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (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)))) (forall ((H2 tptp.real)) (not (= tptp.bot_bot_set_real (@ tptp.set_ord_atMost_real H2)))) (forall ((H2 tptp.nat)) (not (= tptp.bot_bot_set_nat (@ tptp.set_ord_atMost_nat H2)))) (forall ((H2 tptp.int)) (not (= tptp.bot_bot_set_int (@ tptp.set_ord_atMost_int H2)))) (forall ((H3 tptp.int) (L2 tptp.int) (H2 tptp.int)) (not (= (@ tptp.set_ord_atMost_int H3) (@ (@ tptp.set_or1266510415728281911st_int L2) H2)))) (forall ((H3 tptp.real) (L2 tptp.real) (H2 tptp.real)) (not (= (@ tptp.set_ord_atMost_real H3) (@ (@ tptp.set_or1222579329274155063t_real L2) H2)))) (= tptp.set_ord_atMost_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) U2))))) (= tptp.set_or58775011639299419et_int (lambda ((U2 tptp.set_int)) (@ tptp.collect_set_int (lambda ((X2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X2) U2))))) (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) U2))))) (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_eq_num X2) U2))))) (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) U2))))) (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) U2))))) (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))) (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))) (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))) (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))) (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (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.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (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.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer B))) (let ((_let_2 (@ tptp.abs_abs_Code_integer A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) C) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C) D))))))) (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.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat B))) (let ((_let_2 (@ tptp.abs_abs_rat A))) (=> (@ (@ tptp.ord_less_rat _let_2) C) (=> (@ (@ tptp.ord_less_rat _let_1) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C) D))))))) (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.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))) (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.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))) (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 ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))) (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.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))) (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.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))) (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.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))) (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 ((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 ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))) (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.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat 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_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.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B)))) (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) (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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B))) (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 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.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B)))) (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.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.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.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)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B)))) (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)) (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))) (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))))) (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)))) (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)))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X3)) tptp.one_one_real)) (forall ((X3 tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) E2))) (= X3 tptp.zero_zero_real))) (forall ((X3 tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X3)) E2))) (= X3 tptp.zero_zero_rat))) (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X3) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y)) X3) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y) X3))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X3) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X3))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X3) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y)) X3) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y) X3))))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X3) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X3))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (or (@ _let_1 B) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))) (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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))) (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 ((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.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)) (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) (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.rat) (B tptp.rat)) (= (= A (@ tptp.abs_abs_rat B)) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (or (= B A) (= B (@ tptp.uminus_uminus_rat A)))))) (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) (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.rat) (B tptp.rat)) (= (= (@ tptp.abs_abs_rat A) B) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (or (= A B) (= A (@ tptp.uminus_uminus_rat B)))))) (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 ((Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X3)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X3) Y))))) (forall ((Y tptp.rat) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X3)) Y) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X3) Y))))) (forall ((A tptp.code_integer) (N tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))) (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))) (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N))) (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))) (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))) (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))) (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))) (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))) (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.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))) (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))) (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))) (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))) (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger C) D)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) C))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) D))))) (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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat C) D)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D))))) (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.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (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.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (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 ((X3 tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X3) A))) R2) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X3) (@ (@ tptp.ord_le3102999989581377725nteger X3) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))) (forall ((X3 tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) A))) R2) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R2)) X3) (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.plus_plus_real A) R2))))) (forall ((X3 tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X3) A))) R2) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R2)) X3) (@ (@ tptp.ord_less_eq_rat X3) (@ (@ tptp.plus_plus_rat A) R2))))) (forall ((X3 tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X3) A))) R2) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R2)) X3) (@ (@ tptp.ord_less_eq_int X3) (@ (@ tptp.plus_plus_int A) R2))))) (forall ((X3 tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X3) A))) R2) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X3) (@ (@ tptp.ord_le6747313008572928689nteger X3) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))) (forall ((X3 tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) A))) R2) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R2)) X3) (@ (@ tptp.ord_less_real X3) (@ (@ tptp.plus_plus_real A) R2))))) (forall ((X3 tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X3) A))) R2) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R2)) X3) (@ (@ tptp.ord_less_rat X3) (@ (@ tptp.plus_plus_rat A) R2))))) (forall ((X3 tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X3) A))) R2) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R2)) X3) (@ (@ tptp.ord_less_int X3) (@ (@ tptp.plus_plus_int A) R2))))) (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))) (forall ((X3 tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X3 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 X3) U)) Y))) V)))) (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)))))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat A)) (@ tptp.set_ord_lessThan_rat B)) (@ (@ tptp.ord_less_rat A) B))) (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))) (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))) (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))) (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))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial K3) M))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc N)) (@ tptp.suc M)))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X3))) (forall ((X3 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X3)))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X3)))) (forall ((X3 tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X3)))) (forall ((X3 tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X3)))) (forall ((N tptp.int) (X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X3)))) (forall ((N tptp.int) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3)))) (forall ((N tptp.int) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X3)))) (forall ((N tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X3)))) (forall ((N tptp.int) (X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X3)))) (forall ((N tptp.int) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X3)))) (forall ((N tptp.int) (X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X3)))) (forall ((N tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X3) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X3)))) (forall ((A tptp.real) (X3 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y4))) D3) (and (@ (@ tptp.ord_less_eq_real A) Y4) (@ (@ tptp.ord_less_eq_real Y4) B))))))))) (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 ((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)))))) (forall ((Z tptp.rat) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_rat Z))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat Z))))) (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat M)))))) (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((F (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I3)) (@ F (@ tptp.suc I3))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))) (forall ((F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I3)) (@ F (@ tptp.suc I3))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))) (forall ((F (-> tptp.nat tptp.real)) (I2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I3)) (@ F (@ tptp.suc I3))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))) (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (D (-> tptp.nat tptp.complex))) (= (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X2) I3)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ D I3)) (@ (@ tptp.power_power_complex X2) I3)))) _let_1)))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ C I3) (@ D I3)))))) (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (D (-> tptp.nat tptp.real))) (= (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X2) I3)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ D I3)) (@ (@ tptp.power_power_real X2) I3)))) _let_1)))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ C I3) (@ D I3)))))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))) (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((A (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((R2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R2) K3)) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R2) N))) N))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N) M)) tptp.one_one_nat)) M))) (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X3)) (@ tptp.abs_abs_Code_integer Y)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X3) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))))) (forall ((X3 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 X3)) (@ tptp.abs_abs_real Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X3)) (@ tptp.abs_abs_rat Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))) (forall ((X3 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 X3)) (@ tptp.abs_abs_int Y)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))) (forall ((X3 tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X3) tptp.one_one_Code_integer))) (forall ((X3 tptp.rat)) (= (= (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X3) tptp.one_one_rat))) (forall ((X3 tptp.real)) (= (= (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X3) tptp.one_one_real))) (forall ((X3 tptp.int)) (= (= (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X3) tptp.one_one_int))) (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N) (@ (@ tptp.power_8256067586552552935nteger A) N)))) (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N) (@ (@ tptp.power_power_real A) N)))) (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N) (@ (@ tptp.power_power_int A) N)))) (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex W2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ C K) tptp.zero_zero_complex)))) (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real W2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ C K) tptp.zero_zero_real)))) (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (forall ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ C I3) tptp.zero_zero_complex))))) (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat)) (= (forall ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ C I3) tptp.zero_zero_real))))) (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))) (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))) (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))) (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))) (forall ((N tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))) (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K3))) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) N))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K3))) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) N))) (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K3))) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) N))) (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K3)) (@ (@ tptp.minus_minus_nat M) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N)) M)))) (forall ((M tptp.nat) (N tptp.nat) (R2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K3)) (@ (@ tptp.binomial N) (@ (@ tptp.minus_minus_nat R2) K3))))) (@ tptp.set_ord_atMost_nat R2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N)) R2))) (forall ((Y tptp.code_integer) (X3 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X3) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X3)) Y))))) (forall ((Y tptp.real) (X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) Y))))) (forall ((Y tptp.rat) (X3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X3) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X3)) Y))))) (forall ((Y tptp.int) (X3 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 X3) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X3)) Y))))) (forall ((X3 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X3)) tptp.one_one_Code_integer))) (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real))) (forall ((X3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X3)) tptp.one_one_rat))) (forall ((X3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X3)) tptp.one_one_int))) (forall ((X3 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X3)) tptp.one_one_Code_integer))) (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) tptp.one_one_real))) (forall ((X3 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X3)) tptp.one_one_rat))) (forall ((X3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X3)) tptp.one_one_int))) (forall ((N tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))) (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))) (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))) (forall ((I6 tptp.set_nat) (X3 (-> tptp.nat tptp.code_integer)) (A (-> tptp.nat tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X3 I4)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X3) I6) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_real) (X3 (-> tptp.real tptp.code_integer)) (A (-> tptp.real tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X3 I4)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X3) I6) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7713935264441627589nteger (lambda ((I3 tptp.real)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_int) (X3 (-> tptp.int tptp.code_integer)) (A (-> tptp.int tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X3 I4)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X3) I6) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I3 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_complex) (X3 (-> tptp.complex tptp.code_integer)) (A (-> tptp.complex tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X3 I4)))) (=> (= (@ (@ tptp.groups6621422865394947399nteger X3) I6) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups6621422865394947399nteger (lambda ((I3 tptp.complex)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_real) (X3 (-> 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) (@ X3 I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X3) 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 ((I3 tptp.real)) (@ (@ tptp.times_times_real (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_int) (X3 (-> 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) (@ X3 I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X3) 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 ((I3 tptp.int)) (@ (@ tptp.times_times_real (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_complex) (X3 (-> 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) (@ X3 I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X3) 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 ((I3 tptp.complex)) (@ (@ tptp.times_times_real (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_nat) (X3 (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X3 I4)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X3) I6) tptp.one_one_rat) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_real) (X3 (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X3 I4)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X3) I6) tptp.one_one_rat) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups1300246762558778688al_rat (lambda ((I3 tptp.real)) (@ (@ tptp.times_times_rat (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_int) (X3 (-> tptp.int tptp.rat)) (A (-> tptp.int tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X3 I4)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat X3) I6) tptp.one_one_rat) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((I3 tptp.int)) (@ (@ tptp.times_times_rat (@ A I3)) (@ X3 I3)))) I6)) B))) Delta))))) (forall ((X3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X3))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ (@ tptp.times_times_complex (@ _let_2 X3)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))) (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ (@ tptp.times_times_rat (@ _let_2 X3)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))) (forall ((X3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X3))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ (@ tptp.times_times_int (@ _let_2 X3)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))) (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X3))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ (@ tptp.times_times_real (@ _let_2 X3)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))) (forall ((C (-> tptp.nat tptp.complex)) (A tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex A) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex) (not (forall ((B5 (-> tptp.nat tptp.complex))) (not (forall ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z4) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B5 I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))))))))) (forall ((C (-> tptp.nat tptp.rat)) (A tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat A) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat) (not (forall ((B5 (-> tptp.nat tptp.rat))) (not (forall ((Z4 tptp.rat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat Z4) I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z4) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B5 I3)) (@ (@ tptp.power_power_rat Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))))))))) (forall ((C (-> tptp.nat tptp.int)) (A tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int A) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int) (not (forall ((B5 (-> tptp.nat tptp.int))) (not (forall ((Z4 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int Z4) I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z4) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ B5 I3)) (@ (@ tptp.power_power_int Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))))))))) (forall ((C (-> tptp.nat tptp.real)) (A tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real A) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real) (not (forall ((B5 (-> tptp.nat tptp.real))) (not (forall ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z4) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ B5 I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))))))))) (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (A tptp.complex)) (exists ((B5 (-> tptp.nat tptp.complex))) (forall ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z4) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B5 I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex A) I3)))) _let_1))))))) (forall ((C (-> tptp.nat tptp.rat)) (N tptp.nat) (A tptp.rat)) (exists ((B5 (-> tptp.nat tptp.rat))) (forall ((Z4 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z4) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B5 I3)) (@ (@ tptp.power_power_rat Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat A) I3)))) _let_1))))))) (forall ((C (-> tptp.nat tptp.int)) (N tptp.nat) (A tptp.int)) (exists ((B5 (-> tptp.nat tptp.int))) (forall ((Z4 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z4) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ B5 I3)) (@ (@ tptp.power_power_int Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int A) I3)))) _let_1))))))) (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (A tptp.real)) (exists ((B5 (-> tptp.nat tptp.real))) (forall ((Z4 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z4) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ B5 I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real A) I3)))) _let_1))))))) (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X3))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))) (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X3))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))) (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X3))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))) (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X3))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))) (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial N)) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (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 ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((M tptp.nat) (A (-> tptp.nat tptp.complex)) (N tptp.nat) (B (-> tptp.nat tptp.complex)) (X3 tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_complex))) (=> (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J) (= (@ B J) tptp.zero_zero_complex))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X3) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B J3)) (@ (@ tptp.power_power_complex X3) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_complex X3) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))) (forall ((M tptp.nat) (A (-> tptp.nat tptp.rat)) (N tptp.nat) (B (-> tptp.nat tptp.rat)) (X3 tptp.rat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_rat))) (=> (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J) (= (@ B J) tptp.zero_zero_rat))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat X3) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B J3)) (@ (@ tptp.power_power_rat X3) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_rat X3) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))) (forall ((M tptp.nat) (A (-> tptp.nat tptp.int)) (N tptp.nat) (B (-> tptp.nat tptp.int)) (X3 tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_int))) (=> (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J) (= (@ B J) tptp.zero_zero_int))) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X3) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ B J3)) (@ (@ tptp.power_power_int X3) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_int X3) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))) (forall ((M tptp.nat) (A (-> tptp.nat tptp.real)) (N tptp.nat) (B (-> tptp.nat tptp.real)) (X3 tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_real))) (=> (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J) (= (@ B J) tptp.zero_zero_real))) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X3) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ B J3)) (@ (@ tptp.power_power_real X3) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_real X3) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))) (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (K tptp.complex)) (= (forall ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X2) I3)))) (@ tptp.set_ord_atMost_nat N)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)) (= (@ C X2) tptp.zero_zero_complex)))))) (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (K tptp.real)) (= (forall ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X2) I3)))) (@ tptp.set_ord_atMost_nat N)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)) (= (@ C X2) tptp.zero_zero_real)))))) (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)))) (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) M)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) M)))) (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)))) (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex A) B)) N) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_complex A) K3))) (@ (@ tptp.power_power_complex B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) N) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_int A) K3))) (@ (@ tptp.power_power_int B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat A) B)) N) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_rat A) K3))) (@ (@ tptp.power_power_rat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) B)) N) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_real A) K3))) (@ (@ tptp.power_power_real B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) B)) N) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s4660882817536571857er_int A) K3))) (@ (@ tptp.comm_s4660882817536571857er_int B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) B)) N) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat A) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) B)) N) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s7457072308508201937r_real A) K3))) (@ (@ tptp.comm_s7457072308508201937r_real B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))) (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X3 tptp.nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_nat))) (=> (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J) (= (@ B J) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I3)) (@ (@ tptp.power_power_nat X3) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X3) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X3) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N) K3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) N))) (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.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 P2)) (@ (@ 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 P2) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.rat)) (H2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_rat (= J3 K)) tptp.zero_zero_rat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.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 P2)) (@ (@ 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 P2) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.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 P2)) (@ (@ 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 P2) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.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 P2)) (@ (@ 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 P2) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_complex (= J3 K)) tptp.one_one_complex) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_real (= J3 K)) tptp.one_one_real) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.rat)) (H2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_rat (= J3 K)) tptp.one_one_rat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_int (= J3 K)) tptp.one_one_int) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_nat (= J3 K)) tptp.one_one_nat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((M tptp.nat) (A tptp.complex) (X3 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 X3) 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 X3)) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X3) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))) (forall ((M tptp.nat) (A tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) A)) K3)) (@ (@ tptp.power_power_rat X3) K3))) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X3)) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X3) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))) (forall ((M tptp.nat) (A tptp.real) (X3 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 X3) 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 X3)) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X3))) X3))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (forall ((X3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X3))) X3))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (forall ((X3 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) (@ tptp.ring_1_of_int_real N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X3) N))) (forall ((X3 tptp.rat) (N tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X3) (@ tptp.ring_1_of_int_rat N)))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim7778729529865785530nd_rat X3) N))) (forall ((N tptp.nat) (Z tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_int Z) N) A) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= I3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int A)) (@ (@ (@ tptp.if_int (= I3 N)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.power_power_int Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int)))) (forall ((N tptp.nat) (Z tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_complex Z) N) A) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= I3 tptp.zero_zero_nat)) (@ tptp.uminus1482373934393186551omplex A)) (@ (@ (@ tptp.if_complex (= I3 N)) tptp.one_one_complex) tptp.zero_zero_complex))) (@ (@ tptp.power_power_complex Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))) (forall ((N tptp.nat) (Z tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_8256067586552552935nteger Z) N) A) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ (@ tptp.if_Code_integer (= I3 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ (@ tptp.if_Code_integer (= I3 N)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.power_8256067586552552935nteger Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger)))) (forall ((N tptp.nat) (Z tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_rat Z) N) A) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ (@ tptp.if_rat (= I3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_rat A)) (@ (@ (@ tptp.if_rat (= I3 N)) tptp.one_one_rat) tptp.zero_zero_rat))) (@ (@ tptp.power_power_rat Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat)))) (forall ((N tptp.nat) (Z tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_real Z) N) A) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= I3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_real A)) (@ (@ (@ tptp.if_real (= I3 N)) tptp.one_one_real) tptp.zero_zero_real))) (@ (@ tptp.power_power_real Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))) (forall ((X3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X3))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X3 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X3)))))))))) (forall ((X3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X3))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X3 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X3)))))))))) (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X3))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X3 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X3)))))))))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I3)) (@ tptp.semiri8010041392384452111omplex I3))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I3)) (@ tptp.semiri4939895301339042750nteger I3))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I3)) (@ tptp.semiri1314217659103216013at_int I3))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I3)) (@ tptp.semiri681578069525770553at_rat I3))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ tptp.semiri5074537144036343181t_real I3))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))) (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))) (forall ((M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) K3))) K3)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) M))) (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))) (forall ((M tptp.nat) (A tptp.complex) (X3 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 X3) 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 X3) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X3) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))) (forall ((M tptp.nat) (A tptp.rat) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) A)) K3)) (@ (@ tptp.power_power_rat X3) K3))) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat K3)) A)) tptp.one_one_rat)) K3)) (@ (@ tptp.power_power_rat X3) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X3) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))) (forall ((M tptp.nat) (A tptp.real) (X3 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 X3) 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 X3) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.complex)) (X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X3) I3)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex Y) I3)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X3) 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 X3) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.rat)) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat X3) I3)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat Y) I3)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X3) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_rat Y) K3))) (@ (@ tptp.power_power_rat X3) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.int)) (X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X3) I3)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int Y) I3)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X3) 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 X3) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.real)) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X3) I3)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real Y) I3)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X3) 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 X3) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))) (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))))) (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat I3) (@ (@ tptp.binomial N) I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I3)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I3)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I3)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I3)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))) (forall ((E tptp.real) (C (-> tptp.nat tptp.complex)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.real)) (forall ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z4))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_atMost_nat N)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N)))))))))) (forall ((E tptp.real) (C (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.real)) (forall ((Z4 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z4))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_atMost_nat N)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N)))))))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) 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) X3))) X3))) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.complex)) (X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X3) I3)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex Y) I3)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X3) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I3) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_complex X3) J3)))) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.rat)) (X3 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat X3) I3)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat Y) I3)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X3) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I3) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_rat X3) J3)))) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.int)) (X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X3) I3)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int Y) I3)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X3) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I3) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_int X3) J3)))) (@ tptp.set_ord_lessThan_nat N))))))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.real)) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X3) I3)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real Y) I3)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X3) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I3) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_real X3) J3)))) (@ tptp.set_ord_lessThan_nat N))))))) (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)))))) (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (= (@ (@ tptp.groups2906978787729119204at_rat (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat _let_2) (@ tptp.semiri681578069525770553at_rat M))) tptp.one_one_rat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_rat _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))) (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)))))) (forall ((X3 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 X3)) (@ (@ 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) X3))) X3))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1)))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_complex (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I3))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_int (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I3))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_rat (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I3))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_real (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I3))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I3))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I3))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I3))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I3))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))) (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X3 tptp.code_integer)) (=> (forall ((X5 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X5) (@ (@ P X5) (@ (@ tptp.power_8256067586552552935nteger X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_Code_integer X3)) (@ (@ tptp.power_8256067586552552935nteger X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((P (-> tptp.real tptp.real Bool)) (X3 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 X3)) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((P (-> tptp.rat tptp.rat Bool)) (X3 tptp.rat)) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X5) (@ (@ P X5) (@ (@ tptp.power_power_rat X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_rat X3)) (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((P (-> tptp.int tptp.int Bool)) (X3 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 X3)) (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X3) _let_1))))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (= (@ tptp.arctan X3) (@ 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 X3) _let_1))))))))) (= _let_58 (@ 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 ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) 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 X3) _let_1)))))))) (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) N2)) (forall ((X3 tptp.int)) (= (@ (@ tptp.dvd_dvd_int X3) tptp.one_one_int) (= (@ tptp.abs_abs_int X3) tptp.one_one_int))) (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K)))) (@ tptp.summable_real F))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X3)) (@ _let_1 X3)))) (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real))) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))) (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))) (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))) (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 ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X3)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_eq_real X3) Y))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X3)) (@ tptp.arctan Y)))) (forall ((G (-> tptp.nat tptp.real)) (N5 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3)))) (@ tptp.summable_real F)))) (forall ((G (-> tptp.nat tptp.real)) (N5 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3)))) (@ tptp.summable_complex F)))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N6 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))) (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N6 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2))))))) (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ tptp.summable_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2))))))) (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ tptp.summable_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2))))))) (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))))) (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) (@ tptp.summable_real F))) (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K)))))) (forall ((F (-> tptp.nat tptp.real)) (X3 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X3) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))))) (forall ((F (-> tptp.nat tptp.complex)) (X3 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex X3) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)))))) (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)))))) (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)))))) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (=> (not (= C tptp.zero_zero_complex)) (@ tptp.summable_complex F)))) (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))) (forall ((M tptp.int) (N tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M) N)) tptp.one_one_int) (= (@ tptp.abs_abs_int M) tptp.one_one_int))) (@ tptp.summable_real _let_76) (@ tptp.summable_int _let_75) (@ tptp.summable_complex _let_74) (@ _let_70 tptp.pi) (forall ((Y tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y) X3) (= (@ tptp.abs_abs_int (@ (@ tptp.divide_divide_int X3) Y)) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int X3)) (@ tptp.abs_abs_int Y))))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real F)) C) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C)))))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) (@ tptp.suminf_real F))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (= (@ (@ tptp.plus_plus_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2)))))))) (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (= (@ (@ tptp.plus_plus_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)) (@ tptp.suminf_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2)))))))) (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (= (@ (@ tptp.plus_plus_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)) (@ tptp.suminf_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2)))))))) (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.suminf_complex F)) C)))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (@ (@ tptp.divide_divide_real (@ tptp.suminf_real F)) C)))) (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (@ tptp.summable_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3))))))) (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3))))))) (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_58) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.suminf_real F))))) (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))) (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.suminf_int F))))) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (= (= (@ tptp.suminf_real F) tptp.zero_zero_real) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_real)))))) (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (= (= (@ tptp.suminf_nat F) tptp.zero_zero_nat) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_nat)))))) (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (= (= (@ tptp.suminf_int F) tptp.zero_zero_int) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_int)))))) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F N3))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F))))) (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F N3))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))) (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F N3))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F))))) (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))))) (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))))) (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))))) (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))))) (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_int (@ F N2)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N2))))) (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))) (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))) (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))))) (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))))) (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 ((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 ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))) (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))) (forall ((I2 tptp.int) (D tptp.int)) (=> (not (= I2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int D) I2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int D)) (@ tptp.abs_abs_int I2))))) (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N6 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2))))))) (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 ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N6 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))) (forall ((F (-> tptp.nat tptp.real)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_real F))))))) (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_nat F))))))) (forall ((F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_int F))))))) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F)) (exists ((I3 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3))))))) (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F)) (exists ((I3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3))))))) (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F)) (exists ((I3 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I3))))))) (forall ((F (-> tptp.nat tptp.int)) (X3 tptp.int)) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N3))) X3)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X3)))) (forall ((F (-> tptp.nat tptp.nat)) (X3 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N3))) X3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X3)))) (forall ((F (-> tptp.nat tptp.real)) (X3 tptp.real)) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N3))) X3)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X3)))) (forall ((F (-> tptp.nat tptp.real)) (X3 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X3) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X3)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2))))))) (forall ((F (-> tptp.nat tptp.complex)) (X3 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex X3) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2))))))) (forall ((F (-> tptp.nat tptp.int)) (X3 tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N3))) X3)) (@ tptp.summable_int F)))) (forall ((F (-> tptp.nat tptp.nat)) (X3 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N3))) X3)) (@ tptp.summable_nat F)))) (forall ((F (-> tptp.nat tptp.real)) (X3 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N3))) X3)) (@ tptp.summable_real F)))) (forall ((A (-> tptp.nat tptp.int)) (B3 tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int A) (@ tptp.set_ord_atMost_nat N3))) B3)) (@ tptp.summable_int A)))) (forall ((A (-> tptp.nat tptp.nat)) (B3 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat A) (@ tptp.set_ord_atMost_nat N3))) B3)) (@ tptp.summable_nat A)))) (forall ((A (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real A) (@ tptp.set_ord_atMost_nat N3))) B3)) (@ tptp.summable_real A)))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X3)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X3)))) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X3)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X3)))) (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 ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ F tptp.zero_zero_nat))))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_73) (@ tptp.arctan (@ _let_52 (@ tptp.numeral_numeral_real _let_72))))) (@ _let_38 (@ tptp.arctan (@ _let_68 (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_7))))))))) _let_58) (= _let_58 (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real _let_57) (@ tptp.arctan (@ _let_52 _let_73)))) (@ tptp.arctan (@ _let_52 (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_72)))))))))) (@ (@ tptp.ord_less_real tptp.pi) _let_57) (@ (@ tptp.ord_less_eq_real _let_13) tptp.pi) (forall ((M tptp.int) (N tptp.int)) (=> (not (= M tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M) N)) M) (= (@ tptp.abs_abs_int N) tptp.one_one_int)))) (not (= _let_15 _let_13)) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N2))))))) (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2))))))) (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real F) (@ (@ tptp.plus_plus_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K))))) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))) (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))) (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)))))) (not (= _let_15 tptp.zero_zero_real)) (@ (@ tptp.ord_less_real _let_15) _let_13) (@ (@ tptp.ord_less_eq_real _let_15) _let_13) (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))) (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))) (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))) (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2))))) Z))))) (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2))))) Z))))) (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2))))) Z) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2))))) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2))))) Z) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2))))) (@ F tptp.zero_zero_nat))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X3))))) (forall ((F (-> tptp.nat tptp.complex)) (E tptp.real)) (=> (@ tptp.summable_complex F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N7 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) M2) (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N8)))) 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 ((N7 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) M2) (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N8)))) E)))))))))) (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_real F) (exists ((N7 tptp.nat)) (forall ((N8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N8) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N8)))))) R2))))))) (forall ((R2 tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_complex F) (exists ((N7 tptp.nat)) (forall ((N8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N8) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N8)))))) R2))))))) (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I4)) tptp.one_one_real)) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I3)) (@ (@ tptp.power_power_real Z) I3))))))))) (forall ((R2 tptp.real) (R0 tptp.real) (A (-> tptp.nat tptp.complex)) (M7 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_real R2) R0) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N3))) (@ (@ tptp.power_power_real R0) N3))) M7)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N2))) (@ (@ tptp.power_power_real R2) N2)))))))) (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_nat I4) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ F I4) K)))))))) (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex A)) (@ tptp.suminf_complex B)) (@ tptp.suminf_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3)))))))) (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real A)) (@ tptp.suminf_real B)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3)))))))) (forall ((D tptp.int) (Z tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X3) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X3) Z))) tptp.one_one_int)) D))))) (forall ((D tptp.int) (X3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))) (@ _let_71 _let_15) (@ _let_70 _let_15) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_46)) tptp.pi) (forall ((C tptp.real) (N5 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V7735802525324610683m_real (@ F N3)))))) (@ tptp.summable_real F)))) (forall ((C tptp.real) (N5 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V1022390504157884413omplex (@ F N3)))))) (@ tptp.summable_complex F)))) (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N) I2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I2)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))))) (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N) I2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))))) (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N) I2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))))) (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ F I4) K))))))) (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (@ (@ tptp.sums_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3)))) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex A)) (@ tptp.suminf_complex B)))))) (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (@ (@ tptp.sums_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3)))) (@ (@ tptp.times_times_real (@ tptp.suminf_real A)) (@ tptp.suminf_real B)))))) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X3))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))) (@ (@ tptp.ord_less_real _let_24) tptp.zero_zero_real) (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 ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ F I4) K))))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) tptp.zero_zero_complex))) (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))) tptp.zero_zero_complex))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X3)) (@ tptp.arctan Y)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X3) Y)))))))) (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 ((X3 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 X3)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X3)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X3)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1)))))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))) (forall ((C (-> tptp.nat tptp.complex)) (X3 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X3) N2)))) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ C N2))) (@ (@ tptp.power_power_complex X3) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X3) N2))))))) (forall ((C (-> tptp.nat tptp.real)) (X3 tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X3) N2)))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ C N2))) (@ (@ tptp.power_power_real X3) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X3) N2))))))) (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))) (= tptp.topolo6980174941875973593q_real (lambda ((X4 (-> tptp.nat tptp.real))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_real (@ X4 M6)) (@ X4 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_real (@ X4 N2)) (@ X4 M6))))))) (= tptp.topolo3100542954746470799et_int (lambda ((X4 (-> tptp.nat tptp.set_int))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_set_int (@ X4 M6)) (@ X4 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_set_int (@ X4 N2)) (@ X4 M6))))))) (= tptp.topolo4267028734544971653eq_rat (lambda ((X4 (-> tptp.nat tptp.rat))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_rat (@ X4 M6)) (@ X4 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_rat (@ X4 N2)) (@ X4 M6))))))) (= tptp.topolo1459490580787246023eq_num (lambda ((X4 (-> tptp.nat tptp.num))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_num (@ X4 M6)) (@ X4 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_num (@ X4 N2)) (@ X4 M6))))))) (= tptp.topolo4902158794631467389eq_nat (lambda ((X4 (-> tptp.nat tptp.nat))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_nat (@ X4 M6)) (@ X4 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_nat (@ X4 N2)) (@ X4 M6))))))) (= tptp.topolo4899668324122417113eq_int (lambda ((X4 (-> tptp.nat tptp.int))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_int (@ X4 M6)) (@ X4 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_int (@ X4 N2)) (@ X4 M6))))))) (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_real (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo6980174941875973593q_real X8))) (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_set_int (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo3100542954746470799et_int X8))) (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_rat (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo4267028734544971653eq_rat X8))) (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_num (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo1459490580787246023eq_num X8))) (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_nat (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo4902158794631467389eq_nat X8))) (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_int (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo4899668324122417113eq_int X8))) (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex) (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real) (= (@ tptp.cos_real tptp.pi) _let_11) (forall ((X3 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X3)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X3)))) (forall ((X3 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X3) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X3)))) (forall ((X3 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X3) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X3)))) (forall ((X3 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X3)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X3)))) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X3))) (let ((_let_2 (@ tptp.cos_complex X3))) (= (@ (@ 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 ((X3 tptp.real)) (let ((_let_1 (@ tptp.sin_real X3))) (let ((_let_2 (@ tptp.cos_real X3))) (= (@ (@ 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 ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)) (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)) (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)) (= (@ tptp.cos_real _let_15) tptp.zero_zero_real) (= (@ tptp.sin_real _let_46) tptp.zero_zero_real) (= (@ tptp.sin_real _let_15) tptp.one_one_real) (= (@ tptp.cos_real _let_46) tptp.one_one_real) (forall ((X3 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X3))) (forall ((X3 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X3))) (forall ((X3 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X3)) (@ tptp.cos_real X3))) (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))) (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X3)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X3)) _let_1)) tptp.one_one_real))) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X3)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X3)) _let_1)) tptp.one_one_complex))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X3)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X3)) _let_1)) tptp.one_one_real))) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X3)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X3)) _let_1)) tptp.one_one_complex))) (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.zero_zero_real)) (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.one_one_real)) (forall ((X3 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X3)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X3)))) (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)) (forall ((N tptp.int)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.one_one_real)) (= (@ tptp.cos_real _let_69) tptp.zero_zero_real) (= (@ tptp.sin_real _let_69) _let_11) (forall ((N tptp.int)) (let ((_let_1 (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))))) (let ((_let_2 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))))))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X3) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X3)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X3)) (@ tptp.sin_real Y))))) (forall ((X3 tptp.real) (Y tptp.real)) (exists ((R3 tptp.real) (A5 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (and (= X3 (@ _let_1 (@ tptp.cos_real A5))) (= Y (@ _let_1 (@ tptp.sin_real A5))))))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X3)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X3)) (@ tptp.sin_real Y))))) (forall ((X3 tptp.complex)) (=> (= (@ tptp.cos_complex X3) tptp.one_one_complex) (= (@ tptp.sin_complex X3) tptp.zero_zero_complex))) (forall ((X3 tptp.real)) (=> (= (@ tptp.cos_real X3) tptp.one_one_real) (= (@ tptp.sin_real X3) tptp.zero_zero_real))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X3)) (@ tptp.sin_real Y))))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X3) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X3)) (@ tptp.sin_real Y))))) (forall ((X3 tptp.real)) (=> (= (@ tptp.sin_real X3) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X3)) tptp.one_one_real))) (forall ((X3 tptp.complex)) (=> (= (@ tptp.sin_complex X3) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X3)) tptp.one_one_real))) (forall ((X3 tptp.real)) (=> (= (@ tptp.sin_real X3) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X3)) tptp.one_one_real))) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X3)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X3))) (@ tptp.cos_complex X3))))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X3)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X3))) (@ tptp.cos_real X3))))) (forall ((X3 tptp.real)) (exists ((Y3 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ tptp.sin_real Y3) (@ tptp.sin_real X3)) (= (@ tptp.cos_real Y3) (@ tptp.cos_real X3))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X3)) X3))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X3)) tptp.one_one_real)) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X3)) tptp.one_one_real)) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X3))) (@ tptp.abs_abs_real X3))) (forall ((X3 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 X3)) (@ tptp.sin_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y))))) tptp.one_one_real)) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X3)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X3)) _let_1))))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X3)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X3)) _let_1))))) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X3)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X3)) _let_1))))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X3)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X3)) _let_1))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X3)) (@ tptp.sin_real X3)))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (@ _let_1 (@ tptp.sin_real X3)))))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X3))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (=> (= (@ tptp.cos_real X3) (@ tptp.cos_real Y)) (= X3 Y)))))))) (forall ((X3 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 X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (=> (@ _let_2 Y) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y)) (@ _let_1 X3))))))))) (forall ((Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y)))))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X3))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X3))) tptp.one_one_real)) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X3))) tptp.one_one_real)) (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.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.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.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.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)) (= (@ (@ 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)) (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.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.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.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.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 ((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 ((X3 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)) X3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X3)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X3)) _let_2)))))) (forall ((X3 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)) X3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X3)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X3)) _let_2)))))) (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)))))))) (not (= _let_67 tptp.zero_zero_real)) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y)) (@ (@ tptp.ord_less_real Y) X3)))))))) (forall ((Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real Y) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y)))))) (forall ((Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y)) (@ tptp.cos_real X3)))))) (forall ((X3 tptp.real)) (= (= (@ tptp.sin_real X3) tptp.zero_zero_real) (exists ((I3 tptp.int)) (= X3 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) tptp.pi))))) (= tptp.diffs_int (lambda ((C2 (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C2 _let_1))))) (= tptp.diffs_real (lambda ((C2 (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C2 _let_1))))) (= tptp.diffs_rat (lambda ((C2 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ C2 _let_1))))) (forall ((Y tptp.real) (X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) tptp.pi) (= X3 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))) (forall ((X3 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X3))) (= (@ 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 ((X3 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X3))) (= (@ 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 ((C (-> tptp.nat tptp.complex)) (X3 tptp.complex)) (=> (forall ((X5 tptp.complex)) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N2)) (@ (@ tptp.power_power_complex X5) N2))))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X3) N2)))))) (forall ((C (-> tptp.nat tptp.real)) (X3 tptp.real)) (=> (forall ((X5 tptp.real)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ C N2)) (@ (@ tptp.power_power_real X5) N2))))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X3) N2)))))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X3)))))) (@ (@ tptp.ord_less_real _let_67) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real _let_67) 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 ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y4) tptp.zero_zero_real)) (= Y4 X5))))) (forall ((Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_real Y) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y)) (@ tptp.cos_real X3)))))) (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 ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) tptp.pi) (= (@ tptp.cos_real Y4) Y)) (= Y4 X5)))))))) (forall ((X3 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 X3) (=> (@ _let_2 Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X3 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X3 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3))))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (=> (@ (@ tptp.ord_less_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X3 (@ tptp.cos_real T3)) (not (= Y (@ tptp.sin_real T3))))))))))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))) (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)) (= (@ (@ 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)) (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 ((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 ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X3)))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X3)) tptp.zero_zero_real)))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X3))) tptp.one_one_real))))) (= (@ tptp.sin_real _let_53) _let_59) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X3)))))) (forall ((Y tptp.real) (X3 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) X3) (=> (@ (@ tptp.ord_less_eq_real X3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) (@ tptp.sin_real X3))))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X3))) (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 X3) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X3)) (@ tptp.sin_real Y)) (@ _let_1 Y)))))))))) (forall ((X3 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 X3) (=> (@ (@ tptp.ord_less_eq_real X3) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (=> (= (@ tptp.sin_real X3) (@ tptp.sin_real Y)) (= X3 Y))))))))) (= (@ tptp.cos_real _let_55) _let_59) (forall ((X3 tptp.real)) (= (= (@ tptp.cos_real X3) tptp.one_one_real) (exists ((X2 tptp.int)) (= X3 (@ (@ 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 ((X3 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X3))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X3)) (@ (@ 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 ((X3 tptp.real)) (let ((_let_1 (@ tptp.cos_real X3))) (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 X3)) (@ (@ 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 ((X3 tptp.real) (K5 tptp.real) (C (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X3)) K5) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X5)) K5) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ C N2)) (@ (@ tptp.power_power_real X5) N2)))))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X3) N2))))))) (forall ((X3 tptp.complex) (K5 tptp.real) (C (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X3)) K5) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X5)) K5) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N2)) (@ (@ tptp.power_power_complex X5) N2)))))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X3) N2))))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X3)) tptp.zero_zero_real)))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X3)) tptp.zero_zero_real)))) (forall ((Y tptp.real) (X3 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) X3) (=> (@ (@ tptp.ord_less_eq_real X3) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y)) (@ tptp.sin_real X3))))))) (forall ((X3 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 X3) (=> (@ (@ tptp.ord_less_eq_real X3) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X3)) (@ tptp.sin_real Y)) (@ (@ tptp.ord_less_real X3) 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) (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 ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_eq_real Y4) _let_1) (= (@ tptp.sin_real Y4) Y)) (= Y4 X5)))))))))) (forall ((X3 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)) X3) (=> (@ (@ tptp.ord_less_real X3) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X3)))))) (forall ((X3 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)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X3)))))) (forall ((X3 tptp.real)) (= (= (@ tptp.cos_real X3) tptp.one_one_real) (or (exists ((X2 tptp.nat)) (= X3 (@ (@ 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)) (= X3 (@ 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 ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))) (forall ((X3 tptp.real)) (= (= (@ tptp.sin_real X3) tptp.zero_zero_real) (exists ((I3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I3) (= X3 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))) (forall ((X3 tptp.real)) (= (= (@ tptp.cos_real X3) tptp.zero_zero_real) (exists ((I3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I3)) (= X3 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (= (@ tptp.sin_real X3) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3) (= X3 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))) (forall ((X3 tptp.real)) (= (= (@ tptp.sin_real X3) tptp.zero_zero_real) (or (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2) (= X3 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2) (= X3 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (= (@ tptp.cos_real X3) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3)) (= X3 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))) (forall ((X3 tptp.real)) (= (= (@ tptp.cos_real X3) tptp.zero_zero_real) (or (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= X3 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= X3 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))) (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo6980174941875973593q_real X8))) (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo3100542954746470799et_int X8))) (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4267028734544971653eq_rat X8))) (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo1459490580787246023eq_num X8))) (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4902158794631467389eq_nat X8))) (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4899668324122417113eq_int X8))) (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo6980174941875973593q_real X8))) (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo3100542954746470799et_int X8))) (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4267028734544971653eq_rat X8))) (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo1459490580787246023eq_num X8))) (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4902158794631467389eq_nat X8))) (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4899668324122417113eq_int X8))) (= tptp.topolo6980174941875973593q_real (lambda ((X4 (-> tptp.nat tptp.real))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X4 N2)) (@ X4 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X4 (@ tptp.suc N2))) (@ X4 N2)))))) (= tptp.topolo3100542954746470799et_int (lambda ((X4 (-> tptp.nat tptp.set_int))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X4 N2)) (@ X4 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X4 (@ tptp.suc N2))) (@ X4 N2)))))) (= tptp.topolo4267028734544971653eq_rat (lambda ((X4 (-> tptp.nat tptp.rat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X4 N2)) (@ X4 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X4 (@ tptp.suc N2))) (@ X4 N2)))))) (= tptp.topolo1459490580787246023eq_num (lambda ((X4 (-> tptp.nat tptp.num))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X4 N2)) (@ X4 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X4 (@ tptp.suc N2))) (@ X4 N2)))))) (= tptp.topolo4902158794631467389eq_nat (lambda ((X4 (-> tptp.nat tptp.nat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X4 N2)) (@ X4 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X4 (@ tptp.suc N2))) (@ X4 N2)))))) (= tptp.topolo4899668324122417113eq_int (lambda ((X4 (-> tptp.nat tptp.int))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X4 N2)) (@ X4 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X4 (@ tptp.suc N2))) (@ X4 N2)))))) (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_real (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo6980174941875973593q_real X8))) (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_set_int (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo3100542954746470799et_int X8))) (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_rat (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo4267028734544971653eq_rat X8))) (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_num (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo1459490580787246023eq_num X8))) (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_nat (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo4902158794631467389eq_nat X8))) (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_int (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo4899668324122417113eq_int X8))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real X3) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ tptp.cos_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))))) (forall ((X3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X3) (= (@ tptp.cos_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))))) (forall ((X3 tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X3)) (= (@ tptp.cos_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))) (forall ((X3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X3) _let_1))))) (@ tptp.sin_real X3))) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X3))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X3))) (=> (not (= (@ tptp.cos_complex X3) 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 ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X3))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X3))) (=> (not (= (@ tptp.cos_real X3) 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 ((X3 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X3) tptp.pi)) (@ tptp.tan_real X3))) (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex) (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat) (= (@ 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.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex) (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat) (= (@ 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.semiri5044797733671781792omplex _let_34) tptp.one_one_complex) (= (@ tptp.semiri773545260158071498ct_rat _let_34) tptp.one_one_rat) (= (@ tptp.semiri1406184849735516958ct_int _let_34) tptp.one_one_int) (= (@ tptp.semiri2265585572941072030t_real _let_34) tptp.one_one_real) (= (@ tptp.semiri1408675320244567234ct_nat _let_34) tptp.one_one_nat) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri773545260158071498ct_rat _let_1) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.semiri773545260158071498ct_rat N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N))))) (forall ((N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)) (forall ((X3 tptp.real) (N tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N)) tptp.pi))) (@ tptp.tan_real X3))) (forall ((X3 tptp.real) (N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi))) (@ tptp.tan_real X3))) (forall ((X3 tptp.real) (I2 tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) tptp.pi))) (@ tptp.tan_real X3))) (= (@ tptp.semiri5044797733671781792omplex _let_26) _let_42) (= (@ tptp.semiri773545260158071498ct_rat _let_26) _let_66) (= (@ tptp.semiri1406184849735516958ct_int _let_26) _let_36) (= (@ tptp.semiri2265585572941072030t_real _let_26) _let_13) (= (@ tptp.semiri1408675320244567234ct_nat _let_26) _let_26) (forall ((X3 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X3))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri3624122377584611663nteger N)) (@ tptp.semiri3624122377584611663nteger M)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real M)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M)))) (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)) (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)) (= 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 ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))) (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger N))) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.plus_plus_nat K) N)))) (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat N))) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.plus_plus_nat K) N)))) (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int N))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K) N)))) (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real N))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K) N)))) (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat N))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri3624122377584611663nteger N)) (@ tptp.semiri3624122377584611663nteger M)) tptp.zero_z3403309356797280102nteger))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))) (= tptp.semiri1406184849735516958ct_int (lambda ((N2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))) (= tptp.semiri773545260158071498ct_rat (lambda ((N2 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))) (= tptp.semiri2265585572941072030t_real (lambda ((N2 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))) (= tptp.semiri1408675320244567234ct_nat (lambda ((N2 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))) (= tptp.tan_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex X2)))) (= tptp.tan_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X2)) (@ tptp.cos_real X2)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri3624122377584611663nteger N)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri773545260158071498ct_rat N)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri1406184849735516958ct_int N)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri2265585572941072030t_real N)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri1408675320244567234ct_nat N)))) (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.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ 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 ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real _let_1) _let_1)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (= (@ tptp.tan_real _let_58) tptp.one_one_real) (= 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.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.semiri773545260158071498ct_rat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M6)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= 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)))))) (= tptp.semiri1406184849735516958ct_int (lambda ((N2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))) (= tptp.semiri773545260158071498ct_rat (lambda ((N2 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))) (= tptp.semiri2265585572941072030t_real (lambda ((N2 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))) (= tptp.semiri1408675320244567234ct_nat (lambda ((N2 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1406184849735516958ct_int N) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri773545260158071498ct_rat N) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri2265585572941072030t_real N) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1408675320244567234ct_nat N) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ tptp.semiri5044797733671781792omplex N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ tptp.semiri3624122377584611663nteger N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ tptp.semiri1406184849735516958ct_int N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ tptp.semiri773545260158071498ct_rat N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real N)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N)) (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) K))))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K))))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N)) (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K))))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K)))))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X3)))))) (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 ((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 ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_real Y4) _let_1) (= (@ tptp.tan_real Y4) Y)) (= Y4 X5)))))))) (forall ((Y tptp.real) (X3 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) X3) (=> (@ (@ tptp.ord_less_real X3) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X3))))))) (forall ((Y tptp.real) (X3 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 X3) (=> (@ (@ tptp.ord_less_real X3) _let_2) (= (@ _let_1 X3) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X3))))))))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X3))) (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 X3) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_real Y) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X3)) (@ 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_58)) _let_11) (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 ((X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X3))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X3)) (@ tptp.tan_complex Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X3) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X3))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X3)) (@ tptp.tan_real Y)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X3) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))) (= tptp.gbinomial_complex (lambda ((A3 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 A3)) K3))) (@ tptp.semiri5044797733671781792omplex K3)))) (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat A3)) K3))) (@ tptp.semiri773545260158071498ct_rat K3)))) (= tptp.gbinomial_real (lambda ((A3 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 A3)) K3))) (@ tptp.semiri2265585572941072030t_real K3)))) (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex K3))) tptp.one_one_complex)) K3)) (@ tptp.semiri5044797733671781792omplex K3)))) (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A3) (@ tptp.semiri681578069525770553at_rat K3))) tptp.one_one_rat)) K3)) (@ tptp.semiri773545260158071498ct_rat K3)))) (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real K3))) tptp.one_one_real)) K3)) (@ tptp.semiri2265585572941072030t_real K3)))) (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 ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X3)))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X3)) tptp.zero_zero_real)))) (forall ((X3 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)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X3)) (@ tptp.tan_real Y))))))) (forall ((X3 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 X3) (=> (@ (@ tptp.ord_less_real X3) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X3)) (@ tptp.tan_real Y)) (@ (@ tptp.ord_less_eq_real X3) Y))))))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) (@ (@ 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 X3))) tptp.one_one_real))) (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 ((X3 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)) X3) (=> (@ (@ tptp.ord_less_real X3) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X3)) X3))))) (forall ((X3 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)) X3) (=> (@ (@ tptp.ord_less_real X3) _let_1) (=> (= (@ tptp.tan_real X3) Y) (= (@ tptp.arctan Y) X3)))))) (forall ((X3 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X3 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))) (forall ((X3 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X3 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))) (forall ((X3 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.rat tptp.real))) (=> (= X3 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_rat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))) (forall ((X3 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X3 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))) (forall ((X3 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X3 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))) (forall ((H2 tptp.real) (F (-> tptp.real tptp.real)) (J2 (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (exists ((B8 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J2 M6)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B8) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N)) (@ tptp.semiri2265585572941072030t_real N)))))))) (forall ((X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X3))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X3) Y))) (=> (not (= (@ tptp.cos_complex X3) 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 ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X3))) (let ((_let_3 (@ (@ tptp.plus_plus_real X3) Y))) (=> (not (= (@ tptp.cos_real X3) 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 ((X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X3))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X3) Y))) (=> (not (= (@ tptp.cos_complex X3) 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 ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X3))) (let ((_let_3 (@ (@ tptp.minus_minus_real X3) Y))) (=> (not (= (@ tptp.cos_real X3) 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 ((X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X3))) (=> (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 X3)) (@ tptp.tan_complex Y))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X3) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X3))) (=> (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 X3)) (@ tptp.tan_real Y))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X3) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (exists ((Z2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z2) (@ (@ tptp.ord_less_real Z2) _let_1) (= (@ tptp.tan_real Z2) X3)))))) (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_complex A) _let_1) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri5044797733671781792omplex _let_1))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_rat A) _let_1) (@ (@ tptp.divide_divide_rat (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri773545260158071498ct_rat _let_1))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A) _let_1) (@ (@ tptp.divide_divide_real (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri2265585572941072030t_real _let_1))))) (forall ((A tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_int A) _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1406184849735516958ct_int _let_1))))) (forall ((A tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_nat A) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri5044797733671781792omplex _let_3) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex _let_2) _let_3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2)) N))) (@ tptp.semiri5044797733671781792omplex N))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri773545260158071498ct_rat _let_3) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat _let_2) _let_3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2)) N))) (@ tptp.semiri773545260158071498ct_rat N))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri2265585572941072030t_real _let_3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real _let_2) _let_3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) N))) (@ tptp.semiri2265585572941072030t_real N))))))) (= 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.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.cos_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ tptp.semiri2265585572941072030t_real N2))) tptp.zero_zero_real)))) (= tptp.gbinomial_complex (lambda ((A3 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 A3) (@ 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))))) (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.divide_divide_rat (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((L tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A3) (@ tptp.semiri681578069525770553at_rat L))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K3))))) (= tptp.gbinomial_real (lambda ((A3 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 A3) (@ 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))))) (forall ((X3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X3) _let_1))))) (@ tptp.cos_real X3))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X3) (= (@ tptp.sin_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))))) (forall ((X3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) X3) (= (@ tptp.sin_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N)))))))) (forall ((X3 tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X3)) (= (@ tptp.sin_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))) (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_real (and (@ _let_2 P4) (not (@ _let_2 N2)))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4)))) (@ (@ tptp.power_power_real X3) N2))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_real (@ tptp.sin_real X3)) (@ tptp.sin_real Y)))) (forall ((X3 tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_complex (and (@ _let_2 P4) (not (@ _let_2 N2)))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4)))) (@ (@ tptp.power_power_complex X3) N2))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X3)) (@ tptp.sin_complex Y)))) (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) P4)) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real X3) N2))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_real)))) (@ tptp.set_ord_atMost_nat P4)))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X3) Y)))) (forall ((X3 tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat _let_1) P4)) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_complex X3) N2))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_complex)))) (@ tptp.set_ord_atMost_nat P4)))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X3) Y)))) (forall ((X3 tptp.real) (A tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real X3))) (let ((_let_2 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ _let_2 Y)) (@ _let_2 (@ _let_1 Y)))))) (forall ((X3 tptp.complex) (A tptp.real) (Y tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X3))) (let ((_let_2 (@ tptp.real_V2046097035970521341omplex A))) (= (@ _let_1 (@ _let_2 Y)) (@ _let_2 (@ _let_1 Y)))))) (forall ((A tptp.real) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 X3)) Y) (@ _let_1 (@ (@ tptp.times_times_real X3) Y))))) (forall ((A tptp.real) (X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 X3)) Y) (@ _let_1 (@ (@ tptp.times_times_complex X3) Y))))) (forall ((X3 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real tptp.one_one_real) X3) X3)) (forall ((X3 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex tptp.one_one_real) X3) X3)) (forall ((A tptp.real) (B tptp.real) (X3 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real A) (@ (@ tptp.real_V1485227260804924795R_real B) X3)) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.times_times_real A) B)) X3))) (forall ((A tptp.real) (B tptp.real) (X3 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex A) (@ (@ tptp.real_V2046097035970521341omplex B) X3)) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.times_times_real A) B)) X3))) (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))))) (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))))) (forall ((X3 tptp.real) (Y tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.real_V1485227260804924795R_real X3) Y)) N) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.power_power_real Y) N)))) (forall ((X3 tptp.real) (Y tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.real_V2046097035970521341omplex X3) Y)) N) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.power_power_complex Y) N)))) (forall ((X3 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (@ tptp.uminus_uminus_real X3))) (forall ((X3 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (@ tptp.uminus1482373934393186551omplex X3))) (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)) (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)) (forall ((A tptp.real) (X3 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.real_V7735802525324610683m_real X3)))) (forall ((A tptp.real) (X3 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex A) X3)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.real_V1022390504157884413omplex X3)))) (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))))) (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)))) (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))))) (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)))) (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)))))) (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))))) (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)) (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)) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))) (= tptp.real_V1485227260804924795R_real tptp.times_times_real) (forall ((A tptp.real) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X3)) (@ _let_1 Y))))) (forall ((A tptp.real) (X3 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X3) Y)) (@ (@ tptp.plus_plus_complex (@ _let_1 X3)) (@ _let_1 Y))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))) (forall ((X3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_real X3) N2)))) (@ tptp.sin_real X3))) (forall ((X3 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_complex X3) N2)))) (@ tptp.sin_complex X3))) (= tptp.sin_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_real X2) N2)))))) (= tptp.sin_complex (lambda ((X2 tptp.complex)) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_complex X2) N2)))))) (forall ((X3 tptp.real) (Y tptp.real) (Xa2 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real X3) Y)) Xa2) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real X3) Xa2)) (@ (@ tptp.real_V1485227260804924795R_real Y) Xa2)))) (forall ((X3 tptp.real) (Y tptp.real) (Xa2 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.plus_plus_real X3) Y)) Xa2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex X3) Xa2)) (@ (@ tptp.real_V2046097035970521341omplex Y) Xa2)))) (forall ((A tptp.real) (B tptp.real) (X3 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real A) B)) X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) (@ (@ tptp.real_V1485227260804924795R_real B) X3)))) (forall ((A tptp.real) (B tptp.real) (X3 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.plus_plus_real A) B)) X3) (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex A) X3)) (@ (@ tptp.real_V2046097035970521341omplex B) X3)))) (forall ((X3 tptp.real)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_real X3) N2)))))) (forall ((X3 tptp.complex)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_complex X3) N2)))))) (forall ((X3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X3)) N2))))) (@ tptp.sin_real X3))) (forall ((X3 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X3)) N2))))) (@ tptp.sin_complex X3))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))) (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))))) (forall ((A tptp.real) (B tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) (@ (@ tptp.real_V1485227260804924795R_real B) X3))))) (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)))))) (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))))) (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))))) (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)))))) (forall ((X3 tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 X3)) (@ _let_1 Y)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N))))) (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))) (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)))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N)))))))) (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)))) (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))))) (forall ((A tptp.real) (B tptp.real) (X3 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 X3) Y) (=> (@ _let_1 B) (=> (@ _let_1 X3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) (@ (@ tptp.real_V1485227260804924795R_real B) Y)))))))) (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)))))))) (forall ((A tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 X3))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) tptp.zero_zero_real)))) (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))))) (forall ((A tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) X3)))))) (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) tptp.zero_zero_real)))) (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) tptp.zero_zero_real)))) (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))))) (forall ((X3 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X3)) X3)))) (forall ((R2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) R2)))) (@ (@ tptp.power_power_nat N) R2)))) (forall ((X3 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X3) (@ (@ tptp.plus_plus_real X3) X3))) (forall ((X3 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X3) (@ (@ tptp.plus_plus_complex X3) X3))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.binomial N) K)) (@ tptp.semiri1408675320244567234ct_nat N)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))) (forall ((X3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_real X3) N2)))) (@ tptp.cos_real X3))) (forall ((X3 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_complex X3) N2)))) (@ tptp.cos_complex X3))) (= tptp.cos_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_real X2) N2)))))) (= tptp.cos_complex (lambda ((X2 tptp.complex)) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_complex X2) N2)))))) (forall ((X3 tptp.real)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_real X3) N2)))))) (forall ((X3 tptp.complex)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_complex X3) N2)))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M))))) (forall ((X3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X3)) N2)))) (@ tptp.cos_real X3))) (forall ((X3 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X3)) N2)))) (@ tptp.cos_complex X3))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N)) (@ tptp.semiri5074537144036343181t_real _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N))) (@ tptp.semiri5074537144036343181t_real _let_1))))) (= tptp.binomial (lambda ((N2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K3))) (let ((_let_2 (@ tptp.ord_less_nat N2))) (@ (@ (@ tptp.if_nat (@ _let_2 K3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K3))) (@ (@ tptp.binomial N2) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N2) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))) (= tptp.sin_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) tptp.zero_zero_real) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N2)))))) (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_real (and (@ _let_2 P4) (@ _let_2 N2))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real X3) N2))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_real (@ tptp.cos_real X3)) (@ tptp.cos_real Y)))) (forall ((X3 tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_complex (and (@ _let_2 P4) (@ _let_2 N2))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N2))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_complex X3) N2))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P4) N2)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X3)) (@ tptp.cos_complex Y)))) (forall ((X3 tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (= (@ tptp.sin_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N)))))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X3))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X3) (@ (@ 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 ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X3) (@ (@ 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 X3)) (@ tptp.numeral_numeral_nat _let_1))))))))) (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (=> (@ (@ tptp.ord_less_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T3)) (@ tptp.sin_real T3)))))))))) (forall ((X3 tptp.real) (N tptp.nat)) (=> (not (= X3 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T3))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X3)) (= (@ tptp.exp_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X3) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N)))))))))) (forall ((X3 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X3) M6)))) (@ tptp.set_ord_lessThan_nat N))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X3)) N)))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (= A B))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (= A B))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (= A B))) (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A)) (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A)) (forall ((A tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A)) (forall ((X3 tptp.real) (Y tptp.real)) (= (= (@ tptp.sqrt X3) (@ tptp.sqrt Y)) (= X3 Y))) _let_65 _let_64 _let_63 (forall ((A tptp.real)) (= (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (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)))) (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)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)))) (= (@ tptp.inverse_inverse_real tptp.one_one_real) tptp.one_one_real) (= (@ tptp.invers8013647133539491842omplex tptp.one_one_complex) tptp.one_one_complex) (= (@ tptp.inverse_inverse_rat tptp.one_one_rat) tptp.one_one_rat) (forall ((X3 tptp.real)) (= (= (@ tptp.inverse_inverse_real X3) tptp.one_one_real) (= X3 tptp.one_one_real))) (forall ((X3 tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex X3) tptp.one_one_complex) (= X3 tptp.one_one_complex))) (forall ((X3 tptp.rat)) (= (= (@ tptp.inverse_inverse_rat X3) tptp.one_one_rat) (= X3 tptp.one_one_rat))) (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real B) A))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat B) A))) (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real A)))) (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A)))) (forall ((A tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat A)))) (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.abs_abs_real A)))) (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex (@ tptp.abs_abs_complex A)))) (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.abs_abs_rat A)))) (forall ((X3 tptp.real)) (= (= (@ tptp.sqrt X3) tptp.zero_zero_real) (= X3 tptp.zero_zero_real))) (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X3)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_real X3) Y))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X3)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real X3) Y))) (forall ((X3 tptp.real)) (= (= (@ tptp.sqrt X3) tptp.one_one_real) (= X3 tptp.one_one_real))) (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X3)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_eq_real X3) Y))) (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)))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.inverse_inverse_rat A)) (@ _let_1 A)))) (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))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (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)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_rat B) A)))))) (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)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ _let_1 A)))))) (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))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))) (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)))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.inverse_inverse_rat A)) (@ _let_1 A)))) (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex) (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real) (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X3) tptp.zero_zero_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 ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) 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 ((X3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X3)) tptp.one_one_real) (@ (@ tptp.ord_less_real X3) 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 ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X3)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real))) (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 ((X3 tptp.real)) (= (= (@ tptp.exp_real X3) tptp.one_one_real) (= X3 tptp.zero_zero_real))) (forall ((X3 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X3) X3)) (@ tptp.abs_abs_real X3))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))) (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))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_eq_rat B) A))))) (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)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_eq_rat B) A)))))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real A) (@ tptp.inverse_inverse_real A)) tptp.one_one_real))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.invers8013647133539491842omplex A)) tptp.one_one_complex))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.inverse_inverse_rat A)) tptp.one_one_rat))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) A) tptp.one_one_real))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) A) tptp.one_one_rat))) (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)))) (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))) (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ tptp.inverse_inverse_rat _let_1) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_1)))) (= (@ tptp.sqrt _let_57) _let_13) (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X3)) tptp.one_one_real) (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real))) (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X3)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3))) (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X3)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3))) (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X3)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real))) (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)))) (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))) (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ tptp.inverse_inverse_rat _let_1) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_1)))) (forall ((T tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T)) (@ tptp.sin_real T))) tptp.one_one_real)) (forall ((X3 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X3))) (forall ((X3 tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X3))) (forall ((X3 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 X3) _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 ((R2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.real_V2046097035970521341omplex R2) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ _let_1 A)) (@ _let_1 B))))) (forall ((X3 tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X3) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X3)) K))) (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real A)) N) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real A) N)))) (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex A)) N) (@ tptp.invers8013647133539491842omplex (@ (@ tptp.power_power_complex A) N)))) (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat A)) N) (@ tptp.inverse_inverse_rat (@ (@ tptp.power_power_rat A) N)))) _let_65 _let_64 _let_63 (forall ((A tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.real) (B tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= A B))))) (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= A B))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= A B))))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real)))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex)))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat)))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X3))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X3)))) (forall ((X3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X3))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X3)))) (forall ((Y tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real Y))) (let ((_let_2 (@ tptp.times_times_real X3))) (=> (= (@ (@ tptp.times_times_real Y) X3) (@ _let_2 Y)) (= (@ (@ tptp.times_times_real _let_1) X3) (@ _let_2 _let_1)))))) (forall ((Y tptp.complex) (X3 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex Y))) (let ((_let_2 (@ tptp.times_times_complex X3))) (=> (= (@ (@ tptp.times_times_complex Y) X3) (@ _let_2 Y)) (= (@ (@ tptp.times_times_complex _let_1) X3) (@ _let_2 _let_1)))))) (forall ((Y tptp.rat) (X3 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat Y))) (let ((_let_2 (@ tptp.times_times_rat X3))) (=> (= (@ (@ tptp.times_times_rat Y) X3) (@ _let_2 Y)) (= (@ (@ tptp.times_times_rat _let_1) X3) (@ _let_2 _let_1)))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt X3)) (@ tptp.sqrt Y)))) (forall ((A tptp.real) (B tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (= A B))) (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (= A B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (= A B))) (forall ((X3 tptp.real)) (= (@ tptp.sqrt (@ tptp.inverse_inverse_real X3)) (@ tptp.inverse_inverse_real (@ tptp.sqrt X3)))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X3) Y)) (@ (@ tptp.times_times_real (@ tptp.sqrt X3)) (@ tptp.sqrt Y)))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X3) Y)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X3)) (@ tptp.sqrt Y)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X3)) (@ tptp.sqrt 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 ((X3 tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X3)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X3)))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.sqrt X3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.divide_divide_real _let_1) X3) (@ tptp.inverse_inverse_real _let_1))))) (forall ((R2 tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real R2) (@ tptp.real_V7735802525324610683m_real X3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.inverse_inverse_real X3))) (@ tptp.inverse_inverse_real R2))))) (forall ((R2 tptp.real) (X3 tptp.complex)) (=> (@ (@ tptp.ord_less_eq_real R2) (@ tptp.real_V1022390504157884413omplex X3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.invers8013647133539491842omplex X3))) (@ tptp.inverse_inverse_real R2))))) (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)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)))) (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))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))) (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))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ _let_1 tptp.zero_zero_rat) (@ _let_1 A))))) (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))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))) (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)))) (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (=> (not (= A tptp.zero_zero_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))) (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))))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ tptp.inverse_inverse_rat A)) (=> (not (= A tptp.zero_zero_rat)) (@ _let_1 A))))) (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))) (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat))) (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))))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.inverse_inverse_rat A))))) (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)))))) (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)))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A)))))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real A))))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A))))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat A))))) (= (@ tptp.inverse_inverse_real _let_62) _let_62) (= (@ tptp.invers8013647133539491842omplex _let_61) _let_61) (= (@ tptp.inverse_inverse_rat _let_60) _let_60) (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.one_one_real) (= (@ tptp.inverse_inverse_real A) B))) (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.one_one_complex) (= (@ tptp.invers8013647133539491842omplex A) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.one_one_rat) (= (@ tptp.inverse_inverse_rat A) B))) (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real A3) (@ tptp.inverse_inverse_real B2)))) (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex A3) (@ tptp.invers8013647133539491842omplex B2)))) (= tptp.divide_divide_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat A3) (@ tptp.inverse_inverse_rat B2)))) (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real A3) (@ tptp.inverse_inverse_real B2)))) (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex A3) (@ tptp.invers8013647133539491842omplex B2)))) (= tptp.divide_divide_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat A3) (@ tptp.inverse_inverse_rat B2)))) (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B2)) A3))) (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B2)) A3))) (= tptp.divide_divide_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B2)) A3))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (@ _let_1 (@ tptp.sqrt X3))))) (= tptp.inverse_inverse_real _let_52) (= tptp.invers8013647133539491842omplex (@ tptp.divide1717551699836669952omplex tptp.one_one_complex)) (= tptp.inverse_inverse_rat (@ tptp.divide_divide_rat tptp.one_one_rat)) (forall ((X3 tptp.real) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X3) M))) (let ((_let_2 (@ tptp.inverse_inverse_real X3))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))) (forall ((X3 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X3) M))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex X3))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))) (forall ((X3 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X3) M))) (let ((_let_2 (@ tptp.inverse_inverse_rat X3))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))) (forall ((X3 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X3) M))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X3)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))) (forall ((X3 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X3) M))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X3)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))) (forall ((X3 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X3) M))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X3)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (= (@ tptp.sqrt X3) tptp.zero_zero_real) (= X3 tptp.zero_zero_real)))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (@ _let_1 (@ tptp.sqrt X3))))) (forall ((X3 tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X3)) tptp.zero_zero_real))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X3))) (forall ((Xa2 tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real Xa2)))) (= (@ (@ tptp.times_times_real _let_1) X3) (@ (@ tptp.times_times_real X3) _let_1)))) (forall ((Xa2 tptp.nat) (X3 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.semiri8010041392384452111omplex Xa2)))) (= (@ (@ tptp.times_times_complex _let_1) X3) (@ (@ tptp.times_times_complex X3) _let_1)))) (forall ((Xa2 tptp.nat) (X3 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat Xa2)))) (= (@ (@ tptp.times_times_rat _let_1) X3) (@ (@ tptp.times_times_rat X3) _let_1)))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.abs_abs_real A))))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.abs_abs_rat A))))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X3) (@ _let_1 (@ tptp.sqrt X3))))) (forall ((Xa2 tptp.int) (X3 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.ring_1_of_int_real Xa2)))) (= (@ (@ tptp.times_times_real _let_1) X3) (@ (@ tptp.times_times_real X3) _let_1)))) (forall ((Xa2 tptp.int) (X3 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.ring_17405671764205052669omplex Xa2)))) (= (@ (@ tptp.times_times_complex _let_1) X3) (@ (@ tptp.times_times_complex X3) _let_1)))) (forall ((Xa2 tptp.int) (X3 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.ring_1_of_int_rat Xa2)))) (= (@ (@ tptp.times_times_rat _let_1) X3) (@ (@ tptp.times_times_rat X3) _let_1)))) (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X3)) (@ tptp.exp_complex Y)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X3) Y)))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X3)) (@ tptp.exp_real Y)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X3) Y)))) (forall ((X3 tptp.complex) (Y tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X3) Y) (@ (@ tptp.times_times_complex Y) X3)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X3) Y)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X3)) (@ tptp.exp_complex Y))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (= (@ (@ tptp.times_times_real X3) Y) (@ (@ tptp.times_times_real Y) X3)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X3) Y)) (@ (@ tptp.times_times_real (@ tptp.exp_real X3)) (@ tptp.exp_real Y))))) (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X3) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X3)) (@ tptp.exp_complex Y)))) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X3) Y)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X3)) (@ tptp.exp_real Y)))) (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)))) (= tptp.divide_divide_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (@ (@ tptp.times_times_real X2) (@ tptp.inverse_inverse_real Y6)))) (forall ((X3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X3) N2)))) (@ tptp.exp_real X3))) (forall ((X3 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_complex X3) N2)))) (@ tptp.exp_complex X3))) (= tptp.exp_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2)))))) (= tptp.exp_complex (lambda ((X2 tptp.complex)) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_complex X2) N2)))))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.exp_real X3))) (@ (@ 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))))) (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 ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X3)))) (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))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))) (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)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))) (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))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))) (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)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)))) (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real X3)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3)))) (forall ((X3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat X3)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X3)))) (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real X3)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_real X3) tptp.one_one_real)))) (forall ((X3 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X3)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X3) (@ (@ tptp.ord_less_rat X3) tptp.one_one_rat)))) (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))))) (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat A))))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) A) tptp.one_one_real))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) A) tptp.one_one_rat))) (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))))))) (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))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_2)) _let_1))))))) (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))))))) (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))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.plus_plus_rat A) B))) _let_1))))))) (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))))))) (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))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.minus_minus_rat B) A))) _let_1))))))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real A) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex A) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat A) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X3) Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X3)))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.sqrt X3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.divide_divide_real X3) _let_1) _let_1)))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X3) Y))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X3)) (@ tptp.sqrt Y))))))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3)) (@ tptp.exp_real X3))) (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X3) X3)) (@ (@ tptp.times_times_real Y) Y))))) (forall ((X3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X3)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X3))) tptp.one_one_real)) (forall ((X3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X3)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X3))) tptp.one_one_complex)) (forall ((X3 tptp.complex) (N tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X3) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X3)) N))) (forall ((X3 tptp.real) (N tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X3) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.exp_real X3)) N))) (forall ((N tptp.nat) (X3 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) X3)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X3)) N))) (forall ((N tptp.nat) (X3 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X3)) (@ (@ tptp.power_power_real (@ tptp.exp_real X3)) N))) (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 ((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.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 ((X3 tptp.real)) (let ((_let_1 (@ tptp.exp_real X3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.exp_real X3))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) (@ 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))))))) (= tptp.exp_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))))) (= tptp.exp_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X2) _let_1)))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.times_times_rat A) B))) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat B) A)) (=> (@ (@ tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) B)))))) (@ (@ tptp.ord_less_real _let_39) _let_13) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3)) (@ tptp.exp_real X3)))) (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 ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real Y) (@ tptp.ln_ln_real X3)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y)) X3)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y)) Y)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X3)) X3))))) (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))) (forall ((E tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2)))) (and (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E)))))) (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))) (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 ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_real X3) (@ tptp.sqrt Y)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.sqrt Y)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X3)) Y) (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.ord_less_eq_real _let_48) _let_50) (forall ((Y tptp.real) (X3 tptp.real)) (=> (= (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X3) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ tptp.sqrt X3) Y)))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X3)) 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 ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) Y) (= X3 tptp.zero_zero_real)))) (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) X3) (= Y tptp.zero_zero_real)))) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real _let_59)) _let_13) (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) (X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y))) (= (@ tptp.cos_real _let_58) _let_56) (= (@ tptp.sin_real _let_58) _let_56) (= (@ tptp.tan_real _let_55) _let_51) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X3)) Y)))))) (forall ((X3 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 X3) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real X3) Y))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.power_power_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) N) (= (@ tptp.sqrt (@ _let_3 N)) (@ _let_3 (@ (@ tptp.divide_divide_nat N) _let_2)))))))) (forall ((X3 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 X3)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (forall ((Y tptp.real) (X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (forall ((X3 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 X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X3)) (@ tptp.abs_abs_real Y))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ tptp.ln_ln_real (@ tptp.sqrt X3)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (= (@ tptp.cos_real _let_53) _let_54) (= (@ tptp.sin_real _let_55) _let_54) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X3) (@ tptp.inverse_inverse_real X3))))) (forall ((X3 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X3)))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3)) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (forall ((X3 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 X3) _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 ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X3)) N) (@ (@ tptp.power_power_real X3) (@ (@ tptp.divide_divide_nat N) _let_1))))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X3) Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))) (= (@ tptp.tan_real _let_53) (@ _let_52 _let_51)) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X3)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X3))))))) (forall ((X3 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 X3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) tptp.one_one_real))) (forall ((X3 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 X3)) _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 X3) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U))))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3) (= (@ tptp.arcosh_real X3) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X3) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))) (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X3) _let_1))) N)) (@ tptp.exp_real X3)))))) (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real X3) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X3) _let_1))) N)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X3))))))) (forall ((X3 tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X3)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (forall ((X3 tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X3)) (@ (@ tptp.divide_divide_real X3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (forall ((X3 tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X3)) (= (@ tptp.exp_real X3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X3) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))) (forall ((X3 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 X3) _let_4) (=> (@ (@ tptp.ord_less_real Y) _let_4) (=> (@ _let_3 X3) (=> (@ _let_3 Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U)))))))))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X3))))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.sin_real X3))) (=> (@ (@ 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 X3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))) (= 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)))))))))))) (= 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.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 ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X3)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))) (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 ((X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X3)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_eq_real X3) Y))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X3)) (@ _let_1 X3)))) (forall ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real))) (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real) (= (@ tptp.arccos _let_11) tptp.pi) (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)))) (= (@ tptp.arccos tptp.zero_zero_real) _let_15) (= (@ tptp.arcsin tptp.one_one_real) _let_15) (= (@ tptp.arcsin _let_11) _let_24) (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (@ (@ tptp.times_times_complex X2) (@ tptp.invers8013647133539491842omplex Y6)))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X3)) (@ tptp.cosh_real X3))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X3))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X3)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_eq_real X3) Y)))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X3)) (@ tptp.cosh_real Y)) (@ _let_1 X3)))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ tptp.arcosh_real (@ tptp.cosh_real X3)) X3))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X3))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X3)) (@ tptp.cosh_real Y))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X3)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real X3) Y)))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X3)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real Y) X3))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ tptp.arccos X3)))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) 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 X3)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_eq_real Y) X3))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (@ tptp.arccos X3) (@ tptp.arccos Y)) (= X3 Y)))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X3)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X3)))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X3)) (@ tptp.arcsin Y)))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) 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 X3)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_eq_real X3) Y))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (= (@ tptp.arcsin X3) (@ tptp.arcsin Y)) (= X3 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.zero_zero_real) (@ tptp.arccos Y))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y)) (@ tptp.arccos X3)))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X3)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_real Y) X3))))) (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 ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X3)) X3)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X3)) (@ tptp.arcsin Y)))))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X3)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_real X3) 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 ((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 ((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 ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X3)) tptp.zero_zero_real))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X3) (= (@ tptp.arccos (@ tptp.cos_real X3)) (@ tptp.uminus_uminus_real X3))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X3)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X3)))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X3)) tptp.zero_zero_real))))) (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 ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X3)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X3))))) (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)))))) (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 ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X3) (@ tptp.inverse_inverse_real X3))) (@ 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 ((X3 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)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X3)) X3))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X3) (@ tptp.inverse_inverse_real X3))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (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 ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X3))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ _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 X3)) Y) (@ _let_1 (@ tptp.sin_real Y)))))))))) (forall ((X3 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)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) 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 X3)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) X3))))))))) (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 ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X3)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X3)) tptp.zero_zero_real)))) (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))) (forall ((X3 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) X3) (= (@ (@ tptp.log _let_1) X3) (@ (@ 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 X3)))))) (forall ((X3 tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X3))) (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)) (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (@ _let_1 (@ _let_1 X3)) (@ tptp.uminus1482373934393186551omplex X3)))) (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 ((A tptp.real) (X3 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 X3) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_real (@ _let_1 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X3) Y)))))))) (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X3)) tptp.one_one_real) (@ (@ tptp.ord_less_real X3) A))))) (forall ((A tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ _let_1 (@ (@ tptp.log A) X3)) (@ (@ tptp.ord_less_real A) X3)))))) (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X3) tptp.one_one_real))))) (forall ((A tptp.real) (X3 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 X3) (= (@ _let_2 (@ (@ tptp.log A) X3)) (@ _let_1 X3))))))) (forall ((X3 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X3) tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X3))) (= (@ _let_44 tptp.imaginary_unit) _let_45) (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X3)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3))))) (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real))))) (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X3)) (@ (@ tptp.ord_less_eq_real A) X3))))) (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X3)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X3) A))))) (forall ((A tptp.real) (X3 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 X3) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X3) Y)))))))) (forall ((N tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)) (forall ((Z tptp.complex) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ (@ tptp.divide1717551699836669952omplex Z) (@ (@ tptp.times_times_complex _let_1) tptp.imaginary_unit)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z))) _let_1)))) (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))))) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) _let_26) _let_45) (not (= tptp.imaginary_unit tptp.one_one_complex)) (forall ((W tptp.num)) (not (= tptp.imaginary_unit (@ tptp.numera6690914467698888265omplex W)))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (= (@ _let_1 W) Z) (= W (@ tptp.uminus1482373934393186551omplex (@ _let_1 Z)))))) (forall ((W tptp.num)) (not (= tptp.imaginary_unit (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))))) (= tptp.ln_ln_real (@ tptp.log _let_48)) (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)) (forall ((X3 tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.complex2 X3) Y) tptp.imaginary_unit) (and (= X3 tptp.zero_zero_real) (= Y tptp.one_one_real)))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) tptp.imaginary_unit) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))) (forall ((A tptp.real) (B tptp.real) (X3 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) X3) (@ (@ tptp.divide_divide_real (@ _let_1 X3)) (@ _let_1 B))))))) (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))) (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log B) _let_1)))))) (forall ((A tptp.real) (X3 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 X3) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.times_times_real X3) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X3)) (@ _let_1 Y)))))))))) (forall ((A tptp.real) (X3 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 X3) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.divide_divide_real X3) Y)) (@ (@ tptp.minus_minus_real (@ _let_1 X3)) (@ _let_1 Y)))))))))) (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))) (forall ((A tptp.real) (N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N)) X3) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X3)) (@ tptp.semiri5074537144036343181t_real N))))) (forall ((X3 tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ _let_1 (@ (@ tptp.power_power_real X3) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_1 X3)))))) (forall ((A tptp.real) (X3 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 X3) (= (@ _let_1 (@ tptp.inverse_inverse_real X3)) (@ tptp.uminus_uminus_real (@ _let_1 X3))))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))) (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))) (forall ((A tptp.real) (B tptp.real) (X3 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 X3) (= (@ (@ tptp.log A) X3) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X3)))))))))) (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X3)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))) (forall ((X3 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) X3) (= (@ _let_1 X3) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X3)))))) (forall ((X3 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3)) (@ tptp.cot_real X3))) (= (@ tptp.arg _let_47) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_13)) (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))) (= (@ tptp.arg tptp.imaginary_unit) _let_15) (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))) (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 ((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 ((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)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))) (= (@ tptp.cis _let_24) _let_47) (forall ((X3 tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X3)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X3) (@ (@ tptp.ord_less_eq_real X3) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))) (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))) (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))) (forall ((A tptp.real) (X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X3)) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((X3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X3))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))) (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)) (= (@ tptp.cis tptp.zero_zero_real) tptp.one_one_complex) (forall ((A tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X3) tptp.one_one_real) (= X3 tptp.zero_zero_real)))) (forall ((X3 tptp.real)) (= (= (@ (@ tptp.powr_real X3) tptp.one_one_real) X3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.powr_real X3) tptp.one_one_real) X3))) (forall ((X3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X3))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N))))) (= (@ tptp.cis tptp.pi) _let_45) (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) (X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X3) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X3)) X3)))))) (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 ((X3 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.powr_real X3) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat N))))) (= (@ tptp.cis _let_15) tptp.imaginary_unit) (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)))) (= (@ tptp.cis _let_46) tptp.one_one_complex) (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 ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X3)))) (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 ((X3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X3))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B) (@ _let_1 (@ (@ tptp.times_times_real A) B))))) (forall ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X3) Y))) (forall ((A tptp.real) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X3) A)) (@ (@ tptp.powr_real Y) A))))))) (forall ((X3 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X3))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ tptp.ord_less_real A) B))))) (forall ((A tptp.real) (B tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.powr_real X3))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.real) (B tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.powr_real X3))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))) (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)))) (forall ((A tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X3) A)) (@ (@ tptp.powr_real Y) A)))))) (forall ((A tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X3) A)))))) (forall ((A tptp.real) (X3 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 X3) (@ _let_1 Y)) (= X3 Y)))))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.powr_real X3) Y)))))) (forall ((X3 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X3) A)))))) (forall ((A tptp.real) (B tptp.real) (X3 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) X3) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X3) A)) (@ (@ tptp.powr_real Y) B))))))) (forall ((A tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X3) A)) tptp.one_one_real)))))) (forall ((X3 tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X3) Y)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X3) A)) (@ (@ tptp.powr_real Y) A))))))) (forall ((X3 tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X3) Y)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X3) A)) (@ (@ tptp.powr_real Y) A))))))) (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))))) (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 ((X3 tptp.real) (Y tptp.real)) (=> (not (= X3 tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X3) Y)) (@ (@ tptp.times_times_real Y) (@ tptp.ln_ln_real X3))))) (forall ((X3 tptp.real) (B tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X3 tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X3) Y)) (@ (@ tptp.times_times_real Y) (@ _let_1 X3)))))) (forall ((X3 tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X3)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X3) (@ (@ tptp.ord_less_real X3) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))) (forall ((X3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.powr_real X3) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X3) N)))) (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X3) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X3)))))) (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_real X3) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X3)) Y))))) (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X3)) Y) (@ (@ tptp.ord_less_real X3) (@ (@ tptp.powr_real B) Y)))))) (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X3)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X3))))) (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_real R2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2))) tptp.one_one_real))) (forall ((N tptp.int) (X3 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X3) N))))) (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real R2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2))) tptp.one_one_real))) (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2)))) (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2)))) (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.cis A)) N) (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.powr_real X3) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X3)))) (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real X3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.times_times_real X3) (@ _let_1 Y)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y)))))) (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X3))))) (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X3)) Y) (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.powr_real B) Y)))))) (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X3)) Y))))) (forall ((B tptp.real) (X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X3) (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X3)))))) (forall ((N tptp.int) (X3 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X3) (=> (@ (@ tptp.ord_less_real X3) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X3) N))))) (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)))) (forall ((X3 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X3) A)) A))))) (forall ((X3 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X3)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X3))))) (forall ((B tptp.real) (X3 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 X3) (= (@ (@ tptp.plus_plus_real (@ _let_1 X3)) Y) (@ _let_1 (@ (@ tptp.times_times_real X3) (@ (@ tptp.powr_real B) Y)))))))))) (forall ((B tptp.real) (X3 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 X3) (= (@ (@ tptp.plus_plus_real Y) (@ _let_1 X3)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y)) X3))))))))) (forall ((B tptp.real) (X3 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 X3) (= (@ (@ tptp.minus_minus_real Y) (@ _let_1 X3)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y)) X3))))))))) (forall ((B tptp.real) (X3 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 X3) (= (@ (@ tptp.minus_minus_real (@ _let_1 X3)) Y) (@ _let_1 (@ (@ tptp.times_times_real X3) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y))))))))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.powr_real X3) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X3)))) (forall ((X3 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.powr_real X3) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat N)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) _let_2))))) tptp.one_one_int))))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K3 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K3))) (@ tptp.semiri5074537144036343181t_real N))))) (@ tptp.set_ord_lessThan_nat N)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))))) (= (@ tptp.exp_complex (@ _let_43 tptp.imaginary_unit)) _let_45) (= (@ tptp.exp_complex (@ _let_44 _let_41)) _let_45) (= (@ tptp.exp_complex (@ _let_44 (@ _let_43 _let_42))) tptp.one_one_complex) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_42) _let_41)) tptp.imaginary_unit)) tptp.one_one_complex) (forall ((Z tptp.complex)) (exists ((A5 tptp.complex) (R3 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ tptp.exp_complex A5))))) (forall ((R2 tptp.real) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X3) Y)) (@ (@ tptp.complex2 (@ _let_1 X3)) (@ _let_1 Y))))) (forall ((X3 tptp.real) (Y tptp.real) (R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X3) Y)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X3) R2)) (@ (@ tptp.times_times_real Y) R2)))) (forall ((R2 tptp.real) (X3 tptp.real) (Y tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X3) Y)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R2) X3)) Y))) (forall ((X3 tptp.real) (Y tptp.real) (R2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X3) Y)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X3) R2)) Y))) (= tptp.cis (lambda ((B2 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B2))))) (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))) (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))) (= tptp.complex2 (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex A3)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B2))))) (forall ((Z tptp.complex)) (exists ((R3 tptp.real) (A5 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A5))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A5)))))))) (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)) (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A)))))) (@ tptp.abs_abs_real R2))) (= (@ tptp.csqrt tptp.imaginary_unit) (@ (@ tptp.divide1717551699836669952omplex (@ _let_40 tptp.imaginary_unit)) (@ tptp.real_V4546457046886955230omplex _let_39))) (= tptp.arctan (lambda ((Y6 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) Y6))))))) (= tptp.arcsin (lambda ((Y6 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) Y6))))))) (forall ((L2 tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ tptp.sgn_sgn_int L2))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (and (=> _let_7 (= _let_6 (@ _let_3 _let_1))) (=> (not _let_7) (= _let_6 (@ _let_3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat N) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))) _let_1)))))))))))))))) (forall ((Z tptp.complex)) (= (= (@ tptp.csqrt Z) tptp.one_one_complex) (= Z tptp.one_one_complex))) (= (@ tptp.csqrt tptp.one_one_complex) tptp.one_one_complex) (forall ((R2 tptp.int) (L2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) L2)) K) (and (@ (@ tptp.dvd_dvd_int L2) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))) (forall ((L2 tptp.int) (R2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int L2) (@ tptp.sgn_sgn_int R2))) K) (and (@ (@ tptp.dvd_dvd_int L2) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))) (forall ((L2 tptp.int) (R2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) K)) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))) (forall ((L2 tptp.int) (K tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L2))) (= (@ _let_1 (@ (@ tptp.times_times_int K) (@ tptp.sgn_sgn_int R2))) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))) (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)) (forall ((K tptp.int)) (not (forall ((N3 tptp.nat) (L4 tptp.int)) (not (= K (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L4)) (@ tptp.semiri1314217659103216013at_int N3))))))) (forall ((K tptp.int) (L2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L2)) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2))))) (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))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X3) (@ tptp.the_real (lambda ((X2 tptp.real)) false))))) (= tptp.sgn_sgn_int (lambda ((I3 tptp.int)) (@ (@ (@ tptp.if_int (= I3 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I3)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((V tptp.int) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.abs_abs_int K))) (let ((_let_3 (@ tptp.times_times_int (@ tptp.sgn_sgn_int V)))) (=> (not (= V tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) (@ _let_3 _let_1)) (@ (@ tptp.divide_divide_int _let_2) _let_1))))))) (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.dvd_dvd_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int K)) (@ tptp.sgn_sgn_int L2))) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2)))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt X3)) (@ tptp.csqrt (@ tptp.real_V4546457046886955230omplex X3))))) (= tptp.arccos (lambda ((Y6 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) Y6)))))) (forall ((R2 tptp.int) (L2 tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R2) (@ tptp.sgn_sgn_int L2)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R2)) (@ tptp.abs_abs_int L2)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) L2)) R2)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R2)))))) (= tptp.eucl_rel_int (lambda ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A1 K3) (= A22 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A1 K3) (= A22 L) (= A32 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (not (= L tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q4) L)))) (exists ((R5 tptp.int) (L tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A1 K3) (= A22 L) (= A32 (@ (@ tptp.product_Pair_int_int Q4) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) L)) R5))))))) (forall ((A12 tptp.int) (A23 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A12) A23) A33) (=> (=> (= A23 tptp.zero_zero_int) (not (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A12)))) (=> (forall ((Q3 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int)) (=> (not (= A23 tptp.zero_zero_int)) (not (= A12 (@ (@ tptp.times_times_int Q3) A23)))))) (not (forall ((R3 tptp.int) (Q3 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q3) R3)) (=> (= (@ tptp.sgn_sgn_int R3) (@ tptp.sgn_sgn_int A23)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int A23)) (not (= A12 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q3) A23)) R3)))))))))))) (forall ((L2 tptp.int) (K tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (=> (not (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L2))) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2)))) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K)))))))) (= _let_15 (@ 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))))) (= tptp.pi (@ _let_38 (@ 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)))))) (forall ((L2 tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M) N))) (let ((_let_2 (@ tptp.sgn_sgn_int L2))) (let ((_let_3 (@ tptp.sgn_sgn_int K))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (@ tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))))))))))))))) (= 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)))))))))) (= 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))))))))))) (forall ((X3 tptp.real) (I2 tptp.int)) (let ((_let_1 (@ tptp.power_power_real X3))) (let ((_let_2 (@ (@ tptp.powr_real X3) (@ 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) X3) (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)))))))))))) (= 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 ((X3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real))) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X3)) (@ _let_1 X3)))) (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))) (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)))) (= _let_37 _let_34) (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))) (forall ((I2 tptp.int)) (= (= (@ tptp.nat2 I2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int))) (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)))) (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)) (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))) (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))))) (forall ((Y tptp.int) (X3 tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))) (forall ((X3 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N) (@ tptp.nat2 Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N) Y))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))) (forall ((X3 tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X3))) A) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.semiri5074537144036343181t_real A)))) (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))) (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)))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)) A))) (forall ((A tptp.int) (X3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)))) (forall ((X3 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X3)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X3)) N)) A))) (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N)))) (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 ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X3) Y)))))) (= tptp.numeral_numeral_nat (lambda ((I3 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I3)))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X3)) (@ tptp.nat2 Y)))) (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 Z) (@ tptp.nat2 Z6)) (= Z Z6)))))) (= (lambda ((P5 (-> tptp.nat Bool))) (forall ((X7 tptp.nat)) (@ P5 X7))) (lambda ((P6 (-> tptp.nat Bool))) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ P6 (@ tptp.nat2 X2)))))) (= (lambda ((P5 (-> tptp.nat Bool))) (exists ((X7 tptp.nat)) (@ P5 X7))) (lambda ((P6 (-> tptp.nat Bool))) (exists ((X2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ P6 (@ tptp.nat2 X2)))))) (= tptp.one_one_nat _let_37) (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X3) Y)) (@ (@ tptp.bit_se1409905431419307370or_int X3) Y)) (@ (@ tptp.plus_plus_int X3) Y))) (= tptp.bit_se4205575877204974255it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M6) (@ tptp.semiri1314217659103216013at_int N2))))) (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.bit_se2002935070580805687sk_nat N))) (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)))) (forall ((M tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) Z))) (forall ((X3 tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X3)) N) (@ (@ tptp.ord_less_eq_int X3) (@ tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat) (Z tptp.int)) (= (= (@ tptp.semiri1314217659103216013at_int M) Z) (and (= M (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)))) (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))) (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))) (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))))) (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))) (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))) (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))) (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X3))))) (= tptp.divide_divide_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))) (= tptp.modulo_modulo_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))) (= tptp.sgn_sgn_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (= A3 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A3)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))) (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)))) (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)))) (forall ((M tptp.nat) (W tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= M (@ tptp.nat2 W)) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))) (forall ((W tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= (@ tptp.nat2 W) M) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))) (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) K)))) (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))))))) (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))))) (= tptp.suc (lambda ((A3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) tptp.one_one_int)))) (forall ((Z6 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z6) (=> (@ (@ tptp.ord_less_eq_int Z6) Z) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z) Z6)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6)))))) (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X3) Y)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X3)) (@ tptp.nat2 Y))))))) (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))))) (forall ((X3 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X3) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X3)) (@ tptp.nat2 Y))))) (forall ((Y tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X3) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X3)) (@ tptp.nat2 Y))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X3)) tptp.zero_zero_nat))) (forall ((Z tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N)))) (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X3) Y)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X3)) (@ tptp.nat2 Y))))))) (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))))))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) X3) (=> (@ (@ tptp.ord_less_real X3) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X3)) N)))) (forall ((X3 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X3)) A) (@ (@ tptp.ord_less_eq_nat X3) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))) (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.modulo_modulo_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))) (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K))))) (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K))))) (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N)))) (= (@ tptp.nat2 _let_36) _let_35) (forall ((A tptp.real) (N tptp.nat) (X3 tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) X3) (=> (= X3 (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))) (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))))) (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))))) (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)))))) (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))))))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) X3) (=> (@ (@ tptp.ord_less_real X3) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X3)) N)))) (forall ((Z tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z)) M) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z) (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))) (forall ((Z tptp.complex) (X3 tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X3)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (= (@ tptp.arg Z) X3))))) (forall ((X3 tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (=> (@ (@ tptp.ord_less_int X3) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X3) Y)) _let_1)))))) (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))))) (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))))) (= 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)))))))) (forall ((X3 tptp.real) (N tptp.int)) (let ((_let_1 (@ tptp.power_power_real X3))) (let ((_let_2 (@ (@ tptp.powr_real X3) (@ tptp.ring_1_of_int_real N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N)))))))))))) (forall ((X3 tptp.real)) (=> (not (= X3 tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X3)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X3))))) (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))) (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))) (= tptp.arg (lambda ((Z5 tptp.complex)) (@ (@ (@ tptp.if_real (= Z5 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A3 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z5) (@ tptp.cis A3)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A3) (@ (@ tptp.ord_less_eq_real A3) tptp.pi))))))) (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cis (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_complex))) (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 ((X3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))) (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 ((X3 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X3))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3)))) (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))) (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one) (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) tptp.one) (@ tptp.bit0 tptp.one))) (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit1 M)) (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N) M)))) (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))) (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) tptp.one) tptp.one)) (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))) (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))) (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))) (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))) (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))) (forall ((X3 tptp.real)) (= (= (@ tptp.sin_real (@ (@ tptp.times_times_real X3) tptp.pi)) tptp.zero_zero_real) (@ (@ tptp.member_real X3) tptp.ring_1_Ints_real))) (forall ((X3 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 (= X3 tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X3) 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 ((N3 tptp.num)) (= X3 (@ tptp.bit0 N3))) (=> _let_1 (not (= Y (@ tptp.bit0 tptp.one))))) (=> (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (=> (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M5)) (not (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (=> (=> (exists ((N3 tptp.num)) (= X3 (@ tptp.bit1 N3))) _let_2) (=> (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (not (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))))))))))))))))) (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.zero_zero_real))) (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_real))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M6)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))) (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))) (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))))) (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X3)))) (forall ((X3 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X3))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X3)))) (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)))) (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)))) (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))) (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M6)) (not (@ _let_2 N2)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))) (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat _let_33)) (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt) (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))) (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ _let_1 K)))) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))) (forall ((N tptp.nat) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) tptp.zero_zero_int) L2) (@ (@ tptp.bit_se545348938243370406it_int N) L2))) (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))))) (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))))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= tptp.bit_se2159334234014336723it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)))) (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) N) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N))))) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N) K)))) (forall ((X3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X3) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X3) Y)))))) (= tptp.bit_se7882103937844011126it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))) (= tptp.bit_se2161824704523386999it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))) (forall ((Uu2 Bool) (Uv2 Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D) (= D tptp.one_one_nat))) (forall ((M tptp.nat) (K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N) M))))) (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))) (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q2)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1148574629649215175it_nat Q2) (@ (@ tptp.minus_minus_nat N) M))))) (= tptp.bit_concat_bit (lambda ((N2 tptp.nat) (K3 tptp.int) (L tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K3)) (@ (@ tptp.bit_se545348938243370406it_int N2) L)))) (= tptp.bit_concat_bit (lambda ((N2 tptp.nat) (K3 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K3)) (@ (@ tptp.bit_se545348938243370406it_int N2) L)))) (= tptp.bit_se7879613467334960850it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)))) (= tptp.bit_se545348938243370406it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))) (= tptp.bit_se547839408752420682it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))) (forall ((X3 tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (=> (@ (@ tptp.ord_less_int X3) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X3) Y)) _let_1)))))) (= 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)))))))) (= 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)))))))))))) (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A2)))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))) (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or1269000886237332187st_nat L2) U))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_lessThan_nat K))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_atMost_nat K))) (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))) (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))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))) (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N3) (@ F N3))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) U)))))) (= tptp.finite_finite_nat (lambda ((N9 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N9) (@ (@ tptp.ord_less_eq_nat X2) M6)))))) (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))) (= tptp.finite_finite_nat (lambda ((N9 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N9) (@ (@ tptp.ord_less_nat X2) M6)))))) (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) N5) (@ (@ tptp.ord_less_nat X5) N))) (@ tptp.finite_finite_nat N5))) (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)))))) (= 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))))) (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) _let_32) tptp.zero_zero_int) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_32) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int)) (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int))))) (= 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)))) (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 ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N5))) (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))))) (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))))) (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))) (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int)) (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))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))) (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N))) (forall ((M tptp.num) (N tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N) M))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))) (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)))) (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))) (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.zero_zero_int)) (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))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))) (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))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))) (= 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))))))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) K))))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) K))))) (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or1266510415728281911st_int L2) U))) (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I3) (@ (@ tptp.ord_less_eq_int I3) B)))))) (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.ord_less_int A) I3) (@ (@ tptp.ord_less_eq_int I3) B)))))) (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I3) (@ (@ tptp.ord_less_int I3) B)))))) (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))))) (= tptp.finite_finite_nat (lambda ((S4 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S4) (@ tptp.set_ord_atMost_nat K3))))) (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N)))))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C))))))) (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S3) (@ tptp.set_ord_lessThan_nat K2))))) (forall ((N tptp.nat)) (= (@ (@ tptp.root N) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((X3 tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X3) X3)) (forall ((X3 tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X3) tptp.zero_zero_real)) (forall ((N tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X3) (@ _let_1 Y)) (= X3 Y))))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X3) tptp.zero_zero_real) (= X3 tptp.zero_zero_real)))) (forall ((N tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X3) Y))))) (forall ((N tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X3)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X3) Y))))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X3) tptp.one_one_real) (= X3 tptp.one_one_real)))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) tptp.one_one_real) tptp.one_one_real))) (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real)))) (forall ((N 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) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X3) tptp.zero_zero_real)))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X3)) tptp.one_one_real) (@ (@ tptp.ord_less_real X3) tptp.one_one_real)))) (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X3)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real)))) (forall ((N 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) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X3)) N) X3)))) (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.uminus_uminus_real X3)) (@ tptp.uminus_uminus_real (@ _let_1 X3))))) (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.inverse_inverse_real X3)) (@ tptp.inverse_inverse_real (@ _let_1 X3))))) (forall ((N tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X3) Y)) (@ (@ tptp.divide_divide_real (@ _let_1 X3)) (@ _let_1 Y))))) (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.root M))) (let ((_let_2 (@ tptp.root N))) (= (@ _let_1 (@ _let_2 X3)) (@ _let_2 (@ _let_1 X3)))))) (forall ((N tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.times_times_real X3) Y)) (@ (@ tptp.times_times_real (@ _let_1 X3)) (@ _let_1 Y))))) (forall ((M tptp.nat) (N tptp.nat) (X3 tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N)) X3) (@ (@ tptp.root M) (@ (@ tptp.root N) X3)))) (forall ((X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.root N) X3))))) (forall ((N tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_real (@ _let_1 X3)) (@ _let_1 Y)))))) (forall ((N tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X3) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X3)) (@ _let_1 Y)))))) (forall ((N tptp.nat) (X3 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.power_power_real X3) K)) (@ (@ tptp.power_power_real (@ _let_1 X3)) K))))) (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ tptp.abs_abs_real X3)) (@ tptp.abs_abs_real (@ _let_1 X3)))))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N) X3)) (@ tptp.sgn_sgn_real X3)))) (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.root N) X3)))))) (forall ((N tptp.nat) (N5 tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ tptp.ord_less_real (@ (@ tptp.root N5) X3)) (@ (@ tptp.root N) X3)))))) (= tptp.sqrt (@ tptp.root _let_26)) (forall ((N tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y) N))) (@ tptp.abs_abs_real Y)))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N) X3))))) (forall ((N tptp.nat) (N5 tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X3)) (@ (@ tptp.root N5) X3))))))) (forall ((N tptp.nat) (N5 tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N5) X3)) (@ (@ tptp.root N) X3)))))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X3)) N) X3)))) (forall ((N tptp.nat) (Y tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N) X3) (= (@ (@ tptp.root N) X3) Y))))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X3) N)) X3)))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X3)) N) X3))) (forall ((N tptp.nat) (Y tptp.real) (X3 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (= (@ (@ tptp.power_power_real Y) N) X3) (= (@ (@ tptp.root N) X3) Y)))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X3) N)) X3))) (forall ((N tptp.nat) (N5 tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X3)) (@ (@ tptp.root N5) X3))))))) (forall ((N tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N))) Y))) (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ (@ tptp.root N) X3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N)) X3)))) (forall ((N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N)))))) (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N))))))) (forall ((N tptp.nat) (B tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N) B)) X3) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) X3)))))) (forall ((P (-> tptp.real Bool)) (N tptp.nat) (X3 tptp.real)) (= (@ P (@ (@ tptp.root N) X3)) (and (=> (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (forall ((Y6 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N)) X3) (@ P Y6))))))) (forall ((S3 tptp.set_int)) (= (not (@ tptp.finite_finite_int S3)) (forall ((M6 tptp.int)) (exists ((N2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int M6) (@ tptp.abs_abs_int N2)) (@ (@ tptp.member_int N2) S3)))))) (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M6 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N2) (@ (@ tptp.member_nat N2) S3)))))) (forall ((K tptp.nat) (S3 tptp.set_nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M5) (exists ((N8 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N8) (@ (@ tptp.member_nat N8) S3))))) (not (@ tptp.finite_finite_nat S3)))) (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M6 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.member_nat N2) S3)))))) (forall ((N tptp.nat) (X3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.root N) X3) (@ (@ tptp.powr_real X3) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N))))))) (= tptp.finite_finite_nat (lambda ((S4 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S4) (@ tptp.set_ord_lessThan_nat K3))))) (forall ((X3 tptp.num) (Xa2 tptp.num) (Y tptp.num)) (let ((_let_1 (= X3 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (@ (@ tptp.bit_or_not_num_neg X3) Xa2) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X3) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y tptp.one) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bit1 M5)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.bit0 tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y tptp.one) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))) (not (forall ((N3 tptp.num)) (=> (= X3 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))))))))))))))))) (= tptp.int_ge_less_than (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z7) (@ (@ tptp.ord_less_int Z7) Z5))))))) (= tptp.int_ge_less_than2 (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z5) (@ (@ tptp.ord_less_int Z7) Z5))))))) (forall ((X3 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 X3) Y) (=> (@ _let_2 X3) (=> (=> (= X3 _let_1) (=> Y (not (@ _let_2 _let_1)))) (=> (forall ((Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv))) (=> (= X3 _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) true))) (=> (= X3 _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy2))) (=> (= X3 _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))) (=> (= X3 _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or4665077453230672383an_nat L2) U))) (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N) (@ P M6))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N) (@ P M6))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))) (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L2) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L2) U))) (= tptp.set_ord_lessThan_nat _let_9) (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat N) (@ _let_1 N))))) (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N5))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.suc N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N) (@ _let_1 N)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))) (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ tptp.semiri1408675320244567234ct_nat N))) (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)))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))) (forall ((X3 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X3)) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X3) (=> (forall ((Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv))) (=> (= X3 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (=> (forall ((Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) true))) (=> (= X3 _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))) (=> (= X3 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))) (forall ((X3 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 X3) (=> (@ _let_2 X3) (=> (=> (= X3 _let_1) (not (@ _let_2 _let_1))) (not (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy2))) (=> (= X3 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))) (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)))) (forall ((N tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I4 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J) (=> (@ (@ tptp.ord_less_nat J) N) (@ (@ tptp.ord_less_eq_nat (@ A I4)) (@ A J))))) (=> (forall ((I4 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J) (=> (@ (@ tptp.ord_less_nat J) N) (@ (@ tptp.ord_less_eq_nat (@ B J)) (@ B I4))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I3)) (@ B I3)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))) (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int L2) U))) (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))) (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L2) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L2) U))) (= 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 ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N2) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X4 M6)) (@ X4 N2)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))) (= tptp.code_Target_positive tptp.numeral_numeral_int) (= tptp.unique4921790084139445826nteger (lambda ((L tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))) (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)))))) (forall ((V tptp.num)) (= (@ tptp.re (@ tptp.numera6690914467698888265omplex V)) (@ tptp.numeral_numeral_real V))) (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)))) (= tptp.sgn_sgn_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))) (@ _let_31 tptp.zero_z3403309356797280102nteger) (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))) (forall ((K tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger K) tptp.zero_z3403309356797280102nteger) K)) (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L2) L2)) (forall ((K tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)) (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L2) tptp.zero_z3403309356797280102nteger)) (forall ((X3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X3)) (@ tptp.real_V1022390504157884413omplex X3))) (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real) (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.plus_plus_complex X3) Y)) (@ (@ tptp.plus_plus_real (@ tptp.re X3)) (@ tptp.re Y)))) (forall ((R2 tptp.real) (X3 tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R2) X3)) (@ (@ tptp.times_times_real R2) (@ tptp.re X3)))) (forall ((X3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X3))) (@ tptp.real_V1022390504157884413omplex X3))) (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))) (= tptp.one_one_int tptp.one_one_int) (= tptp.one_one_nat tptp.one_one_nat) (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)))))) (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.re (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))) (= 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)))))))))) (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)))))))) (= 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))))))))) (forall ((X3 tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X3) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.power_power_complex X3) N)) tptp.zero_zero_real))) (forall ((V tptp.num)) (= (@ tptp.im (@ tptp.numera6690914467698888265omplex V)) tptp.zero_zero_real)) (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.re Z))) (forall ((X3 tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X3) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.power_power_real (@ tptp.re X3)) N)))) (forall ((Z tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.uminus_uminus_real (@ tptp.im Z)))) (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)))) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.re X3))) (=> (= (@ tptp.im X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= (@ tptp.csqrt X3) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt _let_1))))))) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.im X3))) (=> (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 X3)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X3)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X3)))))) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.re X3))) (=> (= (@ tptp.im X3) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X3) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))) (forall ((Xa2 tptp.int) (X3 tptp.int)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X3)) (@ tptp.code_integer_of_int (@ (@ tptp.modulo_modulo_int Xa2) X3)))) (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real) (= (@ tptp.im tptp.one_one_complex) tptp.zero_zero_real) (forall ((Xa2 tptp.int) (X3 tptp.int)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X3)) (@ tptp.code_integer_of_int (@ (@ tptp.plus_plus_int Xa2) X3)))) (forall ((Xa2 tptp.int) (X3 tptp.int)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X3)) (@ tptp.code_integer_of_int (@ (@ tptp.times_times_int Xa2) X3)))) (= tptp.one_one_Code_integer (@ tptp.code_integer_of_int tptp.one_one_int)) (forall ((Xa2 tptp.int) (X3 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X3)) (@ (@ tptp.ord_less_eq_int Xa2) X3))) (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.plus_plus_complex X3) Y)) (@ (@ tptp.plus_plus_real (@ tptp.im X3)) (@ tptp.im Y)))) (forall ((R2 tptp.real) (X3 tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R2) X3)) (@ (@ tptp.times_times_real R2) (@ tptp.im X3)))) (forall ((X3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X3))) (@ tptp.real_V1022390504157884413omplex X3))) (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X3) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X3)) (@ tptp.im Y))) (@ (@ tptp.times_times_real (@ tptp.im X3)) (@ tptp.re Y))))) (forall ((X3 tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.im X3) (@ tptp.im Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X3))) (@ tptp.abs_abs_real (@ tptp.re Y)))))) (forall ((X3 tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.re X3) (@ tptp.re Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X3)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X3))) (@ tptp.abs_abs_real (@ tptp.im Y)))))) (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X3) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X3)) (@ tptp.re Y))) (@ (@ tptp.times_times_real (@ tptp.im X3)) (@ tptp.im Y))))) (= tptp.plus_plus_complex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real (@ tptp.re X2)) (@ tptp.re Y6))) (@ (@ tptp.plus_plus_real (@ tptp.im X2)) (@ tptp.im Y6))))) (= tptp.real_V2046097035970521341omplex (lambda ((R5 tptp.real) (X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R5))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X2))) (@ _let_1 (@ tptp.im X2)))))) (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))))))) (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))))) (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.im (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))) (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))))) (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))))) (forall ((A tptp.complex)) (= A (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.re A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.im A)))))) (= tptp.times_times_complex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (let ((_let_1 (@ tptp.re Y6))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X2)))) (let ((_let_3 (@ tptp.im Y6))) (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))))))))) (= tptp.exp_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.exp_real (@ tptp.re Z5)))) (@ tptp.cis (@ tptp.im Z5))))) (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))))) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X3) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X3))) (@ tptp.im X3))))) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X3) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X3)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X3)) _let_1))))) (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)))) (= 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)))))) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X3))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X3)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X3)) _let_1))))))) (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)))))) (forall ((X3 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 X3) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X3)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X3)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))) (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)))) (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))))) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X3))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X3)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X3)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))) (forall ((X3 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 X3) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X3)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X3)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))) (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)))) (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))))) (= 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)))))))) (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y6))) (let ((_let_3 (@ tptp.re Y6))) (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)))))))))) (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R2))) (@ tptp.im Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R2)) (@ tptp.re Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= tptp.code_positive tptp.numera6620942414471956472nteger) (forall ((Y tptp.complex) (X3 tptp.complex)) (=> (@ (@ tptp.member_complex Y) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X3) tptp.real_V2521375963428798218omplex) (= (= X3 (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y)) (and (= X3 tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))) (forall ((Y tptp.complex) (X3 tptp.complex)) (=> (@ (@ tptp.member_complex Y) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X3) tptp.real_V2521375963428798218omplex) (= (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y) X3) (and (= X3 tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))) (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)))))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit1 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))) (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.times_times_complex X3) Y)) (@ (@ tptp.times_times_complex (@ tptp.cnj X3)) (@ tptp.cnj Y)))) (forall ((Z tptp.complex)) (= (= (@ tptp.cnj Z) tptp.one_one_complex) (= Z tptp.one_one_complex))) (= (@ tptp.cnj tptp.one_one_complex) tptp.one_one_complex) (forall ((X3 tptp.complex) (N tptp.nat)) (= (@ tptp.cnj (@ (@ tptp.power_power_complex X3) N)) (@ (@ tptp.power_power_complex (@ tptp.cnj X3)) N))) (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.plus_plus_complex X3) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.cnj X3)) (@ tptp.cnj Y)))) (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.cnj _let_1) _let_1))) (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (= (@ tptp.cnj _let_1) _let_1))) (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) tptp.zero_zero_real)) (= tptp.code_integer_of_num tptp.numera6620942414471956472nteger) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))) tptp.zero_zero_real))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))) tptp.zero_zero_real))) (= tptp.real_V1022390504157884413omplex (lambda ((Z5 tptp.complex)) (@ tptp.sqrt (@ tptp.re (@ (@ tptp.times_times_complex Z5) (@ tptp.cnj Z5)))))) (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer) (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))))))) (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))) (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))) (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))))))) (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))))))) (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))) (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))) (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))))))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit0 N)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))) (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))))) (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)))))))) (= (@ tptp.code_integer_of_num _let_6) _let_30) (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)))) (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))))) (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))) (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A3) (@ tptp.cnj B2))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (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)))))) (= 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)))))) (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K3) L)) (@ (@ tptp.modulo364778990260209775nteger K3) L)))) (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_lessThan_nat U)) U)) (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.ord_less_nat I3) N)))) N)) (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))) (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L2) U)) (@ (@ tptp.minus_minus_nat U) L2))) (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I3) N)))) (@ tptp.suc N))) (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))) (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L2)))) (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L2) U)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U) L2)) tptp.one_one_int)))) (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)))) (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))))))))) (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))))))))) (forall ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))) (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)))) (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N5)) N))) (forall ((S3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S3)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) S3))) (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))) N)))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) N))) (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K3 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S5 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S5))) (= S5 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))) (= tptp.code_divmod_abs (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))) (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K3)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L) S5)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L)) S5)))))) _let_1))))))))))) (forall ((X3 tptp.nat)) (= (@ (@ tptp.bezw X3) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))) (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M3)))) M)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M3) N)))) M)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K3 tptp.nat)) K3)) (@ _let_1 N))))) (= 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)))))))) (= tptp.archim3151403230148437115or_rat (lambda ((X2 tptp.rat)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z5)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))) (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (not (forall ((S2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S2) (forall ((T3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T3) (not (= R2 (@ (@ tptp.plus_plus_rat S2) T3)))))))))) (= tptp.sgn_sgn_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (= A3 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A3)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))) (= tptp.ord_less_eq_rat (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y6) (= X2 Y6)))) (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))) (forall ((P2 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A3)) B2)) (@ tptp.abs_abs_int A3))))) (@ tptp.quotient_of P2)))) (= 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)))))) (forall ((X3 tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X3))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X3))) (=> (= (@ (@ tptp.nat_prod_decode_aux X3) Xa2) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X3) Xa2)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))) (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int))) (= (@ tptp.quotient_of tptp.one_one_rat) _let_29) (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K))) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (= (@ tptp.quotient_of _let_4) (@ (@ tptp.product_Pair_int_int _let_5) tptp.one_one_int)) (= tptp.minus_minus_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.plus_plus_rat Q4) (@ tptp.uminus_uminus_rat R5)))) (= tptp.divide_divide_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.times_times_rat Q4) (@ tptp.inverse_inverse_rat R5)))) (= tptp.ord_less_rat (lambda ((P4 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B2 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int C2) B2)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P4)))) (= tptp.ord_less_eq_rat (lambda ((P4 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B2 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int C2) B2)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P4)))) (forall ((X3 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 X3) Xa2)))) (let ((_let_2 (@ tptp.suc X3))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X3))) (=> (= (@ (@ tptp.nat_prod_decode_aux X3) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X3) Xa2)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))) (forall ((A tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A)) (@ (@ tptp.product_Pair_int_int A) tptp.one_one_int))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int B2) C2))) (@ (@ tptp.times_times_int C2) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))) (forall ((P2 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (forall ((Q2 tptp.int) (S tptp.int) (P2 tptp.int) (R2 tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S))) (= (@ (@ tptp.times_times_int P2) S) (@ (@ tptp.times_times_int R2) Q2)))))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) B2)) (@ (@ tptp.times_times_int C2) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int C2) B2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int B2) C2))) (@ (@ tptp.times_times_int C2) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))) (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) (@ tptp.numeral_numeral_int K))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat K)))) (forall ((K tptp.num) (L2 tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int L2))) (@ (@ tptp.divide_divide_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat L2)))) (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)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.divide_divide_nat M) N))) (= (@ tptp.frct _let_29) tptp.one_one_rat) (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int)) (@ tptp.numeral_numeral_rat K))) (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)))))) (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)))) (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R3) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S3))) (forall ((N8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N8) (@ tptp.finite_card_nat S3)) (@ (@ tptp.member_nat (@ R3 N8)) S3))))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N) K)) (@ _let_1 K)))) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se8568078237143864401it_int N) _let_1) _let_1))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.modulo_modulo_nat M) N))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))) (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))))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N) M)) K)))) (= tptp.bit_se8568078237143864401it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))) (forall ((P2 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.sgn_sgn_rat P2)) (@ (@ tptp.product_Pair_int_int (@ tptp.sgn_sgn_int (@ tptp.product_fst_int_int (@ tptp.quotient_of P2)))) tptp.one_one_int))) (forall ((X3 tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X3) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X3) 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 X3) Xa2))))))))))))) (= tptp.bezw (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y6) (@ (@ tptp.modulo_modulo_nat X2) Y6)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y6 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) Y6)))))))))) (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_integer K) L2)) (@ (@ tptp.modulo364778990260209775nteger K) L2))) (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_abs K) L2)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K)) (@ tptp.abs_abs_Code_integer L2)))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N) K)))) (= tptp.bit_se8570568707652914677it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (forall ((Y tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X3) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X3) 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 X3) Y)))))))))) (forall ((X3 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 X3) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X3) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X3) 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 X3) Xa2)))))))) (not _let_1)))))))))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))) (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N)))))) (= tptp.adjust_mod (lambda ((L tptp.int) (R5 tptp.int)) (@ (@ (@ tptp.if_int (= R5 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L) R5)))) (= tptp.normalize (lambda ((P4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P4))) (let ((_let_2 (@ tptp.product_fst_int_int P4))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))) (forall ((M tptp.int)) (= (@ (@ tptp.gcd_gcd_int M) tptp.one_one_int) tptp.one_one_int)) (forall ((N tptp.num) (X3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int _let_1)) X3) (@ (@ tptp.gcd_gcd_int _let_1) X3)))) (forall ((X3 tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.gcd_gcd_int X3))) (= (@ _let_2 (@ tptp.uminus_uminus_int _let_1)) (@ _let_2 _let_1))))) (= tptp.gcd_gcd_int (lambda ((X2 tptp.int) (Y6 tptp.int)) (@ (@ tptp.gcd_gcd_int Y6) (@ (@ tptp.modulo_modulo_int X2) Y6)))) (forall ((X3 tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X3) Y))) (forall ((X3 tptp.int) (Y tptp.int)) (exists ((U3 tptp.int) (V2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U3) X3)) (@ (@ tptp.times_times_int V2) Y)) (@ (@ tptp.gcd_gcd_int X3) Y)))) (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int K)) (@ (@ tptp.gcd_gcd_int M) N)) (@ (@ tptp.gcd_gcd_int (@ _let_1 M)) (@ _let_1 N))))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) A))) (forall ((X3 tptp.int) (Y tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X3))) (let ((_let_2 (@ P (@ _let_1 Y)))) (let ((_let_3 (@ tptp.uminus_uminus_int Y))) (let ((_let_4 (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int X3)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X3) tptp.zero_zero_int))) (let ((_let_7 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (@ _let_7 Y))) (let ((_let_9 (@ _let_7 X3))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (@ P (@ _let_1 _let_3)))) (=> (=> _let_6 (=> _let_8 (@ P (@ _let_4 Y)))) (=> (=> _let_6 (=> _let_5 (@ P (@ _let_4 _let_3)))) _let_2)))))))))))))) (forall ((D tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) D) (@ _let_1 A) (@ _let_1 B) (forall ((E3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int E3))) (=> (and (@ _let_1 A) (@ _let_1 B)) (@ _let_1 D))))) (= D (@ (@ tptp.gcd_gcd_int A) B))))) (forall ((Y tptp.int) (X3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y) (= (@ (@ tptp.gcd_gcd_int X3) Y) (@ (@ tptp.gcd_gcd_int Y) (@ (@ tptp.modulo_modulo_int X3) Y))))) (= tptp.gcd_gcd_int (lambda ((K3 tptp.int) (L tptp.int)) (@ tptp.abs_abs_int (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K3) (@ (@ tptp.gcd_gcd_int L) (@ (@ tptp.modulo_modulo_int (@ tptp.abs_abs_int K3)) (@ tptp.abs_abs_int L))))))) (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K3) (@ tptp.sgn_sgn_Code_integer L))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer L)) S5)))))) _let_1))))))))) (forall ((M tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)) (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M) N)) (or (not (= M tptp.zero_zero_nat)) (not (= N tptp.zero_zero_nat))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.gcd_gcd_nat M) N)) (@ (@ tptp.gcd_gcd_nat (@ _let_1 M)) (@ _let_1 N))))) (= tptp.gcd_gcd_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.gcd_gcd_nat Y6) (@ (@ tptp.modulo_modulo_nat X2) Y6)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) A))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N) M)) N) (@ (@ tptp.gcd_gcd_nat M) N)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M) N)) N) (@ (@ tptp.gcd_gcd_nat M) N)))) (forall ((X3 tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X3) Xa2) Y) (and (=> _let_1 (= Y X3)) (=> (not _let_1) (= Y (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X3) Xa2)))))))) (= tptp.gcd_gcd_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ (@ tptp.if_nat (= Y6 tptp.zero_zero_nat)) X2) (@ (@ tptp.gcd_gcd_nat Y6) (@ (@ tptp.modulo_modulo_nat X2) Y6))))) (forall ((Y tptp.nat) (X3 tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (= (@ (@ tptp.gcd_gcd_nat X3) Y) (@ (@ tptp.gcd_gcd_nat Y) (@ (@ tptp.modulo_modulo_nat X3) Y))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X5 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) (@ (@ tptp.gcd_gcd_nat A) B)))))) (forall ((B tptp.nat) (A tptp.nat)) (exists ((X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y3))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X5))) (let ((_let_6 (@ _let_4 Y3))) (let ((_let_7 (@ _let_2 X5))) (or (and (@ (@ tptp.ord_less_eq_nat _let_6) _let_7) (= (@ (@ tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (@ (@ tptp.ord_less_eq_nat _let_3) _let_5) (= (@ (@ tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))) (= tptp.gcd_gcd_Code_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (@ tptp.abs_abs_Code_integer (@ (@ (@ tptp.if_Code_integer (= L tptp.zero_z3403309356797280102nteger)) K3) (@ (@ tptp.gcd_gcd_Code_integer L) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K3)) (@ tptp.abs_abs_Code_integer L))))))) (forall ((X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X3) Y))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X3) Y)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int X3))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int Y)))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I) (@ P I))) (@ P K2)))) (@ P M)))) (forall ((X3 tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X3) Xa2)))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X3) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X3)) (=> (not _let_2) (= Y (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X3) Xa2))))) (not _let_1)))))))) (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) (@ (@ tptp.plus_plus_int L2) tptp.one_one_int))))) (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or5832277885323065728an_int L2) U))) (= _let_28 _let_28) (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L2) tptp.one_one_int)) U) (@ (@ tptp.set_or5832277885323065728an_int L2) U))) (= tptp.code_negative (@ (@ tptp.comp_C3531382070062128313er_num tptp.uminus1351360451143612070nteger) tptp.numera6620942414471956472nteger)) (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)) (forall ((K tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int K))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 (@ (@ tptp.neg_numeral_sub_int N) tptp.one)))))) (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or5834768355832116004an_nat L2) U))) (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)))) (forall ((N tptp.num) (K tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) K) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.neg_numeral_sub_int N) tptp.one)) K)))) (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or5834768355832116004an_nat L2) U))) (forall ((X3 tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X3)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))) (forall ((N tptp.num)) (= (@ (@ tptp.neg_numeral_sub_int (@ tptp.bitM N)) tptp.one) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.neg_numeral_sub_int N) tptp.one)))) (forall ((K tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K) tptp.zero_zero_nat))) (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y6) X2))) (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.ord_less_nat Y6) X2))) (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))) (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))) (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat) (= 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))))))) (= 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)))))))) (forall ((K tptp.num)) (= (@ tptp.code_int_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_int K))) (forall ((X3 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.plus_p5714425477246183910nteger X3) Xa2)) (@ (@ tptp.plus_plus_int (@ tptp.code_int_of_integer X3)) (@ tptp.code_int_of_integer Xa2)))) (forall ((X3 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.times_3573771949741848930nteger X3) Xa2)) (@ (@ tptp.times_times_int (@ tptp.code_int_of_integer X3)) (@ tptp.code_int_of_integer Xa2)))) (= (@ tptp.code_int_of_integer tptp.one_one_Code_integer) tptp.one_one_int) (forall ((X3 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.modulo364778990260209775nteger X3) Xa2)) (@ (@ tptp.modulo_modulo_int (@ tptp.code_int_of_integer X3)) (@ tptp.code_int_of_integer Xa2)))) (= tptp.ord_le3102999989581377725nteger (lambda ((X2 tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa4)))) (= tptp.ord_le3102999989581377725nteger (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L)))) (forall ((Xa2 tptp.product_prod_nat_nat) (X3 tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X3)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 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 Y6))) (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) X3)))) (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (forall ((Xa2 tptp.product_prod_nat_nat) (X3 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X3)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y6 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) Y6)))) __flatten_var_0))) Xa2) X3))) (forall ((Xa2 tptp.product_prod_nat_nat) (X3 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X3)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y6 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) Y6)))) __flatten_var_0))) Xa2) X3))) (forall ((Xa2 tptp.product_prod_nat_nat) (X3 tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X3)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 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 Y6) V4)))) __flatten_var_0))) Xa2) X3)))) (forall ((Xa2 tptp.product_prod_nat_nat) (X3 tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X3)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 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 Y6) U2)))) __flatten_var_0))) Xa2) X3)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N)))) (=> (not _let_2) (= _let_1 tptp.one)))))) (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)) (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N) N)) (@ tptp.bit0 (@ tptp.num_of_nat N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N))))))) (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y6 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 Y6) V4)) (@ (@ tptp.plus_plus_nat U2) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa4)))) (= tptp.ord_less_int (lambda ((X2 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y6 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 Y6) V4)) (@ (@ tptp.plus_plus_nat U2) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa4)))) (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M6 tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M6)))))) (forall ((X3 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X3))) (= (@ _let_1 (@ tptp.bit1 Y)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y))) X3)))) (forall ((C tptp.nat) (Y tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X3) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X3) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat I3) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X3) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat I3) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat I3) C))) _let_1) tptp.bot_bot_set_nat))))))))) (forall ((M7 tptp.set_nat) (N5 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N5) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N5))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I2) J2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I2)) (@ tptp.suc J2)))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I2) J2)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I2)) (@ tptp.suc J2)))) (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))) (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))) (= (@ tptp.sqr tptp.one) tptp.one) (= tptp.sqr (lambda ((X2 tptp.num)) (@ (@ tptp.times_times_num X2) X2))) (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))) (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (@ tptp.suc N)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))) (forall ((N tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N))))) (forall ((N tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N))))) (forall ((X3 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X3))) (= (@ _let_1 (@ tptp.bit0 Y)) (@ tptp.sqr (@ _let_1 Y))))) (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))) (forall ((N tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc I2))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J2))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N))))) (= tptp.comple4887499456419720421f_real (lambda ((X4 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X4))))) (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat) (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat) (= tptp.finite_finite_int (lambda ((S4 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S4)) (@ tptp.set_ord_atMost_int K3))))) (= tptp.finite_finite_int (lambda ((S4 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S4)) (@ tptp.set_ord_lessThan_int K3))))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or4665077453230672383an_nat A) B)) (@ (@ tptp.set_or4662586982721622107an_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))) (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X8 I4))) (= (@ tptp.suminf_real X8) (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_nat_real (lambda ((I3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X8) (@ tptp.set_ord_lessThan_nat I3)))) tptp.top_top_set_nat)))))) (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) L2))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L2))) (@ (@ tptp.set_or4662586982721622107an_int L2) U))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))) (forall ((U tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) U) (= (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U) (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ tptp.set_ord_lessThan_nat (@ tptp.nat2 U)))))) (= tptp.top_top_set_nat (@ _let_27 _let_23)) (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat) (= (@ tptp.finite_card_o tptp.top_top_set_o) _let_26) (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)))))) (= tptp.root (lambda ((N2 tptp.nat) (X2 tptp.real)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y6 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N2)))) X2)))) (= (@ tptp.finite_card_char tptp.top_top_set_char) _let_8) (= tptp.top_top_set_char (@ (@ tptp.image_nat_char tptp.unique3096191561947761185of_nat) _let_10)) (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))))))))))) (= (@ (@ tptp.image_char_nat tptp.comm_s629917340098488124ar_nat) tptp.top_top_set_char) _let_10) (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))))) (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)))) (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)))) (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))))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_nat _let_1) J2) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J2)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J2))))))) (= tptp.upto_aux (lambda ((I3 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I3)) Js) (@ (@ (@ tptp.upto_aux I3) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))) (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat) (= tptp.sup_sup_nat tptp.ord_max_nat) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J2) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J2)) (@ (@ tptp.set_or4665077453230672383an_nat J2) _let_1))))))) (forall ((X3 tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X3) Xa2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X3) Xa2))) (=> (= (@ (@ tptp.upto X3) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X3) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X3) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))) (forall ((I2 tptp.int) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I2) J2))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I2) J2)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J2)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))) (forall ((I2 tptp.int) (J2 tptp.int)) (= (= (@ (@ tptp.upto I2) J2) tptp.nil_int) (@ (@ tptp.ord_less_int J2) I2))) (forall ((I2 tptp.int) (J2 tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I2) J2)) (@ (@ tptp.ord_less_int J2) I2))) (forall ((J2 tptp.int) (I2 tptp.int)) (=> (@ (@ tptp.ord_less_int J2) I2) (= (@ (@ tptp.upto I2) J2) tptp.nil_int))) (forall ((I2 tptp.int)) (= (@ (@ tptp.upto I2) I2) (@ (@ tptp.cons_int I2) tptp.nil_int))) (forall ((I2 tptp.int) (K tptp.nat) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I2) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J2) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I2) J2)) K) _let_1)))) (forall ((I2 tptp.int) (J2 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I2) J2)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J2) I2)) tptp.one_one_int)))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (= tptp.upto_aux (lambda ((I3 tptp.int) (J3 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I3) J3)) __flatten_var_0))) (= tptp.upto (lambda ((I3 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.upto_aux I3) J3) tptp.nil_int))) (forall ((I2 tptp.int) (J2 tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I2) J2))) (= tptp.set_or1266510415728281911st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) J3)))) (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (=> (@ (@ tptp.ord_less_eq_int J2) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J2)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J2) tptp.one_one_int)) K))))))) (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (=> (@ (@ tptp.ord_less_eq_int J2) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))) (@ (@ tptp.upto J2) K))))))) (= tptp.set_or4662586982721622107an_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))) (forall ((I2 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (= (@ (@ tptp.upto I2) J2) (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J2))))) (forall ((X3 tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X3) Xa2))) (=> (= (@ (@ tptp.upto X3) Xa2) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X3) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X3) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y tptp.nil_int)))))) (= tptp.upto (lambda ((I3 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I3) J3)) (@ (@ tptp.cons_int I3) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3))) tptp.nil_int))) (forall ((I2 tptp.int) (J2 tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (= (@ _let_1 J2) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))) (@ (@ tptp.cons_int J2) tptp.nil_int)))))) (= tptp.set_or5832277885323065728an_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))) (forall ((I2 tptp.int) (J2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (=> (@ (@ tptp.ord_less_eq_int J2) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))) (@ (@ tptp.cons_int J2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J2) tptp.one_one_int)) K)))))))) (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_real X3) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ _let_1 X3)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))))) (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 ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B))))) (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 ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B)) (@ F A))))) (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 ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B)) (@ F A))))) (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 ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_eq_real (@ F A)) (@ F B))))) (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)))))) (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))))) (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X3 tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X3) S3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X3) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F _let_1)))))))))))) (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X3 tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X3) S3)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X3) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X3)))))))))))) (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X3 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X3) 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 X3)) (@ F (@ (@ tptp.plus_plus_real X3) H4))))))))))) (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X3 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X3) 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 X3) H4))) (@ F X3)))))))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> 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) (@ F4 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F4 Z2)))))))) (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)))))) (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X3 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y3)))) (= L2 tptp.zero_zero_real))))) (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X3 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F Y3)) (@ F X3)))) (= L2 tptp.zero_zero_real))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (forall ((N tptp.nat) (X3 tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real X2) N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X3) S))) (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ G X2)) N))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ G X3)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M)) _let_1)))) (forall ((Z tptp.real) (R2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z5 tptp.real)) (@ (@ tptp.powr_real Z5) R2))) (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real Z) (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)))) (forall ((X3 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X3))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X3 tptp.real) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (let ((_let_2 (@ G X3))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.powr_real (@ G X2)) R2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M)) _let_1)))))) (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X3 tptp.real) (F (-> tptp.real tptp.real)) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (let ((_let_2 (@ G X3))) (let ((_let_3 (@ F X3))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R2) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.powr_real (@ G X2)) (@ F X2)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R2) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M) _let_3)) _let_2)))) _let_1)))))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X3))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (forall ((F (-> tptp.real tptp.nat tptp.real)) (F4 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F4 X0))) (=> (forall ((N3 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ F X2) N3))) (@ (@ F4 X0) N3)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((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 ((N3 tptp.nat) (X5 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X5) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X5) N3)) (@ (@ F Y3) N3)))) (@ (@ tptp.times_times_real (@ L5 N3)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X5) Y3)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (@ F X2)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))) (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (forall ((X3 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 X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X3) A2))) (forall ((X3 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 X3)))) (=> (not (= X3 tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X3) 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 X3) tptp.top_top_set_real)))))))) (forall ((X3 tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ (@ 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 X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X3) A2)))) (forall ((X3 tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) 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 X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X3) A2)))) (forall ((R 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 R)) R)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X5) N2)))))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R)) R)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X2) (@ tptp.suc N2))))))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X0) N2))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))) (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X3)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) 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 X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) 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 X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X3 tptp.real) (N 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 ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X3)) (= (@ F X3) (@ (@ 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 X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N)))))))) (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X3 tptp.real) (N 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 ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X3)) (= (@ F X3) (@ (@ 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 X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))))) (forall ((N tptp.nat) (X3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (not (= X3 tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X3)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))))) (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))) (forall ((H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N)))))))))) (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real H2) T3) (@ (@ tptp.ord_less_eq_real T3) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))) (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X3 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X3 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 ((T3 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T3))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X3)) (= (@ F X3) (@ (@ 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 X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N)))))))))))) (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X3 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X3))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X3)) (= (@ F X3) (@ (@ 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 X3) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X3) N))))))))) (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B) (=> (@ _let_1 X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (=> (not (= X3 C)) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T3))) (let ((_let_2 (@ tptp.ord_less_real X3))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T3) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T3) (@ _let_1 X3))) (= (@ F X3) (@ (@ 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 X3) C)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X3) C)) N))))))))))))))))))) (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real C) T3) (@ (@ tptp.ord_less_real T3) B) (= (@ F B) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N)))))))))))) (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real A) T3) (@ (@ tptp.ord_less_real T3) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N)))))))))))) (forall ((N tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B3 tptp.real)) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M2 tptp.nat) (T4 tptp.real)) (let ((_let_1 (@ tptp.suc M2))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M2))) (@ (@ tptp.minus_minus_real (@ (@ Diff M2) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((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 B3) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U2) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T4)) (@ (@ 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 T4) P4)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B3) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T4) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real))))))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X3)) 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 X3) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (forall ((N tptp.nat) (X3 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X3)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X3 tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X3) 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 X3) tptp.top_top_set_real)))))))))))) (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 ((X tptp.real)) (let ((_let_1 (@ F X))) (=> (and (@ (@ tptp.ord_less_eq_real A) X) (@ (@ tptp.ord_less_eq_real X) B)) (and (@ (@ tptp.ord_less_eq_real L6) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M8))))) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L6) Y4) (@ (@ tptp.ord_less_eq_real Y4) M8)) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B) (= (@ F X5) Y4)))))))))) (forall ((X3 tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) tptp.sqrt)) (forall ((X3 tptp.real) (N tptp.nat)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ tptp.root N))) (forall ((A tptp.real) (X3 tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (= (@ G (@ F Z2)) Z2)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X3)) tptp.top_top_set_real)) G)))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) tptp.arcosh_real))) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X2)) (@ tptp.sin_real X2)))) _let_25) (@ _let_17 tptp.top_top_set_real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) tptp.arccos)))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) tptp.arcsin)))) (forall ((B tptp.real) (X3 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real B) X3)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) tptp.artanh_real)))) (forall ((D tptp.real) (X3 tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X3))) D) (= (@ G (@ F Z2)) Z2))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X3))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X3)) tptp.top_top_set_real)) G))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) G)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z2) (=> (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z2)) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z2) (=> (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 Z2)) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))) (exists ((C3 tptp.real)) (and (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G2 C3)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) (@ F4 C3))))))))))) (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 ((N8 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))) (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 ((N8 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))) (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat) (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))) (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))) (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X8 I4))) B3)) (not (forall ((L6 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat))))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.root N2) (@ tptp.semiri5074537144036343181t_real N2)))) _let_21) tptp.at_top_nat) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N3))) (@ G N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N8)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N8))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))) (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N6 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_real R3) (@ X8 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N2)))) _let_25) tptp.at_top_nat) (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.root N2) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))) _let_25) tptp.at_top_nat) (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)) (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) L2)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real L2) (@ (@ tptp.plus_plus_real (@ F N8)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L2)) tptp.at_top_nat))))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_real X3) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X3)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))) (forall ((X3 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X3) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))) (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)))) (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))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X3) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X3) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))) (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)) (forall ((X3 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X3) (@ tptp.semiri5074537144036343181t_real N2)))) N2))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X3))) tptp.at_top_nat)) (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real R2) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)) (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ A N2))))))) (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ A N2)))))))) (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)))))) (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)))) (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat)))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X3)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X3) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))) (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat))))) (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))))))) (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) _let_1) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))) (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat)))) (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))))) (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat))))) (= tptp.real_V5970128139526366754l_real (lambda ((F3 (-> tptp.real tptp.real))) (exists ((C2 tptp.real)) (= F3 (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C2)))))) (forall ((X3 tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X3) Y6))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y6)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X3))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (@ (@ (@ tptp.filterlim_real_real tptp.arcosh_real) _let_25) (@ _let_19 (@ tptp.set_or5849166863359141190n_real tptp.one_one_real))) (@ (@ _let_18 tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_24) (@ tptp.set_or5849166863359141190n_real _let_24))) (@ (@ _let_16 (@ tptp.topolo2815343760600316023s_real _let_24)) tptp.at_bot_real) (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat) (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) _let_23) (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))))) (@ (@ _let_22 (@ tptp.topolo2815343760600316023s_real _let_11)) tptp.at_bot_real) (@ (@ _let_20 tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_11) (@ tptp.set_or5849166863359141190n_real _let_11))) (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))) (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N))) tptp.at_bot_real) F5))))) (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N))) tptp.at_top_real) F5))))) (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_bot_real) tptp.at_infinity_real) (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_top_real) tptp.at_infinity_real) (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real) (@ (@ _let_22 _let_21) tptp.at_top_real) (@ (@ _let_20 tptp.at_top_real) (@ _let_19 (@ tptp.set_or5984915006950818249n_real tptp.one_one_real))) (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)) (forall ((X3 tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X3) Y6))) Y6))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X3))) tptp.at_top_real)) (@ (@ _let_18 tptp.at_top_real) (@ _let_17 (@ tptp.set_or5984915006950818249n_real _let_15))) (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) X5) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))) (@ (@ _let_16 (@ tptp.topolo2815343760600316023s_real _let_15)) tptp.at_top_real) (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))))))))))) (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I3 tptp.nat)) (@ P (@ tptp.suc I3)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N2 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N2) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I3 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I3) K)))) tptp.at_top_nat))) (forall ((F5 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F5) tptp.at_top_nat) (forall ((N9 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N9)) F5)))) (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))) (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N9 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N2) (@ P N2)))))) (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))))) (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.image_nat_real F) tptp.top_top_set_nat)) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (@ (@ tptp.ord_less_eq_real X3) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X3)) tptp.at_top_nat)))) (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or6659071591806873216st_nat L2) U))) (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L2) U)) (@ (@ tptp.minus_minus_nat U) L2))) (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))) (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or6659071591806873216st_nat L2) U))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J2) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J2)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J2))))))) (forall ((N tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J2) I2)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J2))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N))))) (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or6656581121297822940st_int L2) U))) (= (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat) (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or6656581121297822940st_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L2)))) (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))) (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L2) tptp.one_one_int)) U) (@ (@ tptp.set_or6656581121297822940st_int L2) U))) (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real B3) (@ X8 I4))) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))) (= tptp.set_or6656581121297822940st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3)))) (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real B3) (@ 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)))))))))) (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat) (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)))) (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) (Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L4) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L4)))))))) (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)))))))) (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)))))) (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))) (@ _let_12 tptp.arccos) (@ _let_12 tptp.arcsin) (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)))))))) (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))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (X3 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) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (= (@ F X3) (@ F A)))))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))) (@ tptp.order_mono_nat_nat tptp.suc) (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I4)) B3)) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))) (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I4)) B3)) (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))))))))) (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))))) (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)))))) (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N) (@ F N)))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.inj_on_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N)))) tptp.top_top_set_real))) (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)))) (forall ((N5 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N5)) (forall ((N5 tptp.set_nat) (K tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) N5) (@ (@ tptp.ord_less_eq_nat K) N3))) (@ (@ tptp.inj_on_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) K))) N5))) (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)))))) (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)))))) (@ (@ tptp.inj_on_nat_char tptp.unique3096191561947761185of_nat) _let_10) (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))))))) (forall ((X3 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (=> (or (not (= X3 tptp.zero_zero_real)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) N)) (= (@ (@ tptp.powr_real X3) (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.power_int_real X3) N))))) (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X3) Xa2) Y) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X3 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (= 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)))) (=> (= X3 (@ (@ (@ (@ 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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _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)))))))))))) (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList) Summary)) Deg4) (and (= Deg Deg4) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ 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 TreeList) (@ (@ 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 TreeList)) (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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> _let_2 (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)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) 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)) TreeList) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima2)))))) (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X3) Xa2)) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X3 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (= 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)))) (=> (= X3 (@ (@ (@ (@ 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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _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)))))))))) (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X3) Xa2) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X3 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (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)))) (=> (= X3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (not (and (= Deg2 Xa2) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _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))))))))))) (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X3) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X3 _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)))) (=> (= X3 _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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _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)))))))))))))) (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X3) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X3 _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))) (=> (= X3 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _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)))))))))))))) (= tptp.complete_Sup_Sup_int (lambda ((X4 tptp.set_int)) (@ tptp.the_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) X4) (forall ((Y6 tptp.int)) (=> (@ (@ tptp.member_int Y6) X4) (@ (@ tptp.ord_less_eq_int Y6) X2)))))))) (forall ((X3 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X3) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X3) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X3 _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))) (=> (= X3 _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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _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))))))))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M) N))) (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I3 tptp.int) (N2 tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I3)) (@ tptp.semiri5074537144036343181t_real N2))) (not (= N2 tptp.zero_zero_nat))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int A) B))) (let ((_let_2 (@ (@ tptp.fract A) B))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) _let_2) (@ (@ tptp.ord_less_rat _let_2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))) (forall ((X3 tptp.real)) (= (@ (@ tptp.member_real (@ tptp.abs_abs_real X3)) tptp.field_5140801741446780682s_real) (@ (@ tptp.member_real X3) tptp.field_5140801741446780682s_real))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int B) C)))) (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))) (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D)))))) (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))) (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D)))))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.fract A) B)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B))))) (forall ((X3 tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X3) X5)))) (forall ((K tptp.int)) (= (@ (@ tptp.fract K) tptp.one_one_int) (@ tptp.ring_1_of_int_rat K))) (forall ((K tptp.nat)) (= (@ (@ tptp.fract (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int) (@ tptp.semiri681578069525770553at_rat K))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.fract A) B))))) (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (= (@ (@ tptp.fract A) B) (@ (@ tptp.fract C) D)) (= (@ (@ tptp.times_times_int A) D) (@ (@ tptp.times_times_int C) B)))))) (forall ((A tptp.int)) (= (@ (@ tptp.fract A) tptp.zero_zero_int) (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int))) (forall ((X3 tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X5) X3)))) (forall ((X3 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X3) X5) (@ (@ tptp.ord_less_real X5) Y))))) (= tptp.one_one_rat (@ (@ tptp.fract tptp.one_one_int) tptp.one_one_int)) (= tptp.zero_zero_rat (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int)) (= tptp.numeral_numeral_rat (lambda ((K3 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K3)) tptp.one_one_int))) (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.numeral_numeral_int W)) tptp.one_one_int) (@ tptp.numeral_numeral_rat W))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_int A) B)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int B) A)))) (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I3 tptp.int) (J3 tptp.int)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I3)) (@ tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int))))))) (= (@ (@ tptp.fract _let_5) tptp.one_one_int) _let_4) (forall ((N tptp.int) (M tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ (@ tptp.plus_plus_int M) N)) N) (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract M) N)) tptp.one_one_rat)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int B) A)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int A) B)))) (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) tptp.one_one_int) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (forall ((K tptp.num)) (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) (lambda ((Q4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.numeral_numeral_int Q4)))))) (@ (@ tptp.bit_take_bit_num _let_1) N))))) (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))) (forall ((R2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) tptp.one) (@ tptp.some_num tptp.one))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ tptp.some_num tptp.one))) N))) (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))) (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))) (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N) M))))) (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N) M)))) (forall ((R2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R2)) M))))) (forall ((R2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R2)) M)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))) (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M) N)))) (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num) (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit0 M))) (= (@ (@ tptp.bit_and_not_num _let_1) tptp.one) (@ tptp.some_num _let_1)))) (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num tptp.one))) (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N)) tptp.none_num)) (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N2) M)))) N))) (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))) (forall ((M tptp.num) (N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) (@ tptp.some_num Q2)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int Q2)))) (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit1 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N2) M))))) N))) (forall ((M tptp.num) (N tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) tptp.none_num) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N) M)))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.positive (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B)))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ tptp.positive X3) (=> (@ tptp.positive Y) (@ tptp.positive (@ (@ tptp.plus_plus_rat X3) Y))))) (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (@ tptp.positive X3) (=> (@ tptp.positive Y) (@ tptp.positive (@ (@ tptp.times_times_rat X3) Y))))) (= tptp.positive (lambda ((X2 tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X2))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.product_snd_int_int _let_1)))))) (forall ((X3 tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (let ((_let_2 (= X3 tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X3) Xa2) Y) (=> (=> _let_2 (=> (= Xa2 tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit0 N3))) (not (= Y (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit1 N3))) _let_1)) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num _let_1))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (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) N3)))))))) (not (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3))))))))))))))))))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))) (forall ((X3 tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X3 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (@ (@ tptp.bit_and_not_num X3) Xa2) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X3) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.some_num _let_1)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.some_num (@ tptp.bit0 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= 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) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))) (forall ((X3 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 (= X3 tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X3) Xa2) Y) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit0 N3))) _let_4)) (=> (=> _let_5 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit1 N3))) _let_1)) (=> (=> (exists ((M5 tptp.num)) (= X3 (@ tptp.bit0 M5))) (=> _let_2 _let_4)) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (=> (=> (exists ((M5 tptp.num)) (= X3 (@ tptp.bit1 M5))) _let_3) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (not (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (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) N3)))))))))))))))))))))))) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))) (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))) (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num tptp.one))) (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N)) tptp.none_num)) (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))) (forall ((X3 tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X3 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X3) Xa2) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X3) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.some_num tptp.one)) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= 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) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))) (forall ((X3 tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X3 tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X3) Xa2) Y) (=> (=> _let_1 (=> (= Xa2 tptp.one) (not (= Y tptp.none_num)))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y (@ tptp.some_num (@ tptp.bit1 N3))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y (@ tptp.some_num (@ tptp.bit0 N3))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit1 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3))))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3))))))))) (not (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))))))))))))))))))) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N)))) (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))) (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))) (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num (@ tptp.bit0 N)))) (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num (@ tptp.bit1 N)))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N))))) (forall ((X3 tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X3 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X3) Xa2) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X3) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.some_num (@ tptp.bit1 N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.some_num (@ tptp.bit0 N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.some_num (@ tptp.bit1 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X3 _let_1) (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.some_num (@ tptp.bit0 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X3 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))) (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel) (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel) (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num) (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num) (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M6 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A3 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))) A3))) (@ (@ tptp.product_Pair_nat_num N2) M6)))) (= 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))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat M) N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat (@ tptp.pred_numeral K)) N)))) (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) (@ tptp.pred_numeral K))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L2 tptp.int) (R2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit M) (@ (@ (@ tptp.bit_concat_bit N) K) L2)) R2) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.minus_minus_nat M) N)) L2) R2)))) (= tptp.inf_inf_nat tptp.ord_min_nat) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N) Q2)) (@ (@ tptp.ord_min_nat (@ _let_1 N)) (@ _let_1 Q2))))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M) N)) Q2) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N) Q2)))) (forall ((M tptp.nat) (I2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M) I2)) (@ (@ tptp.minus_minus_nat N) I2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M) N)) I2))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ (@ (@ tptp.bit_concat_bit N) K) L2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N)) L2)))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) M) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M3)))) M))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat M) (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M3) N)))) M))) (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q2) tptp.zero_z5237406670263579293d_enat)) (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q2) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)) (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N))) (= (@ tptp.remdups_nat _let_1) _let_1))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (= (@ tptp.hd_nat (@ (@ tptp.upt I2) J2)) I2))) (forall ((M tptp.nat) (I2 tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.drop_nat M) (@ (@ tptp.upt I2) J2)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) M)) J2))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I2) J2)) (@ (@ tptp.minus_minus_nat J2) I2))) (forall ((I2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) M))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ tptp.take_nat M) (@ _let_2 N)) (@ _let_2 _let_1)))))) (forall ((J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.upt I2) J2) tptp.nil_nat))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.upt M) N))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (= (@ (@ tptp.upt I2) J2) tptp.nil_nat) (or (= J2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J2) I2)))) (forall ((I2 tptp.nat) (K tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J2) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I2) J2)) K) _let_1)))) (forall ((I2 tptp.nat)) (= (@ (@ tptp.upt I2) tptp.zero_zero_nat) tptp.nil_nat)) (forall ((I2 tptp.nat) (J2 tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I2) J2))) (forall ((M tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N) Ns))) (= (= (@ (@ tptp.cons_nat M) _let_1) (@ (@ tptp.upt M) Q2)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M)) Q2))))) (= tptp.set_or6659071591806873216st_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) (@ tptp.suc M6))))) (= tptp.set_ord_lessThan_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N2)))) (= tptp.set_or5834768355832116004an_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) M6)))) (= tptp.set_or1269000886237332187st_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N2) (@ tptp.suc M6))))) (= tptp.set_or4665077453230672383an_nat (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I3) J3)))) (= tptp.set_ord_atMost_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N2))))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (= (@ (@ tptp.upt I2) J2) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J2))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J2) K))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J2)) (@ (@ tptp.upt J2) _let_1))))))) (forall ((I2 tptp.nat) (J2 tptp.nat) (X3 tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I2) J2) (@ (@ tptp.cons_nat X3) Xs)) (and (@ (@ tptp.ord_less_nat I2) J2) (= I2 X3) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) tptp.one_one_nat)) J2) Xs)))) (= tptp.upt (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I3) J3)) (@ (@ tptp.cons_nat I3) (@ (@ tptp.upt (@ tptp.suc I3)) J3))) tptp.nil_nat))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (let ((_let_2 (@ _let_1 (@ tptp.suc J2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I2) J2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J2)) (@ (@ tptp.cons_nat J2) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))) (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ _let_1 (@ tptp.suc J2)) (@ (@ tptp.append_nat (@ _let_1 J2)) (@ (@ tptp.cons_nat J2) tptp.nil_nat)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N)))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat I3) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.upt M) N))) (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q4) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat M) N))))) (forall ((M tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ tptp.groups4561878855575611511st_nat L) N5))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L) N5)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L)) tptp.one_one_nat) N5))))))))) (forall ((M tptp.nat) (N5 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ tptp.groups4561878855575611511st_nat L) N5))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N5) M)) tptp.one_one_nat)) N5))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N))) (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))))) (forall ((M tptp.int) (N tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M) N))) (forall ((I2 tptp.int) (J2 tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I2) J2))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) N))) (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)))) (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)))) (forall ((M tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J3)) M)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M)) (lambda ((R5 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) R5)))))) (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S3)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S3))))) (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N2)) M6))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.gcd_gcd_nat M) N) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_1 M) (@ _let_1 N))))))))) (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))) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))) (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M6) N2))) M6)))) (forall ((X3 tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X3) Y) (=> (=> (= X3 tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X5 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X3 (@ (@ tptp.cons_nat X5) Xs3)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs3)))))))))))) (forall ((X3 tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X3) Xs)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs)))))) (forall ((X3 tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X3) Y) (=> (@ _let_1 X3) (=> (=> (= X3 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))) (=> (= X3 _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)))))))))))) (forall ((N5 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N5) (= (@ tptp.gcd_Gcd_nat N5) tptp.one_one_nat))) (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K5))) (= tptp.semiri1316708129612266289at_nat tptp.id_nat) (= tptp.positive (@ (@ (@ tptp.map_fu898904425404107465nt_o_o tptp.rep_Rat) tptp.id_o) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N))) (= (@ (@ tptp.linord738340561235409698at_nat (lambda ((X2 tptp.nat)) X2)) _let_1) _let_1))) (forall ((I2 tptp.int) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J2))) (= (@ (@ tptp.linord1735203802627413978nt_int (lambda ((X2 tptp.int)) X2)) _let_1) _let_1))) (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X3) Y) Y)) (forall ((X3 tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X3) Y) X3)) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X3) Y) Y)) (forall ((X3 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X3) Y) X3)) (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X3) Y) Y)) (forall ((X3 tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X3) Y) X3)) (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X3) Y) Y)) (forall ((X3 tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X3) Y) X3)) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X3) Y) Y)) (forall ((X3 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X3) Y) X3)) (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X4 tptp.real)) (@ P X4)))) (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X3) Y) Y)) (forall ((X3 tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X3) Y) X3)) (forall ((X3 tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X3) Y) Y)) (forall ((X3 tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X3) Y) X3)) (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X3) Y) Y)) (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X3) Y) X3)) (forall ((X3 tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X3) Y) Y)) (forall ((X3 tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X3) Y) X3)) (forall ((X3 tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X3) Y) Y)) (forall ((X3 tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X3) Y) X3)) (forall ((X3 tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X3) Y) Y)) (forall ((X3 tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X3) Y) X3)) (forall ((X3 tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X3) Y) Y)) (forall ((X3 tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X3) Y) X3)) (forall ((X3 (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X3) Y) Y)) (forall ((X3 (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X3) Y) X3)) (forall ((X3 tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X3) Y) Y)) (forall ((X3 tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X3) Y) X3)) (forall ((X3 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X3) Y) Y)) (forall ((X3 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X3) Y) X3)) (forall ((X3 tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X3) Y) Y)) (forall ((X3 tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X3) Y) X3)) (forall ((X3 (-> tptp.nat tptp.int tptp.int)) (Y (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int false) X3) Y) Y)) (forall ((X3 (-> tptp.nat tptp.int tptp.int)) (Y (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int true) X3) Y) X3)) (forall ((X3 (-> tptp.nat tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat false) X3) Y) Y)) (forall ((X3 (-> tptp.nat tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat true) X3) Y) X3)) (forall ((X3 tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X3) Y) Y)) (forall ((X3 tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X3) Y) X3)) (forall ((P Bool)) (or (= P true) (= P false))) (forall ((X3 tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X3) Y) Y)) (forall ((X3 tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X3) Y) X3)) _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 8.14/8.51 )
% 8.14/8.51 % SZS output end Proof for ITP227^3
% 8.14/8.51 % cvc5---1.0.5 exiting
% 8.14/8.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------